universitÀ degli studi di bari “aldo moro ......7.67(stat) 4.82(syst)) 10-3. vii previous...

UNIVERSITÀ DEGLI STUDI DI BARI “ALDO MORO”Dipartimento Interateneo di Fisica “Michelangelo Merlin”

Dottorato di Ricerca in Fisica

ciclo XXIII

Settore Scientifico Disciplinare FIS/01

TITOLO DELLA TESI

Search for CP violation in

singly Cabibbo suppressed

four-body D decays

Dottorando CoordinatoreMaurizio Martinelli Chiar.mo Prof. Francesco Romano

SupervisoreChiar.mo Prof. Antimo Palano

———————————————————–

ESAME FINALE 2011

maurizio martinelli

search for CP violation insingly cabibbo suppressed

four-body D decays

ph. d. thesis

Supervisor: Chiar.mo Prof. A. Palano

Università degli Studi di BariFacoltà di Scienze Matematiche Fisiche e NaturaliDipartimento di FisicaFebruary 2011

Maurizio Martinelli: Search for CP violation in singly Cabibbo suppressedfour-body D decays, Ph. D. Thesis, © february 2011.

“From a long view of the history of mankind — seen from, say, tenthousand years from now, there can be little doubt that the mostsignificant event of the 19th century will be judged as Maxwell’s

discovery of the laws of electrodynamics. The American Civil Warwill pale into provincial insignificance in comparison with this

important scientific event of the same decade.”

Richard Phillips Feynman

For Giuliana, My Family and My Friends.

A B S T R A C T

We search for CP violation in a sample of 4.7× 104 singly Cabibbosuppressed D0 → K+ K− π+ π− decays and 1.8(2.6) × 104 D+

(s)→

K0S K+ π+ π− decays. CP violation is searched for in the difference

between the T -odd asymmetries, obtained using triple product corre-lations, measured for D and D decays. The measured CP violation pa-rameters are AT (D

0) = (1.0± 5.1(stat)± 4.4(syst))× 10−3, AT (D+) =(−11.96 ± 10.04(stat) ± 4.81(syst)) × 10−3 and AT (D

+s ) = (−13.57 ±

7.67(stat)± 4.82(syst))× 10−3.

vii

P R E V I O U S P U B L I C AT I O N S

The analysis on D0 decays shown in this thesis has been publishedon [del Amo Sanchez et al., 2010]. A similar analysis on D+ and D+

s

decays is going toward publication soon.

ix

A C K N O W L E D G M E N T S

First and foremost I wish to thank my supervisor Antimo Palano.He has been incredibly supportive of my scientific pursuits, and I amvery grateful for the many opportunities he has afforded during mygraduate work. He is an impressive physicist, and his advice andsuggestions have been extremely valuable in advancing this analysisand my career.

I wish to thank Daniele Pedrini and Fulvia De Fazio for having re-viewed this thesis. Their suggestions and comments greatly improvedthe quality of this work.

I also wish to thank all the BABAR Collaboration’s members, espe-cially the Charm Analysis Working Group, and among them Bill Dun-woodie, Jon Coleman, Nicola Neri, Milind Purohit, Bill Lockman andBrian Meadows. Their contribution has been fundamental to defineall the details in the analysis. The BABAR’s review committee members,Mike Sokoloff, Ray Cowan, David Lange, Owen Long, Chunhui Chenand Elisa Guido, for the attention they put on my analyses and thewriting of the article that has been published.

I then wish to thank all the Ph. D. students and post-Doc in BABARMarco Pappagallo, Alfio Lazzaro, Diego Milanes, Vincenzo Lombardo,David Lopes Pegna, José Benitez, Kevin Yarritu, Simone Stracka, PietroBiassoni, Elisa Guido, Valentina Santoro, Elisabetta Prencipe, Alessan-dro Gaz and all the others babarians, for their precious suggestionsand the funny time spent together.

Last but not least my fellows in Bari, Domenico, Floriana, Stefano,Francesco, Antonella, Irene e Marco, for the precious time spent to-gether and the mutual support with bureaucracy.

Finally, a special thank to Giuliana and my Family, for the extraordi-nary support, the education and the love I never missed.

Bari, february 2011 M. M.

xi

xii

ringraziamentiPer primo e più di tutti vorrei ringraziare Antimo Palano. Il suo

supporto per il mio lavoro di ricerca è stato fondamentale e gli sonoestremamente grato per tutte le opportunità che mi ha offerto duranteil mio lavoro di dottorato. Le sue qualità come fisico sono eccezionali,e il suo consiglio e i suoi suggerimenti sono stati di enorme impattonell’avanzamento di questa analisi e del mio percorso professionale.

Vorrei ringraziare Daniele Pedrini e Fulvia De Fazio per avere revi-sionato questa tesi. I loro suggerimenti e commenti sono stati preziosiper migliorare la qualità di questo testo.

Vorrei ringraziare anche tutti i membri della Collaborazione BABAR ein particolare del gruppo di analisi del Charm, tra cui Bill Dunwoodie,Jon Coleman, Nicola Neri, Milind Purohit, Bill Lockman and BrianMeadows. Il loro contributo è stato fondamentale per definire tutti idettagli dell’analisi. I membri dei comitati di revisione interna a BABARMike Sokoloff, Ray Cowan, David Lange, Owen Long, Chunui Chen eElisa Guido, per l’attenzione che hanno dedicato alla mia analisi e allarealizzazione dell’articolo che ne è conseguito.

Vorrei quindi ringraziare tutti i miei colleghi dottorandi e post-Docin BABAR Marco Pappagallo, Alfio Lazzaro, Diego Milanes, VincenzoLombardo, David Lopes Pegna, José Benitez, Kevin Yarritu, SimoneStracka, Pietro Biassoni, Elisa Guido, Valentina Santoro, Elisabetta Prencipe,Alessandro Gaz e tutti gli altri babariani, per i preziosi suggerimenti eil piacevole tempo passato insieme.

Infine, ma non per ultimi i miei colleghi dottorandi e amici di Bari,Domenico, Floriana, Stefano, Francesco, Antonella, Irene e Marco, peri divertenti momenti passati insieme e il vicendevole supporto nellequestioni burocratiche.

Per ultimo un ringraziamento speciale va a Giuliana e alla mia famiglia,per lo straordinario supporto, l’educazione e l’amore che non mi hannofatto mai mancare.

Bari, febbraio 2011 M. M.

C O N T E N T S

1 Introduction 1

2 CP violation and D decays 5

2.1 CP violation 5

2.1.1 First Observation of CP Violation 5

2.1.2 Standard Model 6

2.1.3 Alternative Models 7

2.2 Summary of the search for CP violation in charm de-cays 8

2.2.1 Direct CP violation 8

2.2.2 Dalitz Plot Analysis 9

2.2.3 Time Dependent Analysis 9

2.2.4 T -odd correlations 10

2.3 T -odd correlations 10

2.3.1 Definition of the T -odd Observables in this work 10

2.3.2 Previous Searches for CP Violation using T -oddCorrelations 11

2.4 Current Experimental Status 12

3 The BABAR Experiment 15

3.1 PEP− II Collider 15

3.2 The Detector 16

3.3 Particle Identification 21

3.3.1 Pion and Kaon Selection 21

4 D0 → K+K−π+π− Analysis 25

4.1 The Data Set 25

4.2 Events Reconstruction 26

4.3 Contaminations in the D0 Data Sample 27

4.4 CT Distribution 28

4.5 Definition of the Fit Model 29

4.5.1 Signal Category 31

4.5.2 Combinatorial Background 35

4.5.3 D0 Peaking Background 35

4.5.4 ∆m Peaking Background 38

4.5.5 D+s Background Category 38

4.6 The Fit Model 40

4.6.1 Fit to the Data Sample 46

4.7 Systematics 48

4.7.1 Fitting Model 50

4.7.2 Particle Identification 50

4.7.3 p∗(D0) cut 51

4.7.4 Soft Pion Charge 51

4.7.5 Effect of Forward-Backward Asymmetry 51

4.7.6 Fit Bias 52

4.7.7 Detector Asymmetry 53

4.7.8 Systematics Summary 53

xiii

xiv contents

4.8 Final Result 53

5 D+(s)→ K0SK

+π+π− Analysis 57

5.1 The Data Set 57

5.2 Events Reconstruction 58

5.3 Contaminations in the D+(s)

Data Sample 58

5.4 Optimization of the Data Sample 60

5.4.1 Potential Bias from Likelihood Ratio Selection 64

5.5 CT Resolution 65

5.6 Definition of the Fit Model 69

5.6.1 Study of the Events Categories 69

5.6.2 Definition of the Shapes 70

5.7 Data Analysis and Systematics 74

5.7.1 Fit procedure 74

5.7.2 Fit Validation on the Generic Monte Carlo sam-ple 74

5.7.3 Systematics 77

5.7.4 Events selection and Forward-Backward asym-metry 77

5.7.5 Likelihood ratio selection 82

5.7.6 Fit model 83

5.7.7 Particle identification criteria 84

5.7.8 Summary of systematic errors 84

5.8 Final Result 84

6 Conclusions 87

a The cc Asymmetric production in BABAR and Belle 91

b Statistical Techniques Used by BABAR Selectors 93

b.1 Likelihood Ratio 93

b.2 Error Correcting Output Code 94

b.3 Boosted Decision Tree 96

bibliography 99

L I S T O F F I G U R E S

Figure 1 The luminosity delivered by the PEP-II facility(blue) and the luminosity recorded by the BABARdetector (red). The contributions to the total recordedluminosity from each resonance studied are shownwith different colors. 17

Figure 2 Longitudinal (top) and transverse (bottom) sec-tion of BABAR detector. 18

Figure 3 Reconstruction efficiency for pions (top) and kaonsfake-rate (bottom) using likelihood pion selector.The reconstruction efficiency for the positivelycharged particles is shown on the left and for thenegatively charge in the middle. The ratio be-tween data and Monte Carlo reconstruction effi-ciency is shown on the right for both positivelyand negatively charged particles. 22

Figure 4 Reconstruction efficiency for kaons (top) and pi-ons fake-rate (bottom) using likelihood kaon se-lector. The reconstruction efficiency for the posi-tively charged particles is shown on the left andfor the negatively charge in the middle. The ratiobetween data and Monte Carlo reconstruction ef-ficiency is shown on the right for both positivelyand negatively charged particles. 22

Figure 5 Reconstruction efficiency for pions (top) and kaonsfake-rate (bottom) using a pion selector based onlikelihood and neural network techniques. Thereconstruction efficiency for the positively chargedparticles is shown on the left and for the neg-atively charge in the middle. The ratio betweendata and Monte Carlo reconstruction efficiency isshown on the right for both positively and nega-tively charged particles. 23

Figure 6 Reconstruction efficiency for kaons (top) and pi-ons fake-rate (bottom) using boosted decision treekaon selector. The reconstruction efficiency forthe positively charged particles is shown on theleft and for the negatively charge in the mid-dle. The ratio between data and Monte Carloreconstruction efficiency is shown on the rightfor both positively and negatively charged parti-cles. 23

xv

xvi List of Figures

Figure 7 The spectrum of the difference between π+π− in-variant mass and K0S nominal mass. The fit toa model made of a Gaussian over a line is rep-resented by the blue line. The events removedto get rid of the contamination are shown in theblue filled area. On top the pull distribution ofthe residuals is shown. 28

Figure 8 The scatter plot of ∆m versus m(K+ K− π+ π−)(a); the m(K+ K− π+ π−) spectrum in ∆m signalregion (b); the ∆m spectrum in m(K+ K− π+ π−)signal region. 29

Figure 9 CT (a) and CT (b) distributions in the D0 signalbox of the data sample. The total distribution isshown in black, while the distribution of -CT (-CT ) is overdrawn in red to graphically comparethe distribution of the events when CT (CT ) > 0and CT (CT ) < 0. 29

Figure 10 Distribution of Monte Carlo events. On the leftthe two-dimensional distribution of m(K+ K− π+

π−) and ∆m is shown, in the center there is thedistribution of m(K+ K− π+ π−) and on the rightof ∆m. 30

Figure 11 The m(K+ K− π+ π−) versus ∆m (left), m(K+ K−

π+ π−) (center) and ∆m (right) distributions foreach category are shown for each recognized cat-egory of events, from Signal (Category 1- top) toD+s (Category 5 - bottom). Generic Monte Carlo

events. 32

Figure 12 Mean value (left) and RMS (right) of ∆m in slicesof m(K+ K− π+ π−). 33

Figure 13 Fit to the distribution of correctly reconstructedsignal events from Monte Carlo. On top the pro-jections on m(K+ K− π+ π−) and ∆m of the fitmodel (blue line) and its components (color filledareas) are shown using a logarithmic scale on they-axis. In the middle the same plots are shownin linear scale. Over these plots the distribu-tion of the residuals (Pull - see Eq. 4.1) is shown.On the bottom there are the distributions of theresiduals in the two-dimensional [m(K+ K− π+

π−),∆m ] plane (left) and integrated (right). 34

Figure 14 Fit to the distribution of combinatorial backgroundevents in the Monte Carlo. On top the projec-tions on m(K+ K− π+ π−) and ∆m of the fitmodel (blue line) are shown. Over each plot thedistribution of the residuals (Pull - see Eq. 4.1)is shown. On the bottom there are the distri-butions of the residuals in the two-dimensional[m(K+ K− π+ π−),∆m ] plane (left) and inte-grated (right). 36

List of Figures xvii

Figure 15 Fit to the distribution of D0 peaking events fromMonte Carlo. On top the projections on m(K+

K− π+ π−) and ∆m of the fit model (blue line)and its components (color filled areas) are shownusing a logarithmic scale on the y-axis (m(K+

K− π+ π−) only). In the middle the same plotsare shown in linear scale. Over these plots thedistribution of the residuals (Pull - see Eq. 4.1)is shown. On the bottom there are the distri-butions of the residuals in the two-dimensional[m(K+ K− π+ π−),∆m ] plane (left) and inte-grated (right). 37

Figure 16 Fit to the distribution of ∆m peaking events fromMonte Carlo. On top the projections on m(K+ K−

π+ π−) and ∆m of the fit model (blue line) andits components (color filled areas) are shown us-ing a logarithmic scale on the y-axis (∆m only).In the middle the same plots are shown in lin-ear scale. Over these plots the distribution of theresiduals (Pull - see Eq. 4.1) is shown. On the bot-tom there are the distributions of the residualsin the two-dimensional [m(K+ K− π+ π−),∆m ]plane (left) and integrated (right). 39

Figure 17 Fit to the distribution of D+s events from Monte

Carlo. On top the projections on m(K+ K− π+

π−) and ∆m of the fit model (blue line) are shownusing a logarithmic scale on the y-axis (m(K+

K− π+ π−) only). In the middle the same plotsare shown in linear scale. Over these plots thedistribution of the residuals (Pull - see Eq. 4.1)is shown. On the bottom there are the distri-butions of the residuals in the two-dimensional[m(K+ K− π+ π−),∆m ] plane (left) and inte-grated (right). 41

Figure 18 This graphics shows the structure of the fittingmodel: the blue circles represent the variables,while the red ones the PDFs. The arrows showto which variables the PDFs are related to. It canbe seen that some variables are shared betweentwo different PDF. 42

xviii List of Figures

Figure 19 Fit to the distribution of the events from the MonteCarlo sample. On top the projections on m(K+

K− π+ π−) and ∆m of the fit model (blue line)and its components (color filled areas) are shownusing a logarithmic scale on the y-axis. The col-ors refer to the different categories of events: white- signal; yellow - combinatorial; red - D0 peak-ing; blue - ∆m peaking; green - D+

s . In the mid-dle the same plots are shown in linear scale. Un-der each plot the distribution of the residuals(Pull - see Eq. 4.1) is shown. On the bottom thereare the distributions of the residuals in the two-dimensional [m(K+ K− π+ π−),∆m ] plane (left)and integrated (right). 43

Figure 20 Fit to the distribution of the events from datasample. On top the projections on m(K+ K− π+

π−) and ∆m of the fit model (blue line) and itscomponents (color filled areas) are shown usinga logarithmic scale on the y-axis. The colors re-fer to the different categories of events: white -signal; yellow - combinatorial; red - D0 peaking;blue - ∆m peaking; green - D+

s . In the middlethe same plots are shown in linear scale. Undereach plot the distribution of the residuals (Pull- see Eq. 4.1) is shown. On the bottom thereare the distributions of the residuals in the two-dimensional [m(K+ K− π+ π−),∆m ] plane (left)and integrated (right). 47

Figure 21 Deviations from AT measured in different regionsof the detector. The grey shaded area is centeredat 0 and corresponds to AT measured on the fulldata set with errors. 53

Figure 22 Data and fit projections in ∆m signal region. Thefour sub-samples built using the D0 flavor andthe CT (CT ) value are shown. 55

Figure 23 The K+ K0S π+ π− invariant mass after recon-

struction. The D+ and D+s peaks are clearly vis-

ible together with the contamination from D∗+.The red line shows the spectrum before remov-ing the D∗+ contamination box, while the blackline shows the spectrum after the removal of thecontamination. 59

Figure 24 The fit of ∆m = m(K+K0Sπ+π−)−m(K0SK

+π−) isshown on the left. The results of this fit allowedto define a ∆m signal region to plot and fit the K0SK+ π− invariant mass on the right. Both the fitsare made to a model of a Gaussian over a secondorder polynomial background. 59

List of Figures xix

Figure 25 Study of D+ → K0S K0S K

+ contamination. On thetop left the m(π+π−) spectrum is shown in D+

signal region; in the top right the same spectrumis shown in D+ sidebands region; on the bottomleft the subtraction of the two spectra has beenfitted to a Gaussian over a flat function; on thebottom right the events removed applying thecut on D+ → K0S K

0S K

+ are shown in the redfilled area compared to the spectrum before theapplication of this cut. 61

Figure 26 p K0S π+ π− mass spectrum is shown on the left.

The nominal Λ+c mass from PDG is indicated

by a red line (m(Λ+c )=2286.46 MeV/c2). The fit

of the Λ+c peak using a Gaussian over a second

order polynomial background is shown on theright. 61

Figure 27 Signal (red) and sidebands (blue) regions for D+

→ K0S π+ π+ π− (left) and D+

s → K− K0S π+ π+

mass spectra. 62

Figure 28 Signal (red) and sidebands (blue) distributionsfor the D+ (top) and D+

s (bottom) peaks. Fromleft to right p∗(D+

(s)), ∆p and dxy. 63

Figure 29 Plot of the distribution ofD+ (left) andD+s (right)

likelihood ratio evaluated on D+(s)→ K0S K

+ π+

π− data sample. 64

Figure 30 Variation ofD+(s)

peak significance depending onthe selection criteria applied on D+ (left) of D+

s

(right) likelihood ratio. 64

Figure 31 K+ K0S π+ π− mass spectrum optimized using

D+ (left) and D+s (right) likelihood ratios. 65

Figure 32 On top the plots of likelihood ratio for D+ whenCT is greater (black) or less (red) than zero. Onthe bottom the same plot made on D− depend-ing on CT . 66

Figure 33 The K0S K+ π+ π− mass spectrum is comparedwhen CT > 0 (black) or CT < 0 (red) usingthe generic Monte Carlo sample. On the left isshown the comparison between D+ candidates,on the right between D− candidates. Both the Dcandidates distributions are consistent betweenCT (CT ) > 0 and CT (CT ) < 0. 66

Figure 34 The AT observable measured on signal MonteCarlo after the application of all the selectionsusing different cuts on likelihood ratio. The redshaded area shows the AT value and error re-trieved from generated Monte Carlo. The blueshaded area shows the AT value and error afterevents reconstruction and before the cut on like-lihood ratio. 67

xx List of Figures

Figure 35 The distribution of the events in the signal re-gion with the sidebands subtracted with CT (CT )greater or less than zero is compared on top leftfor D+ (D−- right) and on the bottom left for D+

s

(D−s - right) data sample. 68

Figure 36 Composition of the K+ K0S π+ π− mass spectrum

after reconstruction. On the right, the same plotthat is on the left is shown limiting the range ofthe y-axis to [18,000:46,000]. The highlight allowsto show the events categories in detail. 69

Figure 37 Composition of the K+ K0S π+ π− mass spectrum

after the selection on likelihood ratio. The ploton the left shows the D+ mass range; the one onthe right shows the D+

s range. 70

Figure 38 Fit of the background categories using three dif-ferent polynomial shapes: a line (a), a second or-der (b), a third order (c). On left the D+ massrange is shown, on the right the one of D+

s . Theχ2 reduced to the number of degrees of freedomis shown on top left of each plot. The normalizedresiduals shown on top of each plot are evaluatedas outlined in Equation 4.1. 71

Figure 39 Model made of two gaussians and a linear back-ground fitted to the Monte Carlo sample in theD+ (left) and D+

s (right) mass region. The pro-jection of the model on the data is shown bythe blue line; the second Gaussian in the sig-nal shape is shown in red, the background shapeis shown by a dashed blue line. On top of theplots, the normalized residuals (Pull) distribu-tion is shown. 73

Figure 40 Model made of two gaussians and a second or-der polynomial background fitted to the MonteCarlo sample in the D+

s mass region. The pro-jection of the model on the data is shown bythe blue line; the second Gaussian in the sig-nal shape is shown in red, the background shapeis shown by a dashed blue line. On top of theplots, the normalized residuals (Pull) distribu-tion is shown. 73

Figure 41 Fit to the D+(s)→ K0S K

+ π+ π− data sample.The fit has been performed using a model madeof a double gaussian over a linear (second or-der polynomial) background. On the left the fitto the overall sample is shown; on the right theprojections on the four sub-samples are shown.For each plot, the distribution of the normalizedresiduals (Pull) is shown on the top. 76

Figure 42 Reconstruction efficiency in bins of the cosine ofthe cc production angle. 79

Figure 43 Fits to the two-body invariant mass distributionsfor D+ signal events. From left to right, top todown: K0S π+, K∗−→ K0S π

−, K∗0 → K+ π− andρ→ π+π−. 80

Figure 44 Distribution of the weights used to simulate theforward-backward asymmetry effect. 81

Figure 45 The asymmetry parameters AT (left), AT (cen-ter) and AT (right) are compared with their valuebefore the simulation (grey shaded area) and af-ter the introduction of the efficiency, the resonantstructure and the forward-backward asymmetry.On top, the results on D+ peaks, in the bottom,the D+

s . 81

Figure 46 Comparison of the best recent results for CP vi-olation in D0 decays. The result of the analysisoutlined in this thesis is highlighted into a redbox. 89

Figure 47 Comparison of the best recent results for CP vi-olation in D+ decays. The result of the analysisoutlined in this thesis is highlighted into a redbox. 89

Figure 48 Comparison of the best recent results for CP vi-olation in D+

s decays. The result of the analysisoutlined in this thesis is highlighted into a redbox. 89

L I S T O F TA B L E S

Table 1 Previous searches for CP violation inD0 decays. 12

Table 2 Previous searches for CP violation inD+ decays. 13

Table 3 Previous searches for CP violation inD+s decays. 13

Table 4 Hadronic and leptonic cross-sections for e+e−

collisions at the center-of-mass energy of the Υ(4S). 16

Table 5 Recorded luminosity for each of the data takingperiods. 16

Table 6 Number of events for each category from MonteCarlo. The contribution to the total of the sampleis also shown. 31

Table 7 Results of the fit to the full Monte Carlo sample.The values of the masses and the widths are ex-pressed in terms of MeV/c2. 44

Table 8 Reconstructed and fitted number of events foreach of the categories identified in the MonteCarlo sample. The last column shows the num-ber of σ’s between the true and the fitted numberof events: ε = n−nrec

σnrec. 45

xxi

xxii List of Tables

Table 9 Reconstructed and fitted number of signal eventsfor each sub-sample. The last column shows thenumber of σ’s between the true and the fittednumber of events: ε = n−nrec

σnrec. 46

Table 10 Reconstructed and fitted asymmetry parameters.The last column shows the number of σ’s be-tween the true and the fitted parameter: ε =A−ArecσArec

. 46

Table 11 Number of events for each category of events re-trieved from the fit to the data sample. 48

Table 12 Results of the fit to the data sample. The valuesof the masses and the widths are expressed interms of MeV/c2. 49

Table 13 Number of events in the data set after the appli-cation of the selectors using tighter criteria. 51

Table 14 Number of events in the data set after the appli-cation of tighter selections on the momentum ofD0 candidate in the center-of-mass frame. 51

Table 15 Study of slow momentum pion mis-identificationusing correctly reconstructed Monte Carlo. 52

Table 16 Number of signal events, deviation from AT us-ing standard cuts and error on the T violation pa-rameter measured for each sub-sample of cos θ∗ 52

Table 17 Systematic uncertainty evaluation on AT , AT andAT in units of 10−3. 54

Table 18 Definition of signal and sidebands mass regions.The regions are shown in intervals of mass mea-sured in MeV/c2. 62

Table 19 Comparison between the number of events re-trieved by the fit and by Monte Carlo truth. Thelast column shows the number of σ’s betweentrue and fitted number of events: ε = n−ntrue

σn70

Table 20 Comparison between the number of events re-trieved by the fit and by Monte Carlo truth. Thelast column shows the number of σ’s betweentrue and fitted number of events: ε = n−ntrue

σn72

Table 21 Results of the fits to the Monte Carlo sample re-quiring LD+ > 1.50 and LD+

s> 1.50. 72

Table 22 Results of the fits to the data sample requiringLD+

(s)> 1.50 (AT and AT are blind for both D+

and D+s peaks). 75

Table 23 Results of the fits to the generic Monte Carlosample requiring LD+

(s)> 1.50. 78

Table 24 Results of the fits shown in Fig. 43. All the res-onances are fitted to a relativistic Breit-Wignershape. The resulting masses and widths are shownin MeV/c2. 79

Table 25 Statistical error (σ) on AT , AT and AT and theirdeviation (∆) from the best LRD+

(s)cut. All the

values are multiples of ×10−3. 82

List of Tables xxiii

Table 26 Deviation of AT , AT and AT from the best modelto fit the distribution. All the values are multi-ples of ×10−3. 83

Table 27 Statistical error of AT , AT and AT depending onthe model used to fit the distribution. All thevalues are multiples of ×10−3. 83

Table 28 Deviation of AT , AT and AT from the used parti-cle identification criteria. All the values are mul-tiples of ×10−3. 85

Table 29 Statistical error of AT , AT and AT using differentparticle identification criteria. All the values aremultiples of ×10−3. 85

Table 30 Summary of the contributions to systematic er-ror. All the values are multiples of ×10−3. 85

Table 31 Indicator matrix of a multi-class classifier fromthe combination of two binary classifiers. tα andtβ represent how the given class is treated intraining a sample for classifier α and β respec-tively. 1 means signal and 0 means background. 94

Table 32 Hamming distance obtained comparing the out-put in Equation B.7 with the indicator matrix ofTable 31. 95

Table 33 All possible classifiers for a four-classes prob-lem. Among them, there are only 7 valid clas-sifiers. 95

Table 34 Exhaustive Matrix for a four-classes problem. 95

Table 35 Hamming distance for the exhaustive matrix of afour-classes problem when there is one classifierfailing (O=0111111). 97

Table 36 Hamming distance for the exhaustive matrix ofa four-classes problem when there are two clas-sifiers failing (O=0011111). 97

Table 37 Hamming distance for the exhaustive matrix of afour-classes problem when there are three classi-fiers failing (O=0001111). 97

Table 38 Exhaustive Matrix for the BABAR particle identifi-cation. 97

1 I N T R O D U C T I O N

Man has always had a deep interest for symmetries. From the moreancient times the pleasure of building artifacts stimulating our senseof symmetry has represented the main purpose of fine arts.

This interest has reflected in the developing of mathematics andspecifically geometry: the former defining the tools to build the lat-ter, both ideally inspired from perfection.

Anyway, it would be unfair to state that the concept of symmetryis innate in human mind: it has been developed from the observationof nature, that provides us many examples of geometrical symmetriesthat have inspired human beings from the beginning of history. Justthink about the wings of a butterfly, the structure of a leaf and eventhe apparent symmetry among the left and right ends of the humanbody.

Such a concept is so much well represented in what we see fromour first days of life, that is not avoidable in our thinking. That iswhy we defined it even in Physics, without any suspect of how muchfundamental would be for the description of the deep mechanics thatrules the world where we live.

The first and more natural kind of symmetry that we defined inPhysics is Parity (P), the reflection of space coordinates from ~x to −~x.Similarly we defined another discrete symmetry, the Time Reversal (T ),which changes t in −t, reverting the motion. As soon as the conceptof anti-particle was introduced by the Dirac equation [Dirac, 1928], theCharge conjugation (C), transforming a particle into its anti-particle,has been studied.

We have learnt that nature is largely, but not completely, invariantunder these transformations. Although these insights were at firstless than eagerly accepted by the Physics community, they form anessential element of what is called the Standard Model (SM) of par-ticle Physics. This model contains 20 odd parameters, a feature thatcannot be accidental, but must be shaped by some intriguing NewPhysics. The scientific community considers it very likely that a com-prehensive study of how these discrete symmetries are implementedin nature will reveal the intervention of New Physics [Bigi e Sanda,2000].

Furthermore, we believe that time reversal and the combined trans-formation of CP occupy a very unique place in the pantheon of symme-tries. Once charge conjugation and parity were found to be maximallyviolated [Wu et al., 1957], their combination CP was apparently con-served. This point was sustained from the local T invariance derivedfrom Mach’s principle and from the CPT invariance that is natural inquantum field theory [Bjorken e Drell, 1965]: no CP violation is thenallowed if T violation is not found.

It was then a big shock in Physics’ community when the CP violationwas found [Christenson et al., 1964], following the prescription of the

1

2 introduction

CPT theorem, that also means the T is violated, which substantiallymeans that nature makes difference between past and future even inmicroscopic reactions.

There are other aspects that make CP and T violation worth to bestudied in detail:

• from CP violation a characterization of matter and anti-matterthat is more general then the one obtained from C violation canbe retrieved. C violation allows to separate matter and anti-matter from the reaction that involves left and right neutrinosonly. This is anyway a convention that could be reversed untilCP is conserved. Once CP is violated, matter and anti-matter canbe defined in an absolute way: among the K0L decays for example,K0L → e+ νe π

− is favored respect to its CP conjugate [Nakamuraet al., 2010], allowing to define the positron as the anti-electronusing a hint from nature.

• The anti-unitarity of the T operator of symmetry, together withKramers’ degeneracy allow to observe two eigenvalues for T2:T2 = +1 corresponds to boson states, T2 = −1 to fermions.

• CP violation is an excellent phenomenological probe. It wasdiscovered in 1964 studying K0L → π+π− and included in theStandard Model by the Kobayashi-Maskawa ansatz [Kobayashi eMaskawa, 1973] in 1973. This ansatz allowed to forecast a thirdfamily of leptons and quarks that have been confirmed in thefollowing years.

• We can still not give the notion of maximal CP violation, as wellas it can be done for P and C using the right and left-handedneutrino convention. As far as we know, CP violation is allowedin the Standard Model with three quark families, but we cannotassign any meaning to maximal CP violation.

• Finally, any attempt to describe the asymmetry between baryonsand anti-baryons in the universe [Sakharov, 1967], is strictly re-lated to CP violation.

From all of the above items, the validity of a wide range Physics pro-gram to understand CP and T violation follows up.

The work outlined in this thesis contributes to this program search-ing for CP violation in two singly Cabibbo suppressed and one Cabibbofavored four-body D decay modes. The specific final states that aresubject of the analysis are

• D0 → K+ K− π+ π− (singly Cabibbo suppressed);

• D+ → K+ K0S π+ π− (singly Cabibbo suppressed);

• D+s → K+ K0S π

+ π− (Cabibbo favored).

After a brief introduction on the search for CP violation in D decays,the main interesting features of the BABAR detector are outlined; thenthe analysis made on D0 decays is shown; the work made on D+

and D+s decays is described together in the section following the D0

analysis.

introduction 3

Finally, the results of these analyses are compared to the results ob-tained by previous analyses from different experiments, providing theground for a discussion of the results.

2 CP V I O L AT I O N A N D D D E C AY S

contents2.1 CP violation 5

2.1.1 First Observation of CP Violation 5

2.1.2 Standard Model 6

2.1.3 Alternative Models 7

2.2 Summary of the search for CP violation in charm decays 82.2.1 Direct CP violation 8

2.2.2 Dalitz Plot Analysis 9

2.2.3 Time Dependent Analysis 9

2.2.4 T -odd correlations 10

2.3 T -odd correlations 102.3.1 Definition of the T -odd Observables in this work 10

2.3.2 Previous Searches for CP Violation using T -odd Corre-lations 11

2.4 Current Experimental Status 12

2.1 CP violationCP is an operation obtained combining the two discrete transforma-

tions of Parity P and Charge conjugation C. Even if the conservationof P and C was known to be maximally violated, their combination CPwas supposed to be conserved. This assertion was supported by theCPT theorem, that naturally establish the invariance of any quantumfield theory when the three discrete symmetries are applied. Follow-ing this theorem, observing CP violation, T violation is straightforwardand vice-versa. But, if T is violated in fundamental processes, thenthe assertion that locally past and future are not distinguishable fallsdown. Without reminding the central role of CP violation within boththe Standard Model and any alternative model developed to extend it,in the following some details on CP violation and on the searches forCP violation in D decays will be outlined.

2.1.1 First Observation of CP Violation

CP violation was found in 1964, by means of the observation of K0L →π+π− decay [Christenson et al., 1964]. To understand why this obser-vation has been so crucial, let us suppose that K0S and K0L are CP = ±1eigenstates. K0S and K0L are named from their highly different meanlife (τK0S = 0.89 × 10−10s and τK0L

= 5.12 × 10−8s) are made of the

superposition of K0 and K0 states, that are not CP eigenstates. UnlikeK0 and K0, distinguished by their mode of production, K0S and K0L aredistinguished by their decay modes: π+π− and π0 π0 are indeed CP =1

5

6 CP violation and D decays

while π+ π− π0 and π0 π0 π0 are CP =-1 states. These statements fol-low up when considering Bose symmetry, the Q-value of the reactionand the intrinsic Parity of the pions [Perkins, 1982]. The observationof the K0L → π+π− decay is then a clear signal of CP violation.

2.1.2 Standard Model

CP violation is included in the Standard Model by means of theFor the introductionof the KM ansatz, the

two scientists havebeen awarded the

Nobel Prize inPhysics for the year

2008

Kobayashi-Maskawa (KM) ansatz [Kobayashi e Maskawa, 1973]. Inthe KM ansatz the CP violation is introduced through a quark mixingmatrix V to describe the quark states as a mixture of mass eigenstates.In their paper, the authors try to introduce the CP violation in a modelin which the interacting quarks form a quartet: the higher mass quarksc, b and twere still unknown at the time. After struggling to introduceCP violation using a four quark model, they observe that CP violationis naturally introduced in the quark mixing matrix if three familiesof two quarks are considered. It can be shown that the number ofrotational angles and the number of phases to define a matrix that isunitary and orthogonal depend on n, the number of quark families:

Nangles =1

2n(n− 1), Nphases =

1

2(n− 1)(n− 2). (2.1)

Assuming n = 2 there is only one rotational angle, the Cabibbo angleθC [Cabibbo, 1963], and no phase term. Introducing another familyof quarks, n = 3 and the rotational angles become Nangles = 3 and anirreducible phase makes its appearance: Nphases = 1.

This phase is responsible for the introduction of CP violation inthe quark mixing matrix, also known as Cabibbo-Kobayashi-Maskawa(CKM) matrix:Vud Vus Vub

Vcd Vcs VcbVtd Vts Vtb

⇒ 1− λ2

2 λ Aλ3(ρ− iη+ i2ηλ

2)

−λ 1− λ2

2 − iηA2λ4 Aλ2(1+ iηλ2)

Aλ3(1− ρ− iη) −Aλ2 1

(2.2)

here shown in the Wolfenstein representation, approximated at the or-der O(λ5), where λ = sin θC [Wolfenstein, 1983]. In this representation,the phase appears in the matrix elements as the complex componentand can be identified in Vub, Vtd, Vcb and Vcs.

The CP violating effect would show up only if the decay amplitudeis the sum of two different parts, whose phases are made of a weak(CKM) and a strong (final state interaction) contribution. The weakphases change sign when going to the CP-conjugate process, while thestrong ones do not. A decay amplitude of this type can be written as

A = Aeiδ1 +Beiδ2 , (2.3)

while the corresponding charged-conjugate is

A = A∗eiδ1 +B∗eiδ2 . (2.4)

2.1 CP violation 7

For both of them A and B represent the amplitude with the invariantstrong phase divided out and δi is the strong phase itself. The CPviolating asymmetry in the decay rate would be therefore

aCP =|A|2 − |A|2

|A|2 + |A|2=

2=(AB∗) sin(δ2 − δ1)|A|2 + |B|2 + 2<(AB∗) cos(δ2 − δ1)

. (2.5)

In D decays, there are three kind of processes that can interfere andgenerate a CP asymmetry:

• c→ ssu;

• c→ ddu;

• c→ u∑qq.

The last one is represented by a penguin diagram, while the othersare charged current ones. All of these processes contribute to singlyCabibbo suppressed D decays; no CP violation is expected in Cabibbofavored or doubly Cabibbo suppressed decays. The effect of CP viola-tion in D decays has been calculated to have a limit of 0.1% [Buccellaet al., 1995].

There can be effects of indirect CP violation that need to be ac-counted for. All the decays involving a neutral kaon are subjectedto the asymmetry introduced by the K0-K0 mixing. The effect of thismixing on the asymmetry is aK

0mixCP = −3.3× 10−3 [Nakamura et al.,

2010].

2.1.3 Alternative Models

The relative smallness of the effect in the Standard Model allows tostate that the observation of CP violation at the order of 1% inD decaysis a strong evidence for the existence of processes that are not includedin the Standard Model.

There are two ways to introduce CP violation inD decays [Grossmanet al., 2007] in scenarios beyond the Standard Model:

• Direct CP violation at tree-level: extra quark in Standard Modelvector-like representation; supersymmetry without R-parity mod-els; two Higgs doublet models.

• Direct CP violation at one-loop: QCD penguin and dipole opera-tors; Flavor Changing Neutral Currents in supersymmetric flavormodels.

While the first group of models can produce an effect that is much lessthan 1%, the processes having one-loop can even reach the percentlevel, producing effects that are clearly not expected in the StandardModel.


2.2 summary of the search for CP vio-lation in charm decays

In the recent years, many searches for CP violation have been per-formed on charm decays. Four kind of analyses can be recognised:

• search for direct CP violation;

• Dalitz plot analysis;

• time dependent analysis;

• study of T -odd correlations.

The details of each one of these techniques are outlined in the follow-ing.

2.2.1 Direct CP violation

The search for direct CP violation is made by looking for an asym-metry in the number of D and D events decaying into a specific finalstate f. The observable for direct CP violation can be then defined as

ACP =ND −NDND +ND

, (2.6)

where ND and ND indicate respectively the number of D → f andD→ f events.

Many measurements have been performed at the asymmetric B-factories, such as BABAR and BELLE. In these experiments, there is awell known effect, the forward-backward asymmetry, that could biasthese measurement by introducing an asymmetry that is due to theinterference between the weak and the electromagnetic e+e− → ccproduction processes. For further information see Appendix A. Thereare two solutions to remove this bias:

1. evaluate the amount of forward-backward asymmetry itself;

2. delete the effect by normalizing the number of D and D eventsusing Cabibbo favored decay modes.

The former solution leads to measure the amount of forward-backwardasymmetry AFB and evaluate the direct CP asymmetry as

ACP = aCP −AFB, (2.7)

being aCP the asymmetry measured from the data. The latter solutioncan be exploited by measuring the observable

A(norm)CP =

RD − RDRD + RD

, R =NCSNCF

. (2.8)

2.2 summary of the search for CP violation in charm decays 9

2.2.2 Dalitz Plot Analysis

There are many quantities that can be measured in a Dalitz plotanalysis to search for CP violation:

• the Dalitz plot histogram can be compared bin-per-bin betweenD and D to search for asymmetries;

• similarly the distribution of the angular moments can be com-pared;

• once determined the model that best fits the data, the amplitudesof each component can be compared between D and D.

2.2.3 Time Dependent Analysis

The study of the D decay times and the opportunity to search forCP violation is strictly related to D mixing [Bergmann et al., 2000]. It isindeed known that D mixing affects decay times

τ+hh = τKπ[1+ rm(y cosφf − x sinφf)]−1,

τ−hh = τKπ[1+ r−1m (y cosφf − x sinφf)]−1, (2.9)

where h = K or π, τKπ is the lifetime for the Cabibbo favored D0 →K− π+ decay. x, y, rm and φf are defined considering that the two D0

mass eigenstates can be represented as

|D1 > = p|D0 > +q|D0 >,

|D2 > = p|D0 > −q|D0 >, (2.10)

where p2 + q2 = 1. The size of D0 mixing is traditionally quantifiedin terms of the parameters

x ≡ ∆mΓ

and y ≡ ∆Γ2Γ

, (2.11)

where ∆m = m1 −m2, ∆Γ = Γ1 − Γ2 and Γ = (Γ1 + Γ2)/2, being miand Γi the masses and the widths of the two mass eigenstates.

The more relevant parameters for CP violation are

rm ≡∣∣∣∣qp∣∣∣∣ and φf ≡ arg

(q

p

AfAf

), (2.12)

where Af =< f|H|D0 > (Af =< f|H|D0 >), f being the final state theD is decaying to. Observing rm 6= 1 would indicate CP violation inmixing, while a non-zero value of φf would indicate CP violation inthe interference between mixing and decay.

The observable that is used by time-dependent analysis to search forCP violation is

∆Y =τKπτhh

Aτ, (2.13)

where τhh = (τ+hh + τ−hh)/2 and Aτ = (τ+hh − τ−hh)/(τ+hh + τ−hh). In

the Standard Model, ∆Y is expected to be zero. Observing a non-zerovalue would indicate the presence of New Physics.


2.2.4 T-odd correlations

Being the main topic of this thesis, a separate section (the next one)has been left to describe the T -odd correlations.

2.3 T -odd correlationsAnalyses that study T -odd correlations are trying to reverse the

point of view. While other analysis search directly for CP violation,this kind of analysis are searching for T violation and assume the va-lidity of CPT theorem to state if CP violation is found or not.

The validity of the method of T -odd correlations to search for T vi-olation is inferred by many papers [Bensalem et al., 2002a,b; Bensaleme London, 2001]. The original idea of applying this method to D de-cays is from I. Bigi [Bigi, 2001]: he suggested to study the four-bodyD decays building a T -odd observable using the spin or the momen-tum (~vi) of the final state particles in the D center-of-mass frame. Theobservable is

AT =Γ(~v1 · (~v2 ×~v3) > 0) − Γ(~v1 · (~v2 ×~v3) < 0)

Γ(~v1 · (~v2 ×~v3) > 0) + Γ(~v1 · (~v2 ×~v3) < 0)(2.14)

where Γ represents the number of signal events and is measured on Ddecays only.

Anyway this is not a true T violating observable, because of thefinal state interaction effects that can introduce asymmetries. In orderto remove these effects, it is needed to measure the charged conjugateof this observable (AT ) using the D decays and evaluate the true Tviolating observable

AT ≡1

2(AT − AT ). (2.15)

While the T violating phase changes its sign when taking the CP conju-gate, the strong phase (introduced by final state interaction) does not.The difference between AT and AT then removes the strong phase andthe factor 1/2 is placed to normalize the weak phase.

2.3.1 Definition of the T-odd Observables in this work

In this work, the momenta of the final state particles are used tobuild the variables CT and CT .

CT ≡ ~pK+ · (~pπ+ × ~pπ−),CT ≡ ~pK− · (~pπ− × ~pπ+). (2.16)

These variables are used to split the D and D decays and measure theasymmetry parameters AT and AT :

AT =ΓD(CT > 0) − ΓD(CT < 0)

ΓD(CT > 0) + ΓD(CT < 0),

AT =ΓD(−CT > 0) − ΓD(−CT < 0)

ΓD(−CT > 0) + ΓD(−CT < 0). (2.17)

2.3 T -odd correlations 11

Finally the T violating asymmetry parameter is measured as shown inEquation 2.15.

2.3.2 Previous Searches for CP Violation using T-odd Correlations

The first search for CP violation using T -odd correlations inD decayshas been made by the FOCUS (E831) experiment at FermiLab [Linket al., 2005].

Their analysis is made on about 800D0→ K+ K− π+ π− decays thathave been separated among D0 and D0 reconstructing the full D∗+ →D0 π+ decay chain. Using the momenta of the final state particlesin the D0 center-of-mass frame, the CT and CT variables have beenretrieved for any D0 and D0 decay. Measuring the number of D0 andD0 when CT and CT are greater or less than zero, they found

AT (D0) = 0.010± 0.057(stat)± 0.037(syst). (2.18)

The sources of systematics identified in their analysis are five:

1. the splitting of the data sample in four independent sub-samples(due to a possible mismatch in the reproduction of the D mo-mentum and the changing experimental conditions during datacollection);

2. the fit variant (computed by varying, in a reasonable manner, thefitting conditions on the whole data set);

3. the set of cuts applied to extract the signal (estimated using thestandard deviation of the several sets of cuts used);

4. the D∗-tag dilution (actually an erroneous D∗-tag can dilute themeasured asymmetry);

5. the limited Monte Carlo statistics.

The total systematic error has been obtained adding in quadrature eachsource.

The analysis on D+ and D+s decays has been made as the same as

the D0, the only difference in the events reconstruction. Both the D+

and D+s signal decays are reconstructed through their K+ K0S π

+ π−

final state. This way, about 500 signal events have been reconstructedboth for D+ and D+

s . The CT and CT variables have been evaluatedas the same as for the D0 decays and have been used to split the totaldata sample into four sub-samples. Another difference respect to theD0 analysis is that both the D+ and D+

s peaks are shown together intothe same mass spectrum, so that the fit model has to take care aboutthat. A remarkable contamination from Λ+

c→ p K0S π+ π− and D+ →

K0S π+ π+ π− has been found in the dataset and has been included

into the fit model using a polynomial shape.The sources of systematics error have been identified as the same as

the D0 sample. The final results are

AT (D+) = 0.023± 0.062(stat)± 0.022(syst); (2.19)

AT (D+s ) = −0.036± 0.067(stat)± 0.023(syst). (2.20)


The FOCUS experiment did not find any evidence of CP violation inD decays, but their work showed that the T -odd correlations are a cleanand an alternative way to search for CP violation in four-body Cabibbosuppressed D decays. Their results then encouraged higher statisticsexperiment to repeat their measurement with better sensitivity.

2.4 current experimental statusIn the last few years, the statistics collected by the B-factories and

other experiments producing many charmed particles, reached the sen-sitivity required for the CP violation measurements in the Charm sec-tor. The 0.1% sensitivity has not been reached yet, but 0.5% is alreadya standard for the latest measurements. Even if the Standard Modeleffects cannot be probed, the absence of asymmetry at the order of 1%limits the effects of New Physics on this observable.

The measurements made onD0,D+ andD+s decays are shown in Ta-

bles 1, 2 and 3 respectively. In these tables the best measurements arereported only. To review the full list of measurements, please check theHeavy Flavor Averaging Group website: http://www.slac.stanford.edu/xorg/hfag.

Table 1: Previous searches for CP violation in D0 decays.

Decay Experiment (Year) Measurement

Direct CP measurementsD0 → π+π− Belle (2008) (+4.3± 5.2± 1.2)× 10−3

BABAR(2008) (−2.4± 5.2± 2.2)× 10−3D0 → K+ K− Belle (2008) (−4.3± 3.0± 1.1)× 10−3

BABAR(2008) (0.0± 3.4± 1.3)× 10−3D0 → π+ π− π0 BABAR(2008) (−3.1± 4.1± 1.7)× 10−3

Belle (2008) (+4.3± 13.0)× 10−3D0 → K− π+ π0 Cleo-c (2007) (+0.2± 0.4± 0.8)× 10−2D0 → K+ π− π0 Belle (2005) (−0.6± 5.3)× 10−2D0 → K0S π

+ π− Cleo (2004) (−0.9± 2.1+1.6−5.7)× 10

−2

D0 → K− K+ π0 BABAR(2008) (+10.0± 16.7± 2.5)× 10−3D0 → K+ π− π+ π− Belle (2005) (−1.8± 4.4)× 10−2D0 → K+ K− π+ π− FOCUS (2005) (−8.2± 5.6± 4.7)× 10−2

Time dependent CP measurementsD0 → π+π− (+K+ K−) BABAR(2008) (+2.6± 3.6± 0.8)× 10−3

Belle (2007) (+1.0± 3.0± 1.5)× 10−3

T -odd correlations CP measurementsD0 → K+ K− π+ π− FOCUS (2005) (+1.0± 5.7± 3.7)× 10−2

http://www.slac.stanford.edu/xorg/hfag

http://www.slac.stanford.edu/xorg/hfag

2.4 current experimental status 13

Table 2: Previous searches for CP violation in D+ decays.


Direct CP measurementsD+ → µν CLEO-c (2008) +0.08± 0.08D+ → K0S π

+ BABAR(2010) (−4.4± 1.3± 1.0)× 10−3Belle (2010) (−7.1± 1.9± 2.0)× 10−3

CLEO-c (2007) (−0.6± 1.0± 0.3)× 10−2D+ → K0S K

+ Belle (2010) (−1.6± 5.8± 2.5)× 10−3D+ → K− π+ π+ CLEO-c (2007) (−0.5± 0.4± 0.9)× 10−2D+ → K0S π

+ π0 CLEO-c (2007) (+0.3± 0.9± 0.3)× 10−2D+ → K+ K− π+ CLEO-c (2008) (−0.3± 8.4± 2.9)× 10−3

BABAR(2005) (+1.4± 1.0± 0.8)× 10−2FOCUS (2000) (+0.6± 1.1± 0.5)× 10−2

D0 → K− π+ π+ π0 CLEO-c (2007) (+1.0± 0.9± 0.9)× 10−2D0 → K0S π

+ π+ π− CLEO-c (2007) (+0.1± 1.1± 0.6)× 10−2D+ → K0S K

+ π+ π− FOCUS (2005) (−4.2± 6.4± 2.2)× 10−2

T -odd correlations CP measurementsD+ → K0S K

+ π+ π− FOCUS (2005) (+2.3± 6.2± 2.2)× 10−2

Table 3: Previous searches for CP violation in D+s decays.


Direct CP measurementsD+s → π+ η CLEO-c (2008) (−8.2± 5.2± 0.8)× 10−2

D+s → π+ η ′ CLEO-c (2008) (−5.5± 3.7± 1.2)× 10−2

D+s → K0S π

+ Belle (2010) (+5.5± 2.5± 0.3)× 10−2D+s → K+ π0 CLEO-c (2007) (+0.02± 0.29)

D+s → K+ η CLEO-c (2007) (−0.20± 0.18)

D+s → K+ η ′ CLEO-c (2007) (−0.17± 0.37)

D+s → K0S K

+ Belle (2010) (+1.2± 3.6± 2.2)× 10−3CLEO-c (2008) (+4.9± 2.1± 0.9)× 10−2

D+s → π+ π+ π− CLEO-c (2008) (+2.0± 4.6± 0.7)× 10−2

D+s → K+ π+ π− CLEO-c (2008) (+11.2± 7.0± 0.9)× 10−2

D+s → K+ K− π+ CLEO-c (2008) (+0.3± 1.1± 0.8)× 10−2

D+s → K0S K

− π+ π+ CLEO-c (2008) (−0.7± 3.6± 1.1)× 10−2D+s → K+ K− π+ π0 CLEO-c (2008) (−5.9± 4.2± 1.2)× 10−2

T -odd correlations CP measurementsD+s → K0S K

+ π+ π− FOCUS (2005) (−3.6± 6.7± 2.3)× 10−2

3 T H E BABAR E X P E R I M E N T

contents3.1 PEP− II Collider 153.2 The Detector 163.3 Particle Identification 21

3.3.1 Pion and Kaon Selection 21

The B-factories have been playing a very important role in the un-derstanding of the CP sector of the Standard Model. In this chapter theBABAR Experiment will be outlined in its main features.

3.1 PEP − II colliderThe BABAR Detector has been designed to efficiently detect the decay

products of the B mesons, which are produced in e+e− collisions atthe center-of-mass energy of 10.58 GeV, corresponding to the mass ofthe Υ(4S) resonance, that decays half the times in B+ B− and the otherhalf into B0 B0.

The two interacting beams are accumulated in the rings of the PEP-IIcollider, operated by the SLAC National Accelerator Laboratory. ThePEP-II facility also includes the linear accelerator (LINAC) that allowsto reach the energies of 9.0 GeV for the electron and 3.1 GeV for thepositron beams.

The difference in energy between the two beams produces a boostof the center-of-mass βγ = 0.56. The vertices of the decaying B’s havethen a separation (βγcτ ≈ 270µm) that is longer than the one theywould have without any boost (βγ = 0.06, βγcτ ≈ 30µm). A longervertices separation, allows to measure with better definition the decaylength of the two B mesons, hence reduce the error on their properdecay time. This effect is then needed to measure the proper timedifferences between the two decaying particles, a crucial ingredient ofsome of the golden measurements for which BABAR has been designed.

The PEP-II facility provided collisions to the BABAR experiment fromOctober 1999 to April 2008. The design luminosity of 3×1033 cm−2s−1

has been reached on October 2000, while the BABAR’s record luminosityof 1.2× 1034 cm−2s−1 has been achieved on August 16, 2006.

The collisions were mainly at the energy of the Υ(4S), but through-out the data taking many events were recorded “off-peak”, about 40 MeVbelow the Υ(4S) (about 10% of the “on-peak” data). Since the center-of-mass energy of these events is under the BB production threshold(10,560 MeV/c2), they can be used to study the background from thecontinuum production of u, d, s and c quarks. The cross-sections for

15

16 the BABAR experiment

quarks production from e+e− collisions at the energy of the Υ(4S) areshown in Table 4.

Table 4: Hadronic and leptonic cross-sections for e+e− collisions at the center-of-mass energy of the Υ(4S).

e+e− → Cross-Section ( nb)

bb 1.05

cc 1.30

ss 0.35

dd 0.35

uu 1.39

τ+τ− 0.94

µ+µ− 1.16

e+e− ∼ 40

From January 2008, the collider explored the energy ranges of theΥ(3S) (10,335 MeV) and the Υ(2S) (10,023 MeV), collecting the world’slargest sample of Υ(3S) decays. Furthermore a scan of the energyrange above the Υ(4S) has been performed, allowing to measure thee+e−→ bb cross section between

√s = 10.54 GeV and 11.20 GeV [Aubert

et al., 2009].The integrated luminosity for the full data taking period is shown

in Figure 1 and a summary of each of the separate runs is shown inTable 5. From the table can be noticed that a small quantity of eventshas been recorded out of the Υ(2S) and Υ(3S) peaks: the center-of-mass energy of these events is about 5 MeV below the Υ(3S) resonanceand a wide range of non-peaking energies below the Υ(2S). Thesespecific events were recorded while searching for the resonance peak.

Table 5: Recorded luminosity for each of the data taking periods.

Run On Peak ( fb−1) Off Peak ( fb−1)

1 (Υ(4S)) 20.6 2.62 (Υ(4S)) 60.6 6.93 (Υ(4S)) 32.1 2.54 (Υ(4S)) 100.7 10.25 (Υ(4S)) 133.8 14.66 (Υ(4S)) 76.5 7.37 (Υ(3S)) 28.5 2.77 (Υ(2S)) 14.4 1.5

Total 467.2 48.3

3.2 the detectorThe BABAR detector has been designed to satisfy the following needs:

• high and uniform acceptance even at small polar angles respectto the boost’s direction;

3.2 the detector 17

]-1

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Off Peak Luminosity: 53.85/fb

As of 2008/04/11 00:00

2000

2001

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Figure 1: The luminosity delivered by the PEP-II facility (blue) and the lumi-nosity recorded by the BABAR detector (red). The contributions to thetotal recorded luminosity from each resonance studied are shownwith different colors.

• excellent reconstruction efficiency for charged particles in the mo-mentum range of 60MeV/c < pT < 4GeV/c and for neutrals withenergy in the range 20MeV < E < 5GeV;

• very good vertex resolution, both in the beam’s transverse andparallel direction;

• efficient discrimination between e, µ, π, K and p over a widemomentum range;

• reconstruction of neutral hadrons.

BABAR have answered to all these needs through a structure of dedi-cated detectors that can be outlined with the help of Figure 2.

A detailed description of BABAR components can be found in [Aubertet al., 2002]. In the following there will be brief description of themajor subsystems as they are traversed by a particle produced at theinteraction point.

The innermost detector is the Silicon Vertex Tracker (SVT). It is oneof the two BABAR tracking devices and is designed to perform highresolution measurements of the decay vertices. The resolution for


Scale

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3-2001 8583A51

Figure 2: Longitudinal (top) and transverse (bottom) section of BABAR detector.

3.2 the detector 19

a fully reconstructed B vertex is about 80µm and 180µm for a par-tially reconstructed one. The SVT consists of five cylindrical layersof double-sided silicon micro strip detectors, with a total of approxi-mately 150,000 readout channels. It is the only one device that detectscharged particles with a transverse momentum less than 100 MeV/c.The inner radius is 32 mm, the outer radius is 144 mm and the totalstrip length is 26 cm.

Charged particles with a transverse momentum greater than 100 MeV/ccan reach the next layer of BABAR detector, the Drift Chamber (DCH).Together with the SVT, the DCH is part of the BABAR tracking device. Itis a 280 cm long cylinder, with inner radius of 24 cm and outer radiusof 81 cm. The gas filling is a mixture of Helium-Isobutane (80:20) thatis ionized when crossed by a charged particle. The electron-ion cou-ples produced by the ionizing particle induce an electric signal on the20µm diameter anode wires. The anode wires are surrounded by 6

field wires providing the electric field that causes the drift of the elec-trons. The wires are arranged in 40 layers of drift cells . These designprovides the chamber a resolution of about 1 mm, that is needed to re-construct the K0S vertices which decay out of the SVT. Being θ the polarangle respect to the beam axis in the laboratory frame, the acceptanceof the drift chamber is 17.2 < θ < 152.6, corresponding to about 90%of the total.

After leaving the DCH, a particle reaches the long synthetic quartzbars of the BABAR’s ring imaging Cherenkov (DIRC, Detector of Inter-nally Reflected Cherenkov light). The DIRC is designed to provideexcellent particle identification, in particular to separate kaons frompions. The DIRC is most efficient for track momenta up to 4 GeV/c.Charged particles moving faster than speed of light within a radiatorof refractive index n (v > c/n) emit a cone of Cherenkov light under awell defined angle θC so that

cos θC =1

nβ,

where β = v/c and v is the velocity of the particle. If the particle’smomentum is known, the mass of the particle can be inferred by us-ing the velocity from the Cherenkov angle. The DIRC consists of 144

straight fused silica bars (n = 1.473) with a rectangular section. Eachbar is 4.9 m long, 17 mm thick and 35 mm wide. The light emittedby the crossing particle is multiply reflected and travels inside the ra-diator bar until it reaches the rear end, where the Cherenkov imageis allowed to expand into a stand-off box of stainless steel filled with6,000 liters of purified water (nH2O = 1.346 provides good opticalcoupling). The rear end of the DIRC is closely packed with 10,572 pho-tomultipliers tube that detect the Cherenkov light rings, from whichpattern recognition algorithms deduce θC. Due to the presence of thephototubes, the rear end of the DIRC is out of the magnetic field, thatcould damage them. Furthermore, the rear end of the DIRC is placedin the backward region of the detector, where particle multiplicity isexpected to be less than the forward because of the boost, optimizingthe acceptance in the forward region. The geometrical acceptance ofthe DIRC is 80%.


The next detector component, that a traveling particle reaches, is theElectroMagnetic Calorimeter (EMC). It is designed to detect photonsand electrons within an energy range of 20MeV < Eγ < 9GeV. It is themain device for electron-pion separation, the reconstruction of neutralpions and the detection of neutrons and photons. The calorimeter ismade of 6,580 Thallium-doped Cesium iodide crystals. These crystalshave a trapezoidal shape, their typical transverse dimension is 5 ×5 cm2 at the front, flaring out to 6 × 6 cm2 at the back. They havea typical length of 30 cm, corresponding to about X0 = 17 radiationlengths. The calorimeter has a dedicated calibration system, whichuses a neutron generator to activate liquid fluorinert. The fluorinertis pumped through tubes in front of the crystals, emitting 6.1 MeVphotons from the 16N β− − γ cascade. Another monitor system, thelight pulser, is also featured: it distributes the light of a single Xenonlamp to each individual crystal and is able to quickly test the readoutchain. Each crystal is being read by two photodiodes glued to the rearface. The design and the characteristics of the photodiodes allow tokeep them in the magnetic field without being affected.

All of the above components are lying within a strong magnetic fieldof 1.5T , provided by a super-conducting solenoid. The flux return yokeis instrumented (Instrumented Flux Return - IFR) to identify muonsand to detect K0L . The yoke consists of 18 layers of iron plates withincreasing thickness, representing a total of 65 cm. The 17 gaps be-tween the layers house two kinds of detector systems, Resistive PlateChambers (RPC) and Limited Streamer Tubes (LST). The initial designof the IFR was entirely based on RPC layers. However some of themhad to be replaced between 2004 and 2006 by the LST layers because ofthe large inefficiency to muon reconstruction shown by the RPCs [Con-very et al., 2006]. Only the the IFR end-cap in the forward region ofthe detector is still filled by RPCs [Anulli et al., 2005].

The RPCs were installed in the gaps of the finely segmented steelof the IFR. They are made of two bakelite (phenolic polymer) sheets,2 mm-thick and separated by a gap of 2 mm. The gap is kept uni-form by polycarbonate spacers, that are glued to the bakelite and arespaced about 10 cm. The bulk resistivity of the bakelite sheets has beenespecially tuned to 1011 − 1012Ω cm. The external surfaces are coatedwith graphite to achieve a surface resistivity of about 100kΩ/square.These two graphite surfaces are connected to high voltage (≈ 8 kV)and ground, and protected by an insulating mylar film. This detectorsare operated in limited streamer mode and the signals are read outcapacitively, on both sides of the gap, by external electrodes made ofaluminum strips on a mylar substrate.

The LSTs replaced the RPCs in the barrel. They are made of cellsfilled up of a gas mixture (CO2 : Ar : C4H10 = 89 : 3 : 8) and contain-ing a high voltage anode wire (5.5 kV). Whenever a charged particlecrosses the detector, it ionizes the gas and the high voltage induces astreamer, read by the anode wire and by the silicon strips placed uponthe tube. The LSTs work in the region of limited streamer [Iarocci,1983], characterized by a short relaxing time for the detector and bystreamers limited in space around the point of first ionization.

3.3 particle identification 21

3.3 particle identificationIn High Energy Physics (HEP) experiments is crucial to correctly

identify the particles that are produced in the reaction.The informations from each one of the detectors that are part of

BABAR are combined to evaluate a probability for each track to satisfysome identification hypothesis. Once a charged track has been recon-structed from the hits recorded by SVT and DCH, the dE/dx recordedby the two detectors is combined with the angle of the light cone ob-served by the DIRC, with the energy recorded by the calorimeter andeventually the hits in the IFR.

The combination of all these informations is used by many parti-cle identification algorithms that are based on different statistical tech-niques such as Likelihood, Global Likelihood, Boosted Decision Treesand Neural Networks. For each of these algorithms there are somecriteria to identify the particle with tighter or looser conditions. Theanalyst is finally intended to choose the algorithm and the criteria thatbest suit its analysis purpose. In the following, the identification of pi-ons and kaons will be discussed in details, with a focus on the specificselection techniques applied to the dataset.

3.3.1 Pion and Kaon Selection

Both the pion and kaon candidates are retrieved from lists of parti-cles produced at the Event Processing stage. For each track, the selec-tor calculates likelihoods L for several particle hypotheses: pion, kaon,electron, proton and muon.

The information for each one of the tracking detectors are consid-ered in the calculation: the dE/dx and the number of hits in SVT andDCH; the Cherenkov angle and the number of photons measured bythe DIRC; the ratio (E/p) between the energy measured by the EMCand the momentum of the track (measured combining the informationof SVT and DCH).

Once the likelihood for each particle hypothesis has been calculated,the selector combines the results into ratios. The selector then appliessome previously optimized cuts to the ratios in order to accept or rejectthe particle hypothesis.

In Figure 3 the reconstruction efficiency in bin of momentum is com-pared between data and Monte Carlo for the specific pion selector usedin the D0 analysis. In the same figure, the reconstruction efficiency forkaons, i.e. the fake-rate, and the ratio between data and Monte Carloefficiency are also shown. In Figure 4 the same plots are shown for thekaon selector.

The analysis of the charged D+(s)

decays has been performed about

one year later respect to the one on D0 decays. In BABAR, the selectorsfor particle identification have had an improvement throughout all thelife of the collaboration. That is why different selectors have been usedfor the D+

(s)analysis. The performance plot for these more recent set

of selectors are shown in Figures 5 and 6 as the same as the others.The main difference among the selectors used for D0 and D+

(s)anal-

ysis is in the statistics technique used to test the hypotheses. While


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Figure 3: Reconstruction efficiency for pions (top) and kaons fake-rate (bot-tom) using likelihood pion selector. The reconstruction efficiencyfor the positively charged particles is shown on the left and for thenegatively charge in the middle. The ratio between data and MonteCarlo reconstruction efficiency is shown on the right for both posi-tively and negatively charged particles.

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Figure 4: Reconstruction efficiency for kaons (top) and pions fake-rate (bot-tom) using likelihood kaon selector. The reconstruction efficiencyfor the positively charged particles is shown on the left and for thenegatively charge in the middle. The ratio between data and MonteCarlo reconstruction efficiency is shown on the right for both posi-tively and negatively charged particles.

3.3 particle identification 23

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Figure 5: Reconstruction efficiency for pions (top) and kaons fake-rate (bot-tom) using a pion selector based on likelihood and neural networktechniques. The reconstruction efficiency for the positively chargedparticles is shown on the left and for the negatively charge in themiddle. The ratio between data and Monte Carlo reconstructionefficiency is shown on the right for both positively and negativelycharged particles.

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Figure 6: Reconstruction efficiency for kaons (top) and pions fake-rate (bot-tom) using boosted decision tree kaon selector. The reconstructionefficiency for the positively charged particles is shown on the leftand for the negatively charge in the middle. The ratio between dataand Monte Carlo reconstruction efficiency is shown on the right forboth positively and negatively charged particles.


the selectors used for D0 analyses simply used likelihood ratios to de-termine wheter a particle hypothesis could be accepted or not, thesenew selectors use more advanced techniques, such as Error CorrectingOutput Code and Boosted Decision Trees, to determine the validity ofthe hypothesis. For further information upon the different statisticaltechniques used by BABAR selectors, please check Appendix B.

These plots give evidence for the high efficiency and low fake-ratein BABAR particle identification. Furthermore, the comparison betweendata and Monte Carlo shows that the simulation has an excellent agree-ment to the data. This result is very important for these analyses, sinceall the reconstruction techniques and the models used to describe thedata sample have been tested and developed using the Monte Carlo.

4 D 0 → K+K−π+π− A N A LY S I S

contents4.1 The Data Set 254.2 Events Reconstruction 264.3 Contaminations in the D0 Data Sample 274.4 CT Distribution 284.5 Definition of the Fit Model 29

4.5.1 Signal Category 31

4.5.2 Combinatorial Background 35

4.5.3 D0 Peaking Background 35

4.5.4 ∆m Peaking Background 38

4.5.5 D+s Background Category 38

4.6 The Fit Model 404.6.1 Fit to the Data Sample 46

4.7 Systematics 484.7.1 Fitting Model 50

4.7.2 Particle Identification 50

4.7.3 p∗(D0) cut 51

4.7.4 Soft Pion Charge 51

4.7.5 Effect of Forward-Backward Asymmetry 51

4.7.6 Fit Bias 52

4.7.7 Detector Asymmetry 53

4.7.8 Systematics Summary 53

4.8 Final Result 53

The underlying idea is to measure the asymmetry parameter AT di-rectly from a fit to the data sample. In order to perform the fit to thetwo-dimensional distribution of the events in the [m(K+K−π+π−),∆m] ∆m is the difference

in mass between theD∗+ and theD0candidate

plane, the fit model has to be carefully defined. In the following, thedata set and the selection of the events are briefly outlined; then theprocedure to define this model is described in detail; finally the evalu-ation of the systematic error and the final result are reported.

4.1 the data setThe analysis is made using the full BABAR data set recorded at the

Υ(4S) and 40 MeV below the resonance. This corresponds to an in-tegrated luminosity of about 470 fb−1, of which 44 fb−1 are recordedoff-resonance.

Together with the BABAR recorded data set, a large number of MonteCarlo events has been analyzed using the same analysis chain as for thedata. These events are generated using the software Jetset7.4 [Sjos-trand, 1994] and their interactions with the detector have been simu-lated using the GEANT 4 [Agostinelli et al., 2003] program.

25

26 D0 → K+K−π+π− analysis

The Monte Carlo events that have been studied in this work aregenerated from the simulation of e+e− → cc interactions. There aretwo kind of Monte Carlo samples that have been studied:

• simulation of e+e− → cc continuum production; the hadroniza-tion and decay products are generated according to the cross-section from the Review of Particle Physics [Nakamura et al.,2010] (Generic Monte Carlo);

• events generated requiring that the decay chain that is signal forthis analysis is always present (Signal Monte Carlo).

The analysis makes use of about 1.1× 109 Generic Monte Carlo Eventsand 5.2× 106 Signal Monte Carlo Events.

4.2 events reconstructionTheD0→ K+ K− π+ π− candidates are reconstructed together withCharge-conjugation

is implied throughoutthe document

their D∗+ parent:D∗+ → D0π+

- K+K−π+π−

from all the inclusive e+e− → D∗+ X decays, where X indicates anysystem composed of charged and neutral particles. The reconstructionof the full D∗+ decay chain has two major advantages:

1. the D∗+ → D0 π+ decay has about 68% probability and is theunique D∗+ decay involving a D0; this allows to obtain a cleanD0 sample through a simple cut on the mass difference ∆m =m(D∗+) - m(D0);

2. the charge of the slow momentum pion decaying from the D∗+

uniquely tag the D flavor as a D0 (π+s ) or a D0 (π−s ).

The final state consists then of four charged particles with a high effi-ciency for identification into BABAR detector and a slow pion.

The procedure to build the D∗+ candidate is explained in the follow-ing. First a D0 candidate is built: all well identified K+, K−, π+ andπ− tracks combinations have been considered. If the invariant mass ofthe four particles is in the range

1.81GeV/c2 < m(K+K−π+π−) < 1.92GeV/c2

the four tracks are fitted to a common vertex requiring the χ2 fit prob-ability to be greater than 0.1%. The momentum of the D0 candidate inthe e+e− rest frame is required to be p∗(D0) > 2.5GeV/c.

To search for D∗+ → D0 π+s candidates, the reconstructed D0 can-didate is combined with all the remaining charged tracks in the eventhaving a momentum in the laboratory frame

plab(π+s ) < 0.65GeV/c.

A new fit is therefore performed with the constraint that the new vertexis located in the interaction region and requiring the χ2 fit probabilityto be greater than 0.1%.

4.3 contaminations in the D0 data sample 27

A couple of comments upon the selections made on the momenta ofD0 and π+s :

• Requiring the D0 momentum in the center-of-mass frame to begreater than 2.5 GeV/c removes anyD0 coming from B decays, to-gether with many combinatorial events, then reducing the back-ground.

• The π+s coming from the D∗+ decay should be very soft, requir-ing plab(π

+s ) < 0.65GeV/c reduces the background and saves

CPU time.

4.3 contaminations in the D0 data sam-ple

Even the more stringent cut cannot completely rule out some con-tamination to the data sample. These contamination are due to par-ticles that are not correctly identified or from decays with a topol-ogy similar to the ones of interest. While combinatoric backgroundis usually uniformly distributed over the phase space, not influenc-ing dramatically the quantity one measures, the contaminations could,in principle, fake a measurement, since they introduce events in thesignal data sample that could have different properties respect to thedecays that are argument of study. The analyst should then be alwaysaware of all the contaminations that could be into the data sample heis studying and, if they are not avoidable, he should find the best wayto deal with them.

At first, the D∗+ ambiguity has been studied: the selection on ∆mdoes not preserve from taking into account events for which two ormore slow pions form a D∗+ candidate within the signal window.Since the slow pion identification is strictly related to D∗ tagging,which allows to separate among D0 and D0 events, it is crucial toverify that there is no ambiguity. The number of slow pions in thesignal window has been studied using a sub-sample of the data (about13%). In this sample the events in the signal window are 15,850 and21 of them have two or more slow pion candidates. Among them, 12

have slow pions of opposite charge and 9 the same. All these eventshave been removed, with a relative loss of 1.3× 10−3 for the full datasample.

An important contamination comes from the decay D0 → K+ K− K0S(K0S → π+π−). Its presence is highlighted by the peak at 0.5 GeV/c2 inthe π+π− invariant mass, which is shown in Figure 7 together with afit and the distribution of the normalized residuals represented by

Pull =(Ndata −Nfit)√

Ndata, (4.1)

where Ndata is the number of data events and Nfit the number ofevents expected by the fit for each bin of the mass spectrum.

This contamination is from a Cabibbo favored decay channel (BR =[4.65± 0.30]× 10−3 [Nakamura et al., 2010]) and sits in the signal re-gion. The K0S peak can be represented by a Gaussian distribution with


)2 (GeV/cPDG

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Figure 7: The spectrum of the difference between π+π− invariant mass andK0S nominal mass. The fit to a model made of a Gaussian over a lineis represented by the blue line. The events removed to get rid ofthe contamination are shown in the blue filled area. On top the pulldistribution of the residuals is shown.

σ = 4.0 ± 0.2MeV/c2, and which accounts for 5.2% of the selecteddata sample. The fit shows that the π+π− mass distributions peak is4 MeV/c2 below the expected value for the K0S mass [Nakamura et al.,2010], this is due to the constrain on the two pions to vertex togetherwith the other D0 decay products. We veto K0S candidates within awindow of 2.5σ, removing all the events in the blue filled area of Fig-ure 7. This cut, while reducing to negligible level the background fromD0 → K+ K− K0S , removes 5.8% of the signal events.

The backgrounds from charm decay modes with misidentified pionshave been searched by assigning alternatively the pion mass to bothkaons. The resulting spectra show no peak both in the four particlesand three particles invariant mass. No peak in the four, three and two-body invariant masses which could be associated to charm decays hasbeen found.

A search for electrons which could be misidentified as kaons or pi-ons has been made alternatively assigning the electron mass to pairs oftracks with opposite charge. The resulting e+e− invariant mass showsno sign of γ conversions in the SVT, excluding any contamination fromradiative modes such as ργ, φγ or K∗(892)0γ.

4.4 CT distributionThe data set after all the selection shows a clear signal from D∗+ →

D0 π+, D0 → K+ K− π+ π−, as it shown in Figure 8. In this plot, thescatter plot of ∆m versus m(K+ K− π+ π−) is shown, together withthe m(K+ K− π+ π−) spectrum in the ∆m signal region and vice versa.The signal regions have been defined from two previous fit that have

4.5 definition of the fit model 29

1

10

210

)2) (GeV/cπ+π

K

+m(K

1.83 1.84 1.85 1.86 1.87 1.88 1.89 1.9

)2

m (

Ge

V/c

∆

0.14

0.142

0.144

0.146

0.148

0.15

0.152

0.154

(a)

)2) (GeV/cπ

+π

K

+m(K

1.83 1.84 1.85 1.86 1.87 1.88 1.89 1.9

)2

Ev

en

ts/(

0.4

Me

V/c

0

200

400

600

800

1000

1200

1400 (b)

)2m (GeV/c∆

0.14 0.145 0.15

)2

Ev

en

ts/(

75

Ke

V/c

0

500

1000

1500

2000

2500

3000

3500

4000

4500

(c)

Figure 8: The scatter plot of ∆m versus m(K+ K− π+ π−) (a); the m(K+ K−

π+ π−) spectrum in ∆m signal region (b); the ∆m spectrum in m(K+

K− π+ π−) signal region.

been made separately to the m(K+ K− π+ π−) and ∆m spectra usinga single gaussian over a second order polynomial model. The signalbox retrieved from the fits is:

144.94MeV/c2 < ∆m < 145.91MeV/c2,

1857.11MeV/c2 < m(K+K−π+π−) < 1871.47MeV/c2. (4.2)

Using the signal box defined in Equation 4.2, the CT and CT distri-butions have been plot in the D0 signal box, with the results shownin Figure 9. In the same plots, the distribution of the events when

TC

0.03 0.02 0.01 0 0.01 0.02 0.03

)4

10

×E

ve

nts

/(6

0

100

200

300

400

500

600

700T

C

<0)T

(CT

C (a)

TC

0.03 0.02 0.01 0 0.01 0.02 0.03

)4

10

×E

ve

nts

/(6

0

100

200

300

400

500

600

TC

<0)T

C (T

C (b)

Figure 9: CT (a) and CT (b) distributions in the D0 signal box of the datasample. The total distribution is shown in black, while the distri-bution of -CT (-CT ) is overdrawn in red to graphically compare thedistribution of the events when CT (CT ) > 0 and CT (CT ) < 0.

CT (CT ) > 0 and CT (CT ) < 0 is compared. This has been done draw-ing the -CT (-CT ) distribution over the CT (CT ) distribution when CT(CT ) is less then zero. From this plot, the asymmetry of the signalevents when CT (CT ) is greater or less than zero is clear. It is thenexpected that the AT and AT asymmetries are different from zero, in-dicating the effect of final state interaction.

4.5 definition of the fit modelThe fit model has been developed making use of the e+e− → cc

generic Monte Carlo events. These events have been reconstructed


1

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2)

GeV

/c

π+

πK

+m

(K

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1.89

1.9

2) GeV/cπ

+π

K

+m(K

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)2

Even

ts/(

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/c

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0.14 0.145 0.15

)2

Even

ts/(

75 k

eV

/c

0

2000

4000

6000

8000

10000

12000

14000

Figure 10: Distribution of Monte Carlo events. On the left the two-dimensional distribution of m(K+ K− π+ π−) and ∆m is shown,in the center there is the distribution of m(K+ K− π+ π−) and onthe right of ∆m.

and analyzed using the same chain as for the real data sample, addingfor every event the information on the original decay tree from thegenerator. This information allows the analyst to determine, after thereconstruction, if the event has been correctly reconstructed as a signalevent or not. Furthermore, knowing the generated event, the differentsources of background can be divided and studied separately.

The study of the reconstructed events using the generator-level infor-mation allowed to define five categories of events into the data sample:

1. True D0 signal originating from a D∗+ decay. This componenthas characteristic peaks in both observables m(K+ K− π+ π−)and ∆m.

2. Random π+s events where a true D0 is associated to an incorrectπ+s , called D0 peaking. This contribution has the same shape inm(K+ K− π+ π−) as signal events, but does not peak in ∆m.

3. Mis-reconstructed D0 decays where one or more of the D0 decayproducts are either not reconstructed or reconstructed with thewrong particle hypothesis, called ∆m peaking. Some of theseevents show a peak in ∆m, but not in m(K+ K− π+ π−).

4. Combinatorial background where the K+, K−, π+, π− candidatesare not fragments of the same D0 decay, called combinatoric.This contribution does not exhibit any peaking structure in m(K+

K− π+ π−) or ∆m.

5. D+s → K+ K− π+ π− π+ contamination (BR = [8.8± 1.6]× 10−3),

called D+s . This background has been studied on Monte Carlo

simulations and shows a characteristic linear narrow shape in thetwo-dimensional [m(K+ K− π+ π−),∆m ] distribution.

Each one of these categories has been separately studied to deter-mine the model to include into the more general one. The total numberof Monte Carlo events that have been reconstructed from the generice+e− → cc Monte Carlo sample described in Section 4.1 is about2.11× 105. Their two-dimensional distribution into the plane of m(K+

K− π+ π−) versus ∆m and the projections upon these two variables areshown in Figure 10. The number of events for each category identifiedby the previous description is shown in Table 6.


Table 6: Number of events for each category from Monte Carlo. The contribu-tion to the total of the sample is also shown.

Category Events Fraction (%)

Signal 103,561 48.97

D0 peaking 5,706 2.70

∆m peaking 73,138 34.59

Combinatorial 27,306 12.91

D+s 1,753 0.83

Total 211,464 100.00

The plots of the two-dimensional distribution of m(K+ K− π+ π−)and ∆m and their projections are shown for each category of events inFigure 11.

In the following, the Probability Density Functions (PDF) defined foreach category of events will be described in detail. At first, signal andcombinatorial will be studied, then the other categories. This choicehas been made because the latter categories show some features thatare present in the former ones. All the fits that are shown in this thesisare mad using the code MINUIT [James e Roos, 1975] in a RooFit [Verk-erke e Kirkby, 2003] framework.

4.5.1 Signal Category

The Signal category of events shows a distinct peak both in them(K+ K− π+ π−) and ∆m distribution. However these peaks cannotbe simply described by a sum of independent gaussians. While thiscan be considered a good approximation for the m(K+ K− π+ π−)distribution, the ∆m distribution shows a long tail on the higher massside of the spectrum. Furthermore, a correlation is found between theroot mean square (RMS) of ∆m and m(K+ K− π+ π−), as it is shownin Figure 12. Here the mean and the RMS of the distribution of ∆mis shown in slices of m(K+ K− π+ π−), demonstrating that the morelikely the event to be signal, the shorter the variance of ∆m distribu-tion. All the features of the ∆m distribution have been considered inthe fit model.

The probability density functions used in this parametrization are:

• gaussians

g(x; x,σ) = exp(−(x− x)2

2σ2

); (4.3)

• a two-dimensional gaussian including a correlation factor c

s(x,y; x,σx, y,σy, c) =

exp

[−

1

2(1− c2)

((x− x)2

σ2x

(y− y)2

σ2y− 2c

(x− x)

σx

(y− y)

σy

)];

(4.4)


1

10

210

2m GeV/c∆

0.14 0.145 0.15

2)

GeV

/c

π+

πK

+m

(K

1.83

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1.89

1.9Signal

2) GeV/cπ

+π

K

+m(K

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)2

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π+

πK

+m

(K

1.83

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1.86

1.87

1.88

1.89

1.9

peaking0D

2) GeV/cπ

+π

K

+m(K

1.83 1.84 1.85 1.86 1.87 1.88 1.89 1.9

)2

Even

ts/(

1.0

MeV

/c

0

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450

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)2

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πK

+m

(K

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1.9m peaking∆

2) GeV/cπ

+π

K

+m(K

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)2

Even

ts/(

0.5

MeV

/c

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94 k

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(K

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1.84

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1.89

1.9Combinatorial

2) GeV/cπ

+π

K

+m(K

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)2

Even

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0.8

MeV

/c

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)2

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150 k

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+m

(K

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1.9

sD

2) GeV/cπ

+π

K

+m(K

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)2

Even

ts/(

2.0

MeV

/c

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0.14 0.145 0.15

)2

Even

ts/(

375 k

eV

/c

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20

30

40

50

60

70

80

90

Figure 11: The m(K+ K− π+ π−) versus ∆m (left), m(K+ K− π+ π−) (center)and ∆m (right) distributions for each category are shown for eachrecognized category of events, from Signal (Category 1- top) to D+

s

(Category 5 - bottom). Generic Monte Carlo events.


2) GeV/cπ+π

K

+m(K

1.83 1.84 1.85 1.86 1.87 1.88 1.89 1.9

2 M

eV

/c m

∆

145.25

145.3

145.35

145.4

145.45

145.5

145.55

145.6

2) GeV/cπ+π

K

+m(K

1.83 1.84 1.85 1.86 1.87 1.88 1.89 1.9

2 m

) M

eV

/c∆

RM

S(

0.4

0.45

0.5

0.55

0.6

0.65

0.7

0.75

Figure 12: Mean value (left) and RMS (right) of ∆m in slices of m(K+ K− π+

π−).

• a Johnson SU function [Johnson, 1949]

JSU(x; x,σ,γ, δ) =δe−

12 [γ+δ sinh−1( x−xσ )]

2

σ√2π

√1+

(x−xσ

)2 , (4.5)

where sinh−1(z) = ln(z+√z2 + 1

).

With the help of Figure 13 the combination of these functions into asingle PDF can be understood.

The sum of the two distributions made by the product of two inde-pendent gaussians is shown in white. This is the main component ofthe two-dimensional peak:

P3 = g(m;m3,σm3)× g(∆m;∆m3,σ∆m3), (4.6)P4 = g(m;m4,σm4)× g(∆m;∆m4,σ∆m4). (4.7)

The green filled area represent the projection of the distribution whichtakes care of the long tail in ∆m for higher masses. This distribution ismade of the product of a gaussian in m(K+ K− π+ π−) and a JohnsonSU in ∆m:

PJSU = g(m;mJSU,σJSU)× JSU(∆m;∆mJSU,σJSU,γ, δ). (4.8)

Finally the red filled area is the projection of the two-dimensional gaus-sian incorporating a correlation term:

Pwide = s(m,∆m;mCG,σCG,∆mCG,σ∆mCG , cCG). (4.9)

The sum of all these contributions forms the distribution used to parametrizethe signal events:

Fsig = fwidePwide + (1− fwide)

fJSUPJSU + (1− fJSU)[fcoreP3 + (1− fcore)P4] (4.10)

The results of the fit to the distribution of events correctly reconstructedas signal is shown in Figure 13.


)2) (GeV/cπ

+π

K

+m(K

1.83 1.84 1.85 1.86 1.87 1.88 1.89 1.9

)2

Even

ts/(

0.8

0 M

eV

/c

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)2) (GeV/cπ

+π

K

+m(K

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)2

Even

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0 M

eV

/c

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310

)2

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/c

1

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310

1.83 1.84 1.85 1.86 1.87 1.88 1.89 1.9

Pu

ll

3

0

+3

1.83 1.84 1.85 1.86 1.87 1.88 1.89 1.9

Pu

ll

)2m (GeV/c∆

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)2

Even

ts/(

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5 M

eV

/c

2000

4000

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)2m (GeV/c∆

0.14 0.142 0.144 0.146 0.148 0.15 0.152 0.154

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/c

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410

0.14 0.142 0.144 0.146 0.148 0.15 0.152 0.154

Pu

ll

3

0

+3

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Pu

ll

22

5

4

3

2

1

0

1

2

3

4

5

)2m (GeV/c∆

0.14 0.145 0.15

)2

) (G

eV

/c

π+

πK

+m

(K

1.83

1.84

1.85

1.86

1.87

1.88

1.89

1.9

Pull5 4 3 2 1 0 1 2 3 4 5

Ev

en

ts/0

.05

0

50

100

150

200

250

300

350

400

450

Figure 13: Fit to the distribution of correctly reconstructed signal events fromMonte Carlo. On top the projections on m(K+ K− π+ π−) and∆m of the fit model (blue line) and its components (color filledareas) are shown using a logarithmic scale on the y-axis. In themiddle the same plots are shown in linear scale. Over these plotsthe distribution of the residuals (Pull - see Eq. 4.1) is shown. Onthe bottom there are the distributions of the residuals in the two-dimensional [m(K+ K− π+ π−),∆m ] plane (left) and integrated(right).


4.5.2 Combinatorial Background

The distribution of the combinatorial background is flat in the m(K+

K− π+ π−) variable and shows a distinctive threshold distribution in∆m. Since it is combinatorial, no correlation is expected among m(K+

K− π+ π−) and ∆m. The general PDF should be then built assumingthe two variables to be independent. A flat distribution can be used todescribe the m(K+ K− π+ π−) spectrum

l(x;b) = 1+ b(x− 1.865GeV/c2). (4.11)

The description of the ∆m spectrum is made by means of a thresholdfunction with a kinematic endpoint (x0 = mπ+ = 139.57MeV/c2):

a(x; c) =

√(x

x0

)2− 1 · exp

(−c

[(x

x0

)2− 1

]). (4.12)

The PDF defined to describe the combinatorial background is:

Fcomb(m,∆m;b, c) = l(m;b)× a(∆m; c). (4.13)

The results of the fit of this PDF to the combinatorial backgroundevents found in the Monte Carlo are shown in Figure 14.

4.5.3 D0 Peaking Background

The events for which the D0 has been correctly reconstructed, butthe slow pion is randomly assigned, show a peak into the m(K+ K−

π+ π−) distribution and a threshold distribution identical to the one ofcombinatorial background for ∆m. Given the absence of correlationsbetween the D0 and the random pion, the two-dimensional PDF canbe built as the product of two uncorrelated distributions.

The distribution used to describe the m(K+ K− π+ π−) mass spec-trum is taken from the integral on ∆m of the two-dimensional PDFthat describes the signal (see Eq. 4.10). The distribution to describe∆m spectrum is taken from the combinatorial PDF and is the same asEq. 4.12. The two-dimensional PDF for the description of D0 peakingcategory is then:

FD0−peak(m,∆m) =

(fwide ·PD0

wide + (1− fwide) · fJSU ·PD0

JSU+

(1− fJSU) · [fcore ·PD0

3 + (1− fcore) ·PD0

4 ])× a(∆m; c), (4.14)

where

PD0

wide = g(m;mCG,σmCG) (4.15)

PD0

JSU = g(m;mJSU,σmJSU) (4.16)

PD0

3 = g(m;m3,σm3) (4.17)

PD0

4 = g(m;m4,σm4). (4.18)

The results of the fit to the D0 peaking category of Monte Carloevents are shown in Figure 15.


)2

) (GeV/cπ

+π

K

+m(K

1.83 1.84 1.85 1.86 1.87 1.88 1.89 1.9

)2

Even

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) (GeV/cπ

+π

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/c

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ll

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+3

Pu

ll

)2

m (GeV/c∆

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)2

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5 M

eV

/c

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)2

m (GeV/c∆

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)2

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/c

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ll

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+3

Pu

ll

22

5

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)2m (GeV/c∆

0.14 0.145 0.15

)2

) (G

eV

/c

π+

πK

+m

(K

1.83

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1.9

Pull5 4 3 2 1 0 1 2 3 4 5

Ev

en

ts/0

.05

0

50

100

150

200

250

300

350

400

Figure 14: Fit to the distribution of combinatorial background events in theMonte Carlo. On top the projections on m(K+ K− π+ π−) and ∆mof the fit model (blue line) are shown. Over each plot the distribu-tion of the residuals (Pull - see Eq. 4.1) is shown. On the bottomthere are the distributions of the residuals in the two-dimensional[m(K+ K− π+ π−),∆m ] plane (left) and integrated (right).


)2) (GeV/cπ

+π

K

+m(K

1.83 1.84 1.85 1.86 1.87 1.88 1.89 1.9

)2

Even

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0 M

eV

/c

50

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)2) (GeV/cπ

+π

K

+m(K

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)2

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Pu

ll

)2

m (GeV/c∆

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) (G

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πK

+m

(K

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Pull5 4 3 2 1 0 1 2 3 4 5

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140

160

180

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Figure 15: Fit to the distribution of D0 peaking events from Monte Carlo. Ontop the projections on m(K+ K− π+ π−) and ∆m of the fit model(blue line) and its components (color filled areas) are shown usinga logarithmic scale on the y-axis (m(K+ K− π+ π−) only). In themiddle the same plots are shown in linear scale. Over these plotsthe distribution of the residuals (Pull - see Eq. 4.1) is shown. Onthe bottom there are the distributions of the residuals in the two-dimensional [m(K+ K− π+ π−),∆m ] plane (left) and integrated(right).


4.5.4 ∆m Peaking Background

The ∆m peaking background is due to the reconstruction of eventswhere one or more daughters of the D0 meson are not correctly re-constructed. On the other side, the slow pion π+s is correctly recon-structed, producing a broad bump into the ∆m distribution. The smallpeak that corresponds to a π+s coming from a D∗+ decay, is due to thereconstruction of D0 → K− π+ π+ π−, where one of the π+ has beenidentified as a kaon: this way the wrong D0 mass peak is shifted upinto the spectrum, out of the [1.82,1.91] GeV/c2 mass range shown inthe plot, while ∆m peaks in the right place.

Since the distributions of m(K+ K− π+ π−) and ∆m spectra are notcorrelated in this category of events, the two-dimensional PDF is madeof the product of two separate distributions describing m(K+ K− π+

π−) and ∆m spectra. The distribution that describes the m(K+ K−

π+ π−) spectrum is taken from the combinatorial background and isdefined by Eq. 4.11. The description of the ∆m spectrum is made bymeans of a PDF that is composed by two threshold functions and theprojection of the signal PDF on ∆m to describe the small peak that ison top of the bump:

dmpeak(x; x;σx,η, c) = f∆mNar · fJSU ·P∆mJSU + (1− fJSU)·

[fcore ·P∆m3 + (1− fcore) ·P∆m4 ]+ (1− f∆mNar)·[f∆m2 · g(x; x;σx) · a(x;η) + (1− f∆m2) · a(x; c∆m)

], (4.19)

where

P∆mJSU = JSU(∆m;∆mJSU,σ∆mJSU ,γ, δ) (4.20)

P∆m3 = g(∆m;∆m3,σ∆m3) (4.21)

P∆m4 = g(∆m;∆m4,σ∆m4). (4.22)

It can be noticed that the component P∆mwide (see Equation 4.9) has notbeen included in the peak because it consists on a very small amountof events and the three components P∆mJSU, P∆m3 and P∆m4 are enoughto describe this small peak.

The two-dimensional PDF is

F∆m−peak(m,∆m;∆m2,σ∆m2 ,η, c∆m,b) =

(1+ b(m− 1.865GeV/c2))× dmpeak(∆m;∆m2,σ∆m2 ,η, c∆m).(4.23)

The results of the fit to the ∆m peaking category from Monte Carlo areshown in Figure 16.

4.5.5 D+s Background Category

The study of the correctly reconstructed Monte Carlo sample showedthe presence of D+

s → K+ K− π+ π− π+ decays among the recon-structed events. Even if this category of events could not easily beidentified in the data sample, a component of the fit model has been


)2

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Figure 16: Fit to the distribution of ∆m peaking events from Monte Carlo. Ontop the projections on m(K+ K− π+ π−) and ∆m of the fit model(blue line) and its components (color filled areas) are shown usinga logarithmic scale on the y-axis (∆m only). In the middle the sameplots are shown in linear scale. Over these plots the distribution ofthe residuals (Pull - see Eq. 4.1) is shown. On the bottom there arethe distributions of the residuals in the two-dimensional [m(K+ K−

π+ π−),∆m ] plane (left) and integrated (right).


included to describe it. The definition of the PDF for this category ofevents is based on the fact that

m(D+s ) = m(K+K−π+π−π+s ) = m(K+K−π+π−) +∆m

and that the masses of the D+s events should be distributed over a

Gaussian shape. On the other side, the ∆m distribution should be asthe same as combinatorial. One then have

FD+s(m,∆m; mD+

s,σD+

s,h) =

h+ exp

(−(m+∆m− mD+

s)2

2σ2D+s

)× a(∆m, c), (4.24)

where the offset h is included to describe a small amount of continuumevents found in this category. This offset has not been included in thefull fit model because these events are absorbed by the combinatorialshapes.

The results of the fit to the ∆m peaking category from Monte Carloare shown in Figure 17.

4.6 the fit modelThe parametrizations of each category of events have been combined

to build the model for the events that have been reconstructed. Themodel is a sum of all the previously defined PDF:

F = Nsig ·Fsig +Ncomb ·Fcomb +ND+s·FD+

s

+ND0−peak ·FD0−peak +N∆m−peak ·F∆m−peak. (4.25)

Each PDF is normalized and the fit is done on the binned data set usingan extended likelihood to get the number of events for each category.In the model many of the parameters are shared among PDFs refer-ring to different categories of events. The relationship among differentPDFs is shown in detail by means of the pictorial view of Figure 18.

In Figure 19, the excellent agreement to the Monte Carlo sample isshown. Different color are used to highlight each category of eventsand the projections of the fit are shown both in linear and logarithmicscale to show in detail the features of each category. The results of thefit are shown in Table 7.

Given the large number of floating parameters, there might be largecorrelations between them. When many correlations are present, theerror of some of the fit parameters could not be correctly evaluated. Toovertake this problem and measure the asymmetry parameter obtain-ing the correct error, the model is first fitted to the sample leaving allthe parameters floating: this fit is used to fix the parameters directlyrelated to the shapes of the distributions. The other parameters, suchas the asymmetries and the number of events for each category are leftfloating into another fit, that returns them with the correct errors.

The asymmetry parameters are directly included in the fit thanksto the specific way the model is designed. Following the relationship

4.6 the fit model 41

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Figure 17: Fit to the distribution of D+s events from Monte Carlo. On top the

projections on m(K+ K− π+ π−) and ∆m of the fit model (blueline) are shown using a logarithmic scale on the y-axis (m(K+ K−

π+ π−) only). In the middle the same plots are shown in linearscale. Over these plots the distribution of the residuals (Pull - seeEq. 4.1) is shown. On the bottom there are the distributions of theresiduals in the two-dimensional [m(K+ K− π+ π−),∆m ] plane(left) and integrated (right).


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Figure 18: This graphics shows the structure of the fitting model: the bluecircles represent the variables, while the red ones the PDFs. Thearrows show to which variables the PDFs are related to. It can beseen that some variables are shared between two different PDF.


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Figure 19: Fit to the distribution of the events from the Monte Carlo sample.On top the projections on m(K+ K− π+ π−) and ∆m of the fit model(blue line) and its components (color filled areas) are shown usinga logarithmic scale on the y-axis. The colors refer to the differentcategories of events: white - signal; yellow - combinatorial; red -D0

peaking; blue - ∆m peaking; green - D+s . In the middle the same

plots are shown in linear scale. Under each plot the distribution ofthe residuals (Pull - see Eq. 4.1) is shown. On the bottom there arethe distributions of the residuals in the two-dimensional [m(K+ K−

π+ π−),∆m ] plane (left) and integrated (right).


Table 7: Results of the fit to the full Monte Carlo sample. The values of themasses and the widths are expressed in terms of MeV/c2.

Variable Fit Result Variable Fit Result

AT sig (0.40± 0.47)% AT sig (−0.06± 0.46)%AT bkg (−5.26± 1.55)% AT bkg (3.68± 1.73)%AT bkg2 (19.0± 10.0)% AT bkg2 (−23.5± 8.6)%AT bkg3 (0.59± 0.67)% AT bkg3 (−0.66± 0.65)%AT bkg5 (2.85± 7.59)% AT bkg5 (0.73± 8.49)%

N(D0) 51972± 241 N(D0) 52469± 243N(D0) cat2 1682± 165 N(D0) cat2 1959± 164N(D0) cat3 36129± 243 N(D0) cat3 37643± 244N(D0) cat4 14575± 225 N(D0) cat4 12996± 224N(D0) cat5 1080± 82 N(D0) cat5 957± 81mD+

s1910.0± 3.1 σm

D+s

19.3± 0.5b1 3.71± 0.14 c (0.02± 9.23)%∆m2 145.78± 0.05 σ∆m2 4.83± 0.08η 9.95± 0.15 c∆m (0.001± 10.500)%f∆mNar (0.9± 0.3)% f∆m2 (17.0± 0.5)%γ −1.03± 0.03 δ 0.91± 0.04cCG 0.013± 0.013mCG 1863.4± 0.1 σmCG 11.80± 0.13m3 1864.6± 0.1 σm3 4.18± 0.02m4 1864.5± 0.1 σm4 3.86± 0.07mJSU 1864.3± 0.1 σmJSU 4.25± 0.13∆m3 145.45± 0.01 σ∆m3 0.185± 0.001∆m4 145.52± 0.01 σ∆m4 0.581± 0.009∆mCG 145.45± 0.01 σ∆mCG 0.345± 0.004∆mJSU 144.00± 0.01 σ∆mJSU 2.08± 0.09fcore (83.7± 0.3)% fJSU (8.8± 0.2)%fwide (19.2± 0.3)%


between the number of signal events and the asymmetry parameters,one gets:

N(D0,CT > 0) =N(D0)

2(1+AT ) ,

N(D0,CT < 0) =N(D0)

2(1−AT ) ,

N(D0, CT > 0) =N(D0)

2

(1− AT

),

N(D0, CT < 0) =N(D0)

2

(1+ AT

). (4.26)

There is then a mutual correspondence between the following two setsof variables:

N(D0,CT > 0),N(D0,CT < 0),N(D0, CT > 0),N(D0, CT < 0)

lN(D0),N(D0),AT , AT

The latter have been used in the fit to evaluate the above yields.

In order to evaluate directly the asymmetry parameters, the datasample has been split into four sub-samples, depending on D flavorand CT (or CT ) value. These sub-samples have been fitted simultane-ously to the model to get the asymmetry parameters AT and AT andthe number of D0 and D0 decays.

The validation of the fit model has been made using the Monte Carlosample. At first the yields retrieved from the fit for each category ofevents are compared to their true number in Table 8: The only category

Table 8: Reconstructed and fitted number of events for each of the categoriesidentified in the Monte Carlo sample. The last column shows thenumber of σ’s between the true and the fitted number of events: ε =n−nrecσnrec

.

Category MC Events Fit Results ε

Signal 103561 104441± 342 +2.57D0 peaking 5705 3641± 233 −8.86∆m peaking 73138 73772± 344 +1.84Combinatorial 27306 27571± 317 +0.84D+s 1753 2037± 115 +2.47

Signal 211464 211462± 635 −0.003

that shows a fair agreement to the fit result is the D0 peaking one.Since the number of missing events is much less than the number ofevents in the signal category (about 1%), this effect has been neglected.

In Table 9, the signal yields for each sub-sample are compared tothe fit results: every yield has been a little over-estimated by the fit.Anyway, since the trend of the over-estimation is the same for each oneof the yields, the final results of the asymmetry parameters should notbe affected.


Table 9: Reconstructed and fitted number of signal events for each sub-sample.The last column shows the number of σ’s between the true and thefitted number of events: ε = n−nrec

σnrec.

Sub-Sample MC Events Fit Results ε

Γ(D0,CT > 0) 25789 26091± 171 +1.77Γ(D0,CT > 0) 25736 25881± 170 +0.85Γ(D0, CT > 0) 26041 26250± 172 +1.21Γ(D0, CT > 0) 25995 26219± 171 +1.31

Finally, the asymmetry parameters retrieved from the fit have beencompared to their true values reconstructed from Monte Carlo in Ta-ble 10. All the parameters retrieved from the fit are consistent with

Table 10: Reconstructed and fitted asymmetry parameters. The last columnshows the number of σ’s between the true and the fitted parameter:ε = A−Arec

σArec.

Parameter Reconstructed (×10−3) Fit Results (×10−3) ε

AT 1.03 4.04± 4.64 +0.65AT -0.88 −0.59± 4.62 +0.06

AT 0.95 2.33± 3.34 +0.41

the value reconstructed from the Monte Carlo sample. However, thefit bias that has been found

AfitT −ArecoT = 1.38× 10−3, (4.27)

has been taken into account in the evaluation of the systematic error,that will be discussed in the following.

4.6.1 Fit to the Data Sample

The previously defined and validated model has been used to de-scribe the data sample. The only difference here is that the real valueof the asymmetry parameters is kept hidden until the very final stageof the analysis. This general practice, also known as “Blind Analysis”,allows to optimize the cuts and evaluate the systematics before obtain-ing the final results, removing the bias that could be unconsciously (orconsciously) introduced modifying the cuts to enhance or suppress thesearched effect.

The asymmetry parameters have been masked in this analysis addingan unknown random offset. The result is that the T violating parame-ter AT is shifted of an unknown value. Even if the offset is unknown,it is kept under control assuming the same seed every time it is gen-erated. In this way, the difference between the fit results is the sameboth in the case that the offset is on or off.

The results of the fit to the data are shown in Figure 20. The yieldsretrieved from the fit for each category of events are shown in Table 11,while the results for the full set of floating variables are shown inTable 12.


)2

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Figure 20: Fit to the distribution of the events from data sample. On top theprojections on m(K+ K− π+ π−) and ∆m of the fit model (blue line)and its components (color filled areas) are shown using a logarith-mic scale on the y-axis. The colors refer to the different categoriesof events: white - signal; yellow - combinatorial; red - D0 peak-ing; blue - ∆m peaking; green - D+

s . In the middle the same plotsare shown in linear scale. Under each plot the distribution of theresiduals (Pull - see Eq. 4.1) is shown. On the bottom there are thedistributions of the residuals in the two-dimensional [m(K+ K− π+

π−),∆m ] plane (left) and integrated (right).


Table 11: Number of events for each category of events retrieved from the fitto the data sample.

Category Fit Results

Signal 46691± 241D0 peaking 5178± 331∆m peaking 57099± 797Combinatorial 40512± 818D+s 2023± 156

Total 151503± 1223

4.7 systematicsBefore unblinding the final result, all the systematics have been eval-

uated. The sources of systematics recognized in this analysis are:

• the fitting model;

• the particle identification;

• the p∗(D0) cut;

• the identification of the soft pion;

• the effect of forward-backward asymmetry;

• mistag;

• fit bias;

• detector asymmetry.

The procedure to evaluate the contribution to the systematic error as-sociated to each one of these sources can be outlined in a few steps:

1. the specific cut related to the source of systematics is slightlymodified;

2. the asymmetry parameter is evaluated again through a new fitto the data;

3. the deviation from the value measured using standard cuts istaken;

4. the largest among all the measured deviations is assumed as thespecific contribution to the systematic error.

The way the contributions from each source of systematics are eval-uated will be described briefly in the following. At the end the valueof all the contributions will be listed and the systematic error is evalu-ated.

4.7 systematics 49

Table 12: Results of the fit to the data sample. The values of the masses andthe widths are expressed in terms of MeV/c2.

Variable Fit Result Variable Fit Result

AT sig (7.33± 0.73)% AT sig (8.37± 0.73)%AT bkg (0.39± 2.80)% AT bkg (2.07± 2.93)%AT bkg2 (20.55± 10.30)% AT bkg2 (−0.75± 8.39)%AT bkg3 (−2.03± 1.99)% AT bkg3 (−2.59± 1.97)%AT bkg5 (−1.99± 10.50)% AT bkg5 (7.85± 11.59)%

N(D0) sig 23561± 171 N(D0) sig 23129± 170N(D0) cat4 20857± 583 N(D0) cat4 19655± 576N(D0) cat2 2382± 235 N(D0) cat2 2797± 234N(D0) cat3 28497± 567 N(D0) cat3 28603± 562N(D0) cat5 1060± 112 N(D0) cat5 963± 110mD+

s1910.0± 45.3 σm

D+s

25.0± 2.0b1 5.71± 0.52 c (0.001± 7.397)%∆m2 146.08± 0.47 σ∆m2 6.50± 0.48η 8.29± 0.86 c∆m (0.001± 19.972)%f∆mNar (2.0± 0.6)% f∆m2 (74.3± 5.1)%γ −1.33± 0.28 δ 2.54± 0.18cCG 0.04± 0.03mCG 1862.1± 0.3 σmCG 13.0± 0.7m3 1864.2± 0.1 σm3 4.36± 0.08m4 1864.6± 0.1 σm4 2.67± 0.10mJSU 1864.2± 0.1 σmJSU 4.25± 0.20∆m3 145.42± 0.02 σ∆m3 0.195± 0.003∆m4 145.45± 0.01 σ∆m4 0.37± 0.03∆mCG 145.45± 0.01 σ∆mCG 0.44± 0.03∆mJSU 144.16± 0.22 σ∆mJSU 2.62± 0.37fcore (74.4± 2.6)% fJSU (17.4± 1.5)%fwide (19.5± 0.8)%


4.7.1 Fitting Model

The fitting model can introduce a systematic error due to the shapesused to describe each category of events. Another source of systematicerror related to the fit is the binning used.

The systematic error due to the signal PDF shape has been estimatedchanging the PJSU component, substituting the JSU (see Eq. 4.8) witha Crystal Ball shape[Gaiser, 1982]

PCB(x;α,n, x,σ) =exp

(−

(x−x)2

2σ2

)for x−xσ > −α(

n|α|

)nexp

(−

|α|2

2

)(n|α|

− |α|− x−xσ

)−nfor x−xσ 6 −α

(4.28)

obtaining the distribution

PJSUsys = g(m;mJSU,σJSU)×PCB(∆m;αCB,nCB,∆mCB,σCB∆m)

Another source of systematics has been identified in the descriptionof the category 3 background (∆m peaking): an alternative way to de-scribe it, is to use a Johnson SU with threshold instead of the gaussianwith threshold

JthSU(∆m;∆mth,∆mJSU,σ∆mJSU ,γ, δ,η) =

JSU(∆m;∆mJSU,σ∆mJSU ,γ, δ) · a(∆m;η). (4.29)

The binning used to measure the reference value has been set to4× 100× 100 = 40000 bins, where 4 is due to the simultaneous fit onthe 4 data set built from D0 flavour and CT . The choice of the numberof bins has been driven from the requirement of a good resolution.Two other sets of binning have been used to estimate the systematicerror introduced by this choice: 4× 80× 80 = 25600 bins and 4× 120×120 = 57600 bins.

4.7.2 Particle Identification

The pions and the kaons are identified by means of algorithms thatcombine the informations from the detectors in BABAR into selectors us-ing the technique of the likelihood. Two criteria are considered to re-construct the D0 events using these selectors: the looser one is the oneused in the standard reconstruction of events, the tighter one is usedfor systematics. The violation parameter is measured again using thetighter criteria to identify kaons or pions alternatively and the largerdeviation among the different selections of the data sample has beentaken as the systematic’s error due to particle identification. The selec-tion using tighter criteria reduces significantly the number of events tobe considered in the data set, as shown in Table 13. The deviations ofthe measurement of AT from the standard criteria are then influencedby statistics effects. The results on the contribution to systematics errorare not invalidated, but have to be considered a conservative estimate.

4.7 systematics 51

Table 13: Number of events in the data set after the application of the selectorsusing tighter criteria.

Selection Events

KlKlπlπl 151,505

KlKlπtπt 142,449

KtKtπlπl 125,096

KtKtπtπt 117,854

4.7.3 p∗(D0) cut

The selection applied on the D0 momentum in the center-of-massframe has been tightened to higher values of momentum to study thevariation of the asymmetry parameter. Two selections have been con-sidered:

• p∗(D0) > 2.6GeV/c;

• p∗(D0) > 2.7GeV/c.

The number of the events in the data set is reduced by this cut asshown in Table 14, the deviations of AT are then influenced by statisticseffect here too. As well as for particle identification, the contribution

Table 14: Number of events in the data set after the application of tighter se-lections on the momentum of D0 candidate in the center-of-massframe.

Selection Events

p∗(D0) > 2.5GeV/c 151,505

p∗(D0) > 2.6GeV/c 131,569

p∗(D0) > 2.7GeV/c 119,903

to systematics error is considered a conservative estimate.

4.7.4 Soft Pion Charge

The right identification of the charge of the slow momentum pionπ+s is crucial to determine the flavor of the D0 candidate. A systematicerror can be introduced if the charge of the reconstructed π+s is differ-ent from the charge of the D∗ candidate. In order to evaluate the effect,if any, on this analysis, the correctly reconstructed Monte Carlo sam-ple has been used to check how many times the π+s is reconstructedwith the wrong charge. Table 15 shows the results of this study foreach Run of data taking. The net amount of π+s mis-identification is 4,corresponding to 2× 10−5 the total.

4.7.5 Effect of Forward-Backward Asymmetry

The effect of forward-backward asymmetry (see Appendix A) onthis analysis has been studied evaluating the T asymmetry parameter


Table 15: Study of slow momentum pion mis-identification using correctly re-constructed Monte Carlo.

Run Wrong D∗+ Wrong D∗− Missed Total % Total

1 4 2 0 14,995 4× 10−42 7 7 1 39,309 4× 10−43 1 4 1 19,280 3× 10−44 25 26 1 53,517 10× 10−45 21 24 5 63,707 8× 10−46 6 5 3 20,656 7× 10−4

Sum 64 68 11 211,464 7× 10−4

AT in regions of cos θ∗, the cosine of the production angle of D0 in thecenter-of-mass frame. The three considered regions are:

• −1.0 6 cos θ∗ < −0.3;

• −0.3 6 cos θ∗ < +0.3;

• +0.3 6 cos θ∗ 6 +1.0.

The results of this study are shown in Table 16 and in Figure 21.

Table 16: Number of signal events, deviation from AT using standard cuts anderror on the T violation parameter measured for each sub-sample ofcos θ∗

cos θ∗ Region Signal Events ∆× 10−3 σ× 10−3

−1.0 6 cos θ∗ < −0.3 20202± 158 +6.21 7.79

−0.3 6 cos θ∗ < +0.3 16707± 144 -0.74 8.58

+0.3 6 cos θ∗ 6 +1.0 10548± 120 -11.16 11.38

Total 47457± 245 0.94

The contribution to systematic error cannot be measured simplytaking the larger among the three deviations found. This procedurewould lead to an overestimation of the error itself due to statistical ef-fects introduced by the splitting of the data set. In order to account forthe statistical effects, the deviations are weighted to the error of theirmeasurement:

σFB(syst) =

∑i∆iσ2i∑i1σ2i

.

4.7.6 Fit Bias

The difference between the generated and reconstructed T viola-tion parameter has been evaluated using Monte Carlo simulations (seeEq. 4.27).

4.8 final result 53

*θcos

1 0.8 0.6 0.4 0.2 0 0.2 0.4 0.6 0.8 1

)3

10

× (

Tv

iol

A∆

30

20

10

0

10

20

30

0D

Figure 21: Deviations from AT measured in different regions of the detector.The grey shaded area is centered at 0 and corresponds to AT mea-sured on the full data set with errors.

4.7.7 Detector Asymmetry

The Monte Carlo sample made of signal events decaying by phasespace has been used to test for asymmetries in the reconstruction fromthe detector. The generated asymmetry has been compared to the oneretrieved from correctly reconstructed signal decays. The deviationhas been assumed as the systematic error.

4.7.8 Systematics Summary

Finally, the systematic error has been evaluated summing in quadra-ture all the contributions shown in Table 17. In this table the contribu-tions to systematic error for AT and AT are quoted as well: they aremeasured as the same as AT .

4.8 final resultAfter unblinding, the following results for the asymmetry parame-

ters have been retrieved:

AT = (−68.5± 7.3(stat)± 5.8(syst))× 10−3,

AT = (−70.5± 7.3(stat)± 3.9(syst))× 10−3. (4.30)

It can be observed nonzero values of AT and AT indicating that finalstate interaction effects are significant in this D0 decay. This asymme-


Table 17: Systematic uncertainty evaluation on AT , AT and AT in units of10−3.

Effect AT AT AT

Alternative signal PDF 0.2 0.3 0.2Alternative mis-reconstructed D0 PDF 0.5 0.1 0.9Bin size 0.2 0.4 0.3Particle identification 3.5 4.2 2.9p∗(D0) cut 1.7 1.6 2.4cos θ∗ dependence 0.9 0.0 0.2Fit bias 1.4 3.0 0.3Mistag 0.0 0.0 0.0Detector asymmetry 1.1 2.1 0.0

Total 4.4 5.8 3.9

tries are clearly observable from the projections of the fit results intothe four sub-samples depending on D0 flavor and CT (CT ). No effectis found, on the other hand, in the analysis of Monte Carlo samples. Fi-nal state interaction effects are common in hadronic D decays becauseof the complex interference patterns between intermediate resonancesformed between hadrons in the final states [Oller, 2005].

The final result for the CP violation parameter, AT , is

AT = (1.0± 5.1(stat)± 4.4(syst))× 10−3. (4.31)

In conclusion, this search for CP violation using T -odd correlations inthe high statistics sample of Cabibbo suppressed D0 → K+ K− π+

π− decays gives a T -violationg asymmetry consistent with zero witha sensitivity of the order of 0.5%.

4.8 final result 55

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Figure 22: Data and fit projections in ∆m signal region. The four sub-samplesbuilt using the D0 flavor and the CT (CT ) value are shown.

5 D+( s ) → K 0SK

+π+π− A N A LY S I S

contents5.1 The Data Set 575.2 Events Reconstruction 585.3 Contaminations in the D+

(s)Data Sample 58

5.4 Optimization of the Data Sample 605.4.1 Potential Bias from Likelihood Ratio Selection 64

5.5 CT Resolution 655.6 Definition of the Fit Model 69

5.6.1 Study of the Events Categories 69

5.6.2 Definition of the Shapes 70

5.7 Data Analysis and Systematics 745.7.1 Fit procedure 74

5.7.2 Fit Validation on the Generic Monte Carlo sample 74

5.7.3 Systematics 77

5.7.4 Events selection and Forward-Backward asymmetry 77

5.7.5 Likelihood ratio selection 82

5.7.6 Fit model 83

5.7.7 Particle identification criteria 84

5.7.8 Summary of systematic errors 84

5.8 Final Result 84

The analysis of the charged D decay modes is somewhat similar towhat has been done on the D0 data set. The idea is to retrieve theasymmetry parameter directly from a fit to the data sample. The maindifference here is that there is no information about the D mother, soa technique based on the topology of the signal decays is needed toenhance the signal to background ratio.

In the following the data set is described; then the procedure usedto select the events is outlined; finally the fit model is defined and theresults on the data sample are shown.

5.1 the data setTogether with the full BABAR data set recorded at the Υ(4S) and

40 MeV below the resonance, the events recorded at the Υ(3S), Υ(2S)and below these resonances have been included, pushing the total in-tegrated luminosity to about 531 fb−1.

As well as described in Section 4.1, a large number of Monte Carloevents has been analyzed as the same as the data. The Monte Carloevents are again of two kinds: the Generic Monte Carlo, that simulatesthe continuum production of cc from e+e− and the Signal Monte Carlothat is made of events generated requiring that the signal decay chainis always present at generator level. The analysis makes use of about

57

58 D+(s)→ K0SK

+π+π− analysis

1.1× 109 Generic Monte Carlo Events and 4× 106 Signal Monte CarloEvents.

5.2 events reconstructionThe inclusive D+

(s)→ K0S K

+ π+ π− events are reconstructed to-

gether with all the D+(s)

decaying to three hadrons and a K0S :

D+(s)→ K0Sh

+h+h−, being h = π,K.

First a K0S candidate is built combining a couple of oppositely chargedpions. The invariant mass of the K0S candidate is required to be

0.35GeV/c2 < m(π+π−) < 0.65GeV/c2

and the vertex is fitted requiring a probability greater than 0.1% andapplying a mass constraint.

The successful K0S candidate is then combined to all the combina-tions of three charged tracks, previously identified as kaons or pionsusing boosted decision tree and error correcting output code selectorsrespectively, to form a D+

(s)candidate. This candidate is required to

have mass in the range

1.80GeV/c2 < m(K0Sh+h+h−) < 2.05GeV/c2

and momentum in the center-of-mass frame

p∗(D+(s)

) > 2.5GeV/c.

The probability of the fit of the vertex is again required to be greaterthan 0.1%.

The D+(s)

candidate passing all these selections is fitted again con-

straining the vertex into the interaction region. The χ2 probabilityretrieved from this fit is recorded for further studies.

5.3 contaminations in the D+(s) data sam-

pleA strong contamination from

D∗+ → D0π+

- K0SK+π−

has been found in the data sample. The D∗+ peak is visible in the K+

K0S π+ π− invariant mass spectrum that is shown in Figure 23. This

contamination is removed applying a combined cut on the K0S K+ π−

invariant mass and on ∆m = m(K+K0Sπ+π−) −m(K0SK

+π−):

144.46MeV/c2 < ∆m < 146.47MeV/c2,

1850.38MeV/c2 < m(K0SK+π−) < 1878.16MeV/c2. (5.1)

5.3 contaminations in the D+(s)

data sample 59

]2) [GeV/cπ

+π

+K

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70000

Figure 23: The K+ K0S π+ π− invariant mass after reconstruction. The D+ andD+s peaks are clearly visible together with the contamination from

D∗+. The red line shows the spectrum before removing the D∗+

contamination box, while the black line shows the spectrum afterthe removal of the contamination.

The sides of this box have been retrieved from two separate fits to theK0S K

+ π− invariant mass and to ∆m. They correspond to ±2σ massregion around the mean value of the Gaussian used in the fit. At firstthe ∆m has been fitted to a Gaussian over a second order polynomialbackground, then the K0S K+ π− invariant mass has been plotted inthe D∗+ signal region retrieved by the fit to ∆m spectrum. Finally theK0S K

+ π− invariant mass has been fitted to a Gaussian over a secondorder polynomial background and the D∗+ signal box is found. Theresults of these fits are shown in Figure 24. This cut removes all theevents that are shown by the red line in Figure 23 and does not affectsignal events.

Similarly to what has been found in the D0 → K+ K− π+ π− datasample, a contamination from D+

(s)→ K+ K0S K

0S , where both the

)2) (GeV/cπ

+K0

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7000

8000

)2) (GeV/cπ

+K0

Sm(K

1.81 1.82 1.83 1.84 1.85 1.86 1.87 1.88 1.89 1.9 1.91

2E

ven

ts/1

MeV

/c

0

500

1000

1500

2000

2500

3000

3500 2m = 1.86427 +/ 0.00003 GeV/c

2s = 0.00463 +/ 0.00003 GeV/c

)2) (GeV/cπ

+K0

Sm(K

1.81 1.82 1.83 1.84 1.85 1.86 1.87 1.88 1.89 1.9 1.91

2E

ven

ts/1

MeV

/c

0

500

1000

1500

2000

2500

3000

3500

Figure 24: The fit of ∆m = m(K+K0Sπ+π−) −m(K0SK

+π−) is shown on theleft. The results of this fit allowed to define a ∆m signal region toplot and fit the K0S K+ π− invariant mass on the right. Both the fitsare made to a model of a Gaussian over a second order polynomialbackground.

60 D+(s)→ K0SK

+π+π− analysis

two K0S decay into π+π− is observed. In Figure 25 the spectrum ofπ+π− invariant mass is shown in signal region and into the sidebands.The events in the sidebands have been subtracted to the events in thesignal region to obtain a clear K0S → π+π− signal peak. This peakhas been fitted to a Gaussian over a flat function finding σ = (2.94±0.02)MeV/c2 and a mean µ = (494.43± 0.07)MeV/c2. The mean valueof the K0S mass peak is again 3 MeV/c2 below to the K0S mass valuereported by the Particle Data Group (PDG) [Nakamura et al., 2010]m(K0S) = (497.614± 0.024)MeV/c2: this is due to the constrain of theK0S daughters to originate from the D vertex. The contamination iscompletely removed together with all the events for which

488.55MeV/c2 < m(π+π−) < 500.31MeV/c2.

Other sources of contamination have been found looking for wronglyidentified particles. A small contaminations from Λ+

c→ p K0S π+ π−

has been found by substituting the proton mass to the mass of thecharged kaon in the final state. The contamination is shown in Fig-ure 26, together with a fit of the Λ+

c peak. The number of Λ+c events

is estimated to be about 34,000, about 0.6% of the total. Their impacton the K+ K0S π

+ π− spectrum will be studied further in the analysis.

5.4 optimization of the data sampleA logarithmic likelihood ratio (see Appendix B) has been defined in

order to optimize separately the D+ and D+s peak in our data sample.

The likelihood ratio is built once identified the variables that show thebest separation between the signal and background distribution. Thechoice has been done following the prescription of a previous BABARanalysis [Aubert et al., 2005], where three variables are considered:

• the momentum of theD+(s)

in the center-of-mass frame, p∗(D+(s)

);

• the difference in the probability between the fits of the vertexwithout and with the constrain in the interaction region (IR),

∆p = probfit(D+(s)

) − probIRfit (D+(s)

);

• the distance of flight of the D+(s)

candidate in the (x,y) plane,~Dvtx and ~IP are thevectors pointing

respectively to thefittedD vertex and

to the InteractionPoint in the BABARcoordinates system

dxy =~pxy(D

+(s)

) ·~vxy(D+(s)

)

|~pxy(D+(s)

)|,(~v = ~Dvtx − ~IP

).

The distributions of these three variables are drawn in the sidebandssubtracted signal region an in the sidebands. For any event in the datasample the likelihood ratio is evaluated as follows:

logL = logPsigp∗ + logP

sig∆p + logP

sigdxy

− logPbkgp∗ − logP

bkg∆p − logP

bkgdxy

,(5.2)

5.4 optimization of the data sample 61

]2) [GeV/cσ2±+

) (Dπ

+πm(

0.4 0.45 0.5 0.55 0.6

)2

Ev

en

ts/(

2 M

eV

/c

0

500

1000

1500

2000

2500

3000

]2) [GeV/cσ 57+

) (Dπ

+πm(

0.4 0.45 0.5 0.55 0.6

)2

Ev

en

ts/(

2 M

eV

/c

0

200

400

600

800

1000

1200

1400

1600

1800

2000

2200

)2) (GeV/cπ

+πm(

0.4 0.45 0.5 0.55 0.6

)2

Even

ts/(

2 M

eV

/c

0

200

400

600

800

1000

fsig = 0.179 +/ 0.004

2m = 0.49443 +/ 0.00007 GeV/c

2s = 0.00294 +/ 0.00006 GeV/c

)2) (GeV/cπ

+πm(

0.4 0.45 0.5 0.55 0.6

)2

Even

ts/(

2 M

eV

/c

0

200

400

600

800

1000

]2

) [GeV/cπ

+π

+K

S

0m(K

1.8 1.85 1.9 1.95 2 2.05

)2

Ev

en

ts/(

2 M

eV

/c

0

10000

20000

30000

40000

50000

60000

70000

Figure 25: Study of D+ → K0S K0S K+ contamination. On the top left them(π+π−) spectrum is shown in D+ signal region; in the top rightthe same spectrum is shown inD+ sidebands region; on the bottomleft the subtraction of the two spectra has been fitted to a Gaussianover a flat function; on the bottom right the events removed apply-ing the cut on D+ → K0S K

0S K

+ are shown in the red filled areacompared to the spectrum before the application of this cut.

]2

) [GeV/cπ

+πp

S

0m(K

2 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3

)2

Ev

en

ts/(

10

Me

V/c

0

20

40

60

80

100

120

140

160

180

200

310×

)2) (GeV/cπ

+πp

S

0m(K

2.24 2.26 2.28 2.3 2.32 2.34

)2

Even

ts/(

1 M

eV

/c

0

2000

4000

6000

8000

10000

12000

14000

16000

18000

20000

22000

2m = 2.28592 +/ 0.00009 GeV/c

2s = 0.0040 +/ 0.0001 GeV/c

)2) (GeV/cπ

+πp

S

0m(K

2.24 2.26 2.28 2.3 2.32 2.34

)2

Even

ts/(

1 M

eV

/c

0

2000

4000

6000

8000

10000

12000

14000

16000

18000

20000

22000

870± = 34074 cΛ

N

Figure 26: p K0S π+ π− mass spectrum is shown on the left. The nominal Λ+c

mass from PDG is indicated by a red line (m(Λ+c )=2286.46 MeV/c2).

The fit of the Λ+c peak using a Gaussian over a second order poly-

nomial background is shown on the right.

62 D+(s)→ K0SK

+π+π− analysis

where the value of Psig(bkg)var is obtained from the distributions defined

above.In order to obtain the better definition for the signal and background

distributions, they have been retrieved from theD+ andD+s peaks that

have the higher yield among all the D+(s)→ K0S h

+h+h− decays. Theyare

• D+ → K0S π+ π+ π−;

• D+s → K− K0S π

+ π+.

These decays have been reconstructed as the same as the D+(s)→ K+

K0S π+ π− and the distribution of the kinematic variables should be

the same between the D+ and D+s peaks reconstructed in each one

of the different D+(s)→ K0S h

+h+h− decays. Furthermore, the highstatistics of these decay modes gives an excellent resolution for the sig-nal and background distributions, which allows to obtain a continuosdistribution for the likelihood ratio.

The signal and sidebands regions for D+ and D+s spectra are shown

in Figure 27 and are defined in Table 18. They have been retrieved

]2) [GeV/c+π

π

+π

S

0m(K

1.82 1.84 1.86 1.88 1.9 1.92

)2

Ev

en

ts/(

1 M

eV

/c

0

20

40

60

80

100

120

140

160

180

200

310×

]2) [GeV/c+π

+π

K

S

0m(K

1.92 1.94 1.96 1.98 2 2.02

)2

Ev

en

ts/(

1 M

eV

/c

0

5000

10000

15000

20000

25000

30000

Figure 27: Signal (red) and sidebands (blue) regions for D+ → K0S π+ π+ π−

(left) and D+s → K− K0S π

+ π+ mass spectra.

Table 18: Definition of signal and sidebands mass regions. The regions areshown in intervals of mass measured in MeV/c2.

Decay Mode Signal ( MeV/c2) Sidebands ( MeV/c2)

D+ → K0S π+ π+ π− [1858.07,1879.35] [1820.83,1842.11]

[1895.31,1916.59]

D+ → K− K0S π+ π+ [1959.0,1976.6] [1928.2,1945.8]

[1989.8,2007.4]

from a fit to the mass spectrum using a model made of a Gaussianover a second order polynomial: the signal region is defined as themass region within 2 standard deviations from the mean value of theGaussian, while the sidebands regions are made of the events withinvariant mass between 5 and 9 standard deviations from the Gaus-sian’s mean. The sidebands region has double width with respect to

5.4 optimization of the data sample 63

the signal region: this choice has been made in order to guarantee thecontinuity of the likelihood ratio distribution. If an event is found outof the phase space defined by the signal and sidebands distributionsoutlined in this section, given the definition of the likelihood ratio, itwould not be possible to evaluate the value of the likelihood ratio itselffor that event because it would produce a divergence in the logarithm.Two solutions have been found:

1. enlarge the sidebands regions to include as many events as pos-sible to define the distributions;

2. set a standard value of the likelihood ratio whenever the vari-ables are out of the range of the distributions.

Both the two solutions have been applied in this analysis. Since theeffect of the second solution is to create regions of the likelihood ratiothat are separated from the main peak, the application of the first sig-nificantly reduces the number of events out of range and, consequently,aggregates all the events into a continuous distribution.

The distributions retrieved from the signal and sidebands regionspreviously defined are shown in Figure 28. The distribution of the

) (GeV/c)π+π+π0

Sp*(K

2.5 3 3.5 4 4.5 5

Ev

en

ts/(

25

Me

V/c

)

0

0.02

0.04

Signal

Sidebands

)π+π+π0

Sp(K∆

0.2 0 0.2 0.4 0.6 0.8 1

Ev

en

ts/(

1.2

5 %

)

0

0.02

0.04

0.06

0.08

) (cm)π+π+π0

S(K

xyd

0.1 0.05 0 0.05 0.1 0.15 0.2 0.25 0.3

m)

µE

ve

nts

/(4

0

0

0.02

0.04

0.06

π+π+π

0SK

) (GeV/c)+π+πK0

Sp*(K

2.5 3 3.5 4 4.5 5

Ev

en

ts/(

25

Me

V/c

)

0

0.01

0.02

0.03

0.04 Signal

Sidebands

)+π+πK0

Sp(K∆

0.2 0 0.2 0.4 0.6 0.8 1

Ev

en

ts/(

1.2

5 %

)

0

0.02

0.04

0.06

0.08

) (cm)+π+πK0

S(K

xyd

0.1 0.05 0 0.05 0.1 0.15

m)

µE

ve

nts

/(2

5

0

0.01

0.02

0.03

0.04

+π+π

K0SK

Figure 28: Signal (red) and sidebands (blue) distributions for theD+ (top) andD+s (bottom) peaks. From left to right p∗(D+

(s)), ∆p and dxy.

likelihood ratios defined by Equation 5.2 and obtained from the eventsin the D+

(s)→ K0S K

+ π+ π− data sample using the distributions inFigure 28 are shown in Figure 29.

The best cut to apply on Likelihood ratio has been determined study-ing the significance of D+

(s)peak using many different cuts. The signif-

icance of the peak is defined as

S =S√S+B

, (5.3)

where S is the number of signal events, obtained subtracting the eventsin the sidebands from the ones in the signal region; B is the number of

64 D+(s)→ K0SK

+π+π− analysis

Likelihood Ratio

8 6 4 2 0 2 4 6 8 10

Even

ts/(

0.1

8)

1

10

210

310

410

510

+D

Likelihood Ratio

8 6 4 2 0 2 4 6 8 10

Even

ts/(

0.1

8)

1

10

210

310

410

510 s

+D

Figure 29: Plot of the distribution of D+ (left) and D+s (right) likelihood ratio

evaluated on D+(s)→ K0S K

+ π+ π− data sample.

background events, evaluated as half the events in the sidebands (con-sidering that the sidebands region is two times wide respect to signalregion). The cut for which the best significance is found is regarded asthe best to optimize the data sample. Following the results shown inFigure 30, LD+ > 1.5 is used to optimize D+ peak, while LD+

s> 0.0 is

used for D+s , obtaining the spectra shown in Figure 31.

LR cut

5 4 3 2 1 0 1 2 3 4 5

Sig

nif

ican

ce

60

65

70

75

80

85

90

95

100

105

π

+π

+K

0

SK

LR cut

5 4 3 2 1 0 1 2 3 4 5

Sig

nif

ican

ce

20

40

60

80

100

120

140

160

180

π

+π

+K

0

SK

Figure 30: Variation of D+(s)

peak significance depending on the selection cri-teria applied on D+ (left) of D+

s (right) likelihood ratio.

5.4.1 Potential Bias from Likelihood Ratio Selection

The potential bias introduced by the selection made on likelihoodratio has been studied considering three data sets:

• data sidebands;

• generic Monte Carlo sample without D+(s)

signal events;

• D+(s)

signal Monte Carlo samples generated by phase space.

Many tests have been performed on these data sets:

5.5 CT resolution 65

]2

) [GeV/cπ

+π

+K

0

Sm(K

1.8 1.85 1.9 1.95 2 2.05

)2

Ev

en

ts/(

2 M

eV

/c

0

1000

2000

3000

4000

5000

6000

7000

8000

]2

) [GeV/cπ

+π

+K

0

Sm(K

1.8 1.85 1.9 1.95 2 2.05

)2

Ev

en

ts/(

2 M

eV

/c

0

2000

4000

6000

8000

10000

12000

14000

16000

18000

20000

22000

24000

Figure 31: K+ K0S π+ π− mass spectrum optimized using D+ (left) and D+

s

(right) likelihood ratios.

1. The likelihood ratio output has been compared for the three sam-ples described above forD+ (D−) when CT (CT ) is greater or lessthan zero (Figure 32). All the distributions show a difference inχ2 about equal to 1, demonstrating that they are consistent.

2. The K+ K0S π+ π− mass spectrum is reconstructed from generic

Monte Carlo for D+ when CT > 0 and CT < 0. The same hasbeen done for D− using CT . The results are shown in Figure 33.

3. All the selections developed on the data sample have been ap-plied to signal Monte Carlo, then AT has been evaluated bycounting the D+

(s)(D−

(s)) events with CT (CT ) > 0 and CT (CT ) <

0. The results are shown in Figure 34 for many cuts on like-lihood ratio. The deviations observed between generated andreconstructed AT (before the selection on likelihood ratio) havebeen regarded as a statistical effect.

For some of the previously mentioned tests a χ2 has been evaluatedto determine whether a bias is found or not:

χ2 =∑i

N1,i −N2,i

σ21,i + σ22,i

i = bin, (5.4)

where Nj,i and σj,i are the number of events and its relative error inbin i of histogram j.

5.5 CT resolutionThe distribution of CT and CT for both D+ and D+

s sideband sub-tracted signal region is shown in Figure 35. This test, similar to the onemade on D0 signal sample and shown in Figure 9, shows the effectsof final state interaction. Also for D+ and D+

s , it can be observed anasymmetry in the CT distribution from which a non-zero value of ATand AT can be expected.

66 D+(s)→ K0SK

+π+π− analysis

)+

LLR (D

6 4 2 0 2 4 6 8 10

Even

ts/0

.16

0

500

1000

1500

2000

2500

3000

3500

LHR Ct>0 Sidebands

LHR Ct<0 Sidebands

= 0.902χ

Pu

ll

3

0

+3

)+

LLR (D

6 4 2 0 2 4 6 8 10

Even

ts/0

.16

0

5000

10000

15000

20000

25000

30000

35000

LHR Ct>0 sig removed

LHR Ct<0 sig removed

= 0.922χ

Pu

ll

3

0

+3

)+

LLR (D

6 4 2 0 2 4 6 8 10

Even

ts/0

.16

0

500

1000

1500

2000

2500

LHR Ct>0 D+ sig MC

LHR Ct<0 D+ sig MC

= 1.102χ

Pu

ll

3

0

+3

)

LLR (D

6 4 2 0 2 4 6 8 10

Even

ts/0

.16

0

500

1000

1500

2000

2500

3000

LHR Ctb>0 Sidebands

LHR Ctb<0 Sidebands

= 1.102χ

Pu

ll

3

0

+3

)

LLR (D

6 4 2 0 2 4 6 8 10

Even

ts/0

.16

0

5000

10000

15000

20000

25000

30000

35000

LHR Ctb>0 sig removed

LHR Ctb<0 sig removed

= 0.962χ

Pu

ll

3

0

+3

)

LLR (D

6 4 2 0 2 4 6 8 10

Even

ts/0

.16

0

500

1000

1500

2000

2500LHR Ctb>0 D sig MC

LHR Ctb<0 D sig MC

= 0.962χ

Pu

ll

3

0

+3

Figure 32: On top the plots of likelihood ratio for D+ when CT is greater(black) or less (red) than zero. On the bottom the same plot madeon D− depending on CT .

)+

) (Dπ+π+K

S

0m(K

1.8 1.85 1.9 1.95 2 2.05

)2

Ev

en

ts/(

2 M

eV

/c

0

1000

2000

3000

4000

5000

6000

7000

8000

D mass Ct>0 MC

D mass Ct<0 MC

= 0.882χ

MC

Pu

ll

3

0

+3

)

) (Dπ+π+K

S

0m(K

1.8 1.85 1.9 1.95 2 2.05

)2

Ev

en

ts/(

2 M

eV

/c

0

1000

2000

3000

4000

5000

6000

7000

8000

D mass Ctb>0 MC

D mass Ctb<0 MC

= 1.092χ

MC

Pu

ll

3

0

+3

Figure 33: The K0S K+ π+ π− mass spectrum is compared when CT > 0 (black)or CT < 0 (red) using the generic Monte Carlo sample. On theleft is shown the comparison between D+ candidates, on the rightbetween D− candidates. Both the D candidates distributions areconsistent between CT (CT ) > 0 and CT (CT ) < 0.

5.5 CT resolution 67

+D

LR

1.5 1 0.5 0 0.5 1 1.5 2 2.5 3 3.5

AT

V t

ru

e

0.01

0.008

0.006

0.004

0.002

0

0.002

0.004

0.006

0.008

0.01 Sig MC

+D

s

+D

LR

1.5 1 0.5 0 0.5 1 1.5 2 2.5 3 3.5

AT

V t

ru

e

0.01

0.008

0.006

0.004

0.002

0

0.002

0.004

0.006

0.008

0.01 Sig MCs

+D

Figure 34: The AT observable measured on signal Monte Carlo after the appli-cation of all the selections using different cuts on likelihood ratio.The red shaded area shows the AT value and error retrieved fromgenerated Monte Carlo. The blue shaded area shows the AT valueand error after events reconstruction and before the cut on likeli-hood ratio.

68 D+(s)→ K0SK

+π+π− analysis

TC

0 0.01 0.02 0.03 0.04

)3

10

×E

ve

nts

/(0

.4

0

100

200

300

400

500

600

700>0

TC

<0T

C

= 1.182χ

+D

Pu

ll

3

0

+3

TC

0 0.01 0.02 0.03 0.04

)3

10

×E

ve

nts

/(0

.4100

0

100

200

300

400

500

600

700 >0T

C

<0T

C

= 1.002χ

D

Pu

ll

3

0

+3

TC

0 0.01 0.02 0.03 0.04

)3

10

×E

ve

nts

/(0

.4

0

200

400

600

800

>0T

C

<0T

C

= 1.892χ

+

sD

Pu

ll

3

0

+3

TC

0 0.01 0.02 0.03 0.04

)3

10

×E

ve

nts

/(0

.4

0

200

400

600

800

>0T

C

<0T

C

= 1.692χ

sD

Pu

ll

3

0

+3

Figure 35: The distribution of the events in the signal region with the side-bands subtracted with CT (CT ) greater or less than zero is com-pared on top left for D+ (D−- right) and on the bottom left for D+

s

(D−s - right) data sample.


2) GeV/cπ+π

+K0

Sm(K

1.8 1.85 1.9 1.95 2 2.05

)2

Ev

en

ts/(

2 M

eV

/c

0

5000

10000

15000

20000

25000

30000

35000

40000

45000

+D+sD

+π)π+K

0

SK→(

0D→

*+D

misπ+π+π

0

SK→ +D

+K0

SK

0

SK→ +D

misπ+π+p

0

SK→ +

cΛ

combinatorial

2) GeV/cπ+π

+K0

Sm(K

1.8 1.85 1.9 1.95 2 2.05

)2

Ev

en

ts/(

2 M

eV

/c

20000

25000

30000

35000

40000

45000

+D+sD

+π)π+K

0

SK→(

0D→

*+D

misπ+π+π

0

SK→ +D

+K0

SK

0

SK→ +D

misπ+π+p

0

SK→ +

cΛ

combinatorial

Figure 36: Composition of the K+ K0S π+ π− mass spectrum after reconstruc-

tion. On the right, the same plot that is on the left is shown limitingthe range of the y-axis to [18,000:46,000]. The highlight allows toshow the events categories in detail.

5.6 definition of the fit modelSince the AT measurement is made separately on D+ and D+

s signalevents, the K+ K0S π

+ π− mass spectrum has been split in two regions:

1.81 < m(K+K0Sπ+π−) < 1.92GeV/c2

1.91 < m(K+K0Sπ+π−) < 2.02GeV/c2, (5.5)

the former mass region to measure AT on D+, the latter on D+s .

The model to be used to describe the mass spectrum has been devel-oped on the generic e+e− → cc Monte Carlo.

5.6.1 Study of the Events Categories

Using the informations from the generator, the correctly reconstructedMonte Carlo allowed to identify the following categories of events inthis analysis:

• signal, made of events with all the final state particles correctlyidentified, coming from a D+

(s)decay.

• D+→ K0S π+ π+ π− reflection, where the π+ has been identified

as a K+. This category of events manifests itself into a bump formasses higher than 1.94 GeV/c2.

• Λ+c→ p K0S π

+ π− reflection where the proton has been identi-fied as a K+. These events are widely distributed on the spectrumas shown in Figure 36.

• combinatorial background;

Applying the selection on likelihood ratio a strong suppression ofΛ+c→ p K0S π

+ π− reflection and combinatorial background has beenobserved, as shown in Figure 37. In the same figure can be observedthat the D+ → K0S π

+ π+ π− reflection seems to be enhanced respect

70 D+(s)→ K0SK

+π+π− analysis

]2) [GeV/cπ+πS

0K

+m(K

1.82 1.84 1.86 1.88 1.9 1.92

)2

Ev

en

ts/(

1 M

eV

/c

0

500

1000

1500

2000

2500

3000

Signal

S0K

S0K+K→

+D

+π)S0Kπ

+K→(0D→+D*

π+π+π

S

0K→

+D

π+π

S0K+p→

+cΛ

Combinatorial

> 1.5+DLR

]2) [GeV/cπ+πS

0K

+m(K

1.92 1.94 1.96 1.98 2 2.02

)2

Ev

en

ts/(

1 M

eV

/c

0

200

400

600

800

1000

1200

1400

1600

1800

2000

2200

Signal

S0K

S0K+K→

+D

+π)S0Kπ

+K→(0D→+D*

π+π+π

S

0K→

+D

π+π

S0K+p→

+cΛ

Combinatorial

> 0.0+sD

LR

Figure 37: Composition of the K+ K0S π+ π− mass spectrum after the selectionon likelihood ratio. The plot on the left shows the D+ mass range;the one on the right shows the D+

s range.

to the background: this effect is due to its kinematic topology, equiva-lent to the D+ signal events.

5.6.2 Definition of the Shapes

At first, a shape for the background description has been searchedfor. A line, a second order and a third order polynomial have beenfitted to the generic Monte Carlo sample once removed the correctlyreconstructed signal events. The results for both the two mass regionsare shown in Figure 38.

As a preliminary approach a line is assumed for the description ofthe background distribution for both the two ranges of mass. Usinga model of two Gaussians with common mean to describe the signaldistribution, the number of signal events retrieved from the fit hasbeen compared to the number of correctly reconstructed signal eventsin order to validate the fit model. The results of the fit to the MonteCarlo distribution are shown in Figure 39.

The model is validated comparing the retrieved number of signalevents to their true number, as shown in Table 19. While the results

Table 19: Comparison between the number of events retrieved by the fit andby Monte Carlo truth. The last column shows the number of σ’sbetween true and fitted number of events: ε = n−ntrue

σn

Category Events True ε

D+ signal 17068± 281 16848 +0.78

D+ background 104998± 408 105219 -0.54

D+s signal 37615± 396 39679 -5.22

D+s background 426189± 738 424125 +2.80

for the D+ mass range are quite consistent within the errors, the fit to


2) GeV/c

π+

π+

KS

0m(K

1.82 1.84 1.86 1.88 1.9 1.92

)2

Even

ts / (

1 M

eV

/c

0

200

400

600

800

1000

p0 = 0.112 +/ 0.005

= 0.7535dof

/n2χ

+(a) D

2) GeV/c

π+

π+

KS

0m(K

1.82 1.84 1.86 1.88 1.9 1.92

)2

Even

ts / (

1 M

eV

/c

0

200

400

600

800

1000

1.82 1.84 1.86 1.88 1.9 1.92

Pu

ll

3

0

+3

1.82 1.84 1.86 1.88 1.9 1.92

Pu

ll

2) GeV/c

π+

π+

KS

0m(K

1.92 1.94 1.96 1.98 2 2.02 )

2E

ven

ts / (

1 M

eV

/c0

500

1000

1500

2000

2500

3000

3500

4000

4500

p0 = 0.123 +/ 0.003

= 1.1848dof

/n2χ

s

+(a) D

2) GeV/c

π+

π+

KS

0m(K

1.92 1.94 1.96 1.98 2 2.02 )

2E

ven

ts / (

1 M

eV

/c0

500

1000

1500

2000

2500

3000

3500

4000

4500

1.92 1.94 1.96 1.98 2 2.02

Pu

ll

3

0

+3

1.92 1.94 1.96 1.98 2 2.02

Pu

ll

2) GeV/c

π+

π+

KS

0m(K

1.82 1.84 1.86 1.88 1.9 1.92

)2

Even

ts / (

1 M

eV

/c

0

200

400

600

800

1000

p0 = 0.112 +/ 0.005

p1 = 0.0042 +/ 0.005

= 0.7474dof

/n2χ

+(b) D

2) GeV/c

π+

π+

KS

0m(K

1.82 1.84 1.86 1.88 1.9 1.92

)2

Even

ts / (

1 M

eV

/c

0

200

400

600

800

1000

1.82 1.84 1.86 1.88 1.9 1.92

Pu

ll

3

0

+3

1.82 1.84 1.86 1.88 1.9 1.92

Pu

ll

2) GeV/c

π+

π+

KS

0m(K

1.92 1.94 1.96 1.98 2 2.02

)2

Even

ts / (

1 M

eV

/c

0

500

1000

1500

2000

2500

3000

3500

4000

4500

p0 = 0.124 +/ 0.003

p1 = 0.007 +/ 0.003

= 1.1146dof

/n2χ

s

+(b) D

2) GeV/c

π+

π+

KS

0m(K

1.92 1.94 1.96 1.98 2 2.02

)2

Even

ts / (

1 M

eV

/c

0

500

1000

1500

2000

2500

3000

3500

4000

4500

1.92 1.94 1.96 1.98 2 2.02

Pu

ll

3

0

+3

1.92 1.94 1.96 1.98 2 2.02

Pu

ll

2) GeV/c

π+

π+

KS

0m(K

1.82 1.84 1.86 1.88 1.9 1.92

)2

Even

ts / (

1 M

eV

/c

0

200

400

600

800

1000

p0 = 0.106 +/ 0.006

p1 = 0.0046 +/ 0.005

p2 = 0.0087 +/ 0.005

= 0.7204dof

/n2χ

+(c) D

2) GeV/c

π+

π+

KS

0m(K

1.82 1.84 1.86 1.88 1.9 1.92

)2

Even

ts / (

1 M

eV

/c

0

200

400

600

800

1000

1.82 1.84 1.86 1.88 1.9 1.92

Pu

ll

3

0

+3

1.82 1.84 1.86 1.88 1.9 1.92

Pu

ll

2) GeV/c

π+

π+

KS

0m(K

1.92 1.94 1.96 1.98 2 2.02

)2

Even

ts / (

1 M

eV

/c

0

500

1000

1500

2000

2500

3000

3500

4000

4500

p0 = 0.125 +/ 0.003

p1 = 0.007 +/ 0.003

p2 = 0.003 +/ 0.003

= 1.1012dof

/n2χ

s

+(c) D

2) GeV/c

π+

π+

KS

0m(K

1.92 1.94 1.96 1.98 2 2.02

)2

Even

ts / (

1 M

eV

/c

0

500

1000

1500

2000

2500

3000

3500

4000

4500

1.92 1.94 1.96 1.98 2 2.02

Pu

ll

3

0

+3

1.92 1.94 1.96 1.98 2 2.02

Pu

ll

Figure 38: Fit of the background categories using three different polynomialshapes: a line (a), a second order (b), a third order (c). On leftthe D+ mass range is shown, on the right the one of D+

s . The χ2

reduced to the number of degrees of freedom is shown on top leftof each plot. The normalized residuals shown on top of each plotare evaluated as outlined in Equation 4.1.

72 D+(s)→ K0SK

+π+π− analysis

the D+s mass range returns some values that are not consistent to the

Monte Carlo.In order to retrieve the correct number of events from the fit, some

variations to the model are applied. A second order polynomial forthe background significantly improves the quality of the fit, but is notenough: the cut on the likelihood ratio has been tightened to LD+

s>

1.5 in order to obtain a number of fitted signal events consistent tothe true value from Monte Carlo. The results of this fit are shown inFigure 40 and the relative difference in the number ofD+

s signal eventsis shown in Table 20.

Table 20: Comparison between the number of events retrieved by the fit andby Monte Carlo truth. The last column shows the number of σ’sbetween true and fitted number of events: ε = n−ntrue

σn

Category Events True ε

D+s signal 17599± 324 18063 -1.43

D+s background 99911± 423 99447 +1.10

In Table 21 the results for each parameter in the fit are shown bothfor the D+ and D+

s fit models. It can be noticed that the width of the

Table 21: Results of the fits to the Monte Carlo sample requiring LD+ > 1.50and LD+

s> 1.50.

(a) D+ → K0S K+ π+ π−

Parameter Final Value

N(D+) 17068± 281N(bkg) 104998± 408

mean D+ (1870.0± 0.1)MeV/c2

σ1 (3.30± 0.11)MeV/c2

σ2/σ1 (2.69± 0.33)fG1 (75.34± 4.06)%

p0 (1.09± 0.05)× 10−1

(b) D+s → K0S K

+ π+ π−

Parameter Final Value

N(D+s ) 17598± 296

N(bkg) 426189± 738

mean D+s (1969.8± 0.1)MeV/c2

σ1 (3.47± 0.27)MeV/c2

σ2/σ1 (1.78± 0.24)fG1 (65.21± 16.50)%

p0 (1.43± 0.06)× 10−1p1 (1.83± 0.03)× 10−2


)2) (GeV/cπ

+π

S

0K

+m(K

1.82 1.84 1.86 1.88 1.9 1.92

)2

Ev

en

ts/(

1.1

0 M

eV

/c

0

500

1000

1500

2000

2500

3000

)2) (GeV/cπ

+π

S

0K

+m(K

1.82 1.84 1.86 1.88 1.9 1.92

)2

Ev

en

ts/(

1.1

0 M

eV

/c

0

500

1000

1500

2000

2500

3000 +D

Pu

ll

3

0

+3

Pu

ll

)2) (GeV/cπ

+π

S

0K

+m(K

1.92 1.94 1.96 1.98 2 2.02

)2

Ev

en

ts/(

1.1

0 M

eV

/c

0

1000

2000

3000

4000

5000

6000

7000

8000

)2) (GeV/cπ

+π

S

0K

+m(K

1.92 1.94 1.96 1.98 2 2.02

)2

Ev

en

ts/(

1.1

0 M

eV

/c

0

1000

2000

3000

4000

5000

6000

7000

8000 s

+D

Pu

ll

3

0

+3

Pu

ll

Figure 39: Model made of two gaussians and a linear background fitted to theMonte Carlo sample in the D+ (left) and D+

s (right) mass region.The projection of the model on the data is shown by the blue line;the second Gaussian in the signal shape is shown in red, the back-ground shape is shown by a dashed blue line. On top of the plots,the normalized residuals (Pull) distribution is shown.

)2) (GeV/cπ

+π

S

0K

+m(K

1.92 1.94 1.96 1.98 2 2.02

)2

Ev

en

ts/(

1.1

0 M

eV

/c

0

500

1000

1500

2000

2500

3000

)2) (GeV/cπ

+π

S

0K

+m(K

1.92 1.94 1.96 1.98 2 2.02

)2

Ev

en

ts/(

1.1

0 M

eV

/c

0

500

1000

1500

2000

2500

3000

s

+D

Pu

ll

3

0

+3

Pu

ll

Figure 40: Model made of two gaussians and a second order polynomial back-ground fitted to the Monte Carlo sample in the D+

s mass region.The projection of the model on the data is shown by the blue line;the second Gaussian in the signal shape is shown in red, the back-ground shape is shown by a dashed blue line. On top of the plots,the normalized residuals (Pull) distribution is shown.

74 D+(s)→ K0SK

+π+π− analysis

second Gaussian is expressed in multiples of the width of the mainGaussian in the model.

5.7 data analysis and systematics5.7.1 Fit procedure

The model developed in the previous section has been used to per-form an unbinned maximum likelihood simultaneous fit to the fourdata samples obtained dividing the data set depending on D chargeand CT value. Each histogram is fitted simultaneously to the samemodel and the yield of each peak is evaluated separately in the samefit. Given the relationship between the following sets of observables[

N(D+(s)

, CT > 0) N(D+(s)

, CT < 0)N(D−

(s), CT > 0) N(D−

(s), CT < 0)

]l

N(D+(s)

) ,N(D−(s)

) , AT , AT

,

the signal yields for each sub sample can be expressed as:

N(D+(s)

, CT > 0) =N(D+ )

2(1 + AT )

N(D+(s)

, CT < 0) =N(D+ )

2(1 − AT )

N(D−(s)

, CT > 0) =N(D− )

2

(1 − AT

)N(D−

(s), CT < 0) =

N(D− )

2

(1 + AT

).

The latter set of variables has been used in the fit: this way AT canbe calculated directly from fit results as

AT =1

2

(AT − AT

)σAT =

1

2

√σ2AT

+ σ2AT

.

The fit to the D+ and D+s data samples are shown in Fig. 41. Sim-

ilarly to what has been done for the D0 analysis (see Section 4.6.1),these fits are “blind”, because the central values of asymmetry param-eters are masked by means of the addition of an unknown randomoffset. The quality of the fit is excellent.

5.7.2 Fit Validation on the Generic Monte Carlo sample

The same procedure has been applied to fit the generic Monte Carlosample. This is done to check some of the results that have been ob-tained from the data sample. In particular, it can be observed from Ta-ble 22 that the asymmetriesAT and AT in the background events of the

5.7 data analysis and systematics 75

Table 22: Results of the fits to the data sample requiring LD+(s)

> 1.50 (ATand AT are blind for both D+ and D+

s peaks).

(a) D+ → K0S K+ π+ π−

Floating Parameter Final Value

AT D+ (x.xx± 1.41)× 10−2

AT bkg (−1.71± 4.86)× 10−3AT D

+ (x.xx± 1.42)× 10−2AT bkg (−2.48± 4.90)× 10−3

N(D+) 10701± 257N(D+) bkg 52118± 328N(D−) 10526± 254N(D−) bkg 51245± 324

mean D+ (1869.9± 0.1)MeV/c2

σ1 (3.75± 0.07)MeV/c2

σ2/σ1 3.40± 0.47fG1 (81.50± 2.32)%

p0 (1.05± 0.05)× 10−1

(b) D+s → K0S K

+ π+ π−


AT D+s (x.xx± 1.34)× 10−2

AT bkg (−14.54± 4.85)× 10−3AT D

+s (x.xx± 1.09)× 10−2

AT bkg (−9.33± 4.87)× 10−3

N(D+s ) 15083± 233

N(D+s ) bkg 51732± 301

N(D−s ) 14717± 232

N(D−s ) bkg 51315± 300

mean D+s (1969.0± 0.1)MeV/c2

σ1 (3.65± 0.20)MeV/c2

σ2/σ1 1.76± 0.15MeV/c2

fG1 (65.20± 12.00)%

p0 (1.12± 0.05)× 10−1p1 (−2.31± 7.65)× 10−3

76 D+(s)→ K0SK

+π+π− analysis

)2) (GeV/cπ

+πS

0K

+m(K

1.82 1.84 1.86 1.88 1.9 1.92

)2

Ev

en

ts/(

1.1

0 M

eV

/c

0

500

1000

1500

2000

2500

3000a)

1.82 1.84 1.86 1.88 1.9 1.92

Pu

ll

3

0

+3

)2) (GeV/cπ

+πS

0K

+m(K

1.82 1.84 1.86 1.88 1.9 1.92

)2

Even

ts/(

1.1

0 M

eV

/c

0

100

200

300

400

500

600

700

800

900

>0)T

(C+D

1.82 1.84 1.86 1.88 1.9 1.92

Pu

ll

3

0

+3

)2) (GeV/cπ

+πS

0K

+m(K

1.82 1.84 1.86 1.88 1.9 1.92

)2

Even

ts/(

1.1

0 M

eV

/c

0

100

200

300

400

500

600

700

800 <0)T

(C+D

1.82 1.84 1.86 1.88 1.9 1.92

Pu

ll

3

0

+3

)2) (GeV/cπ

+πS

0K

+m(K

1.82 1.84 1.86 1.88 1.9 1.92

)2

Even

ts/(

1.1

0 M

eV

/c

0

100

200

300

400

500

600

700

800>0)TC (

D

1.82 1.84 1.86 1.88 1.9 1.92

Pu

ll

3

0

+3

)2) (GeV/cπ

+πS

0K

+m(K

1.82 1.84 1.86 1.88 1.9 1.92

)2

Even

ts/(

1.1

0 M

eV

/c

0

100

200

300

400

500

600

700

800 <0)TC (

D

1.82 1.84 1.86 1.88 1.9 1.92

Pu

ll

3

0

+3

(a) D+ → K0S K+ π+ π−

)2) (GeV/cπ

+πS

0K

+m(K

1.92 1.94 1.96 1.98 2 2.02

)2

Ev

en

ts/(

1.1

0 M

eV

/c

0

500

1000

1500

2000

2500

3000

3500

4000 b)

1.92 1.94 1.96 1.98 2 2.02

Pu

ll

3

0

+3

)2) (GeV/cπ

+πS

0K

+m(K

1.92 1.94 1.96 1.98 2 2.02

)2

Even

ts/(

1.1

0 M

eV

/c

0

200

400

600

800

1000>0)

T (C

+sD

1.92 1.94 1.96 1.98 2 2.02

Pu

ll

3

0

+3

)2) (GeV/cπ

+πS

0K

+m(K

1.92 1.94 1.96 1.98 2 2.02

)2

Even

ts/(

1.1

0 M

eV

/c

0

200

400

600

800

1000

1200

<0)T

(C+sD

1.92 1.94 1.96 1.98 2 2.02

Pu

ll

3

0

+3

)2) (GeV/cπ

+πS

0K

+m(K

1.92 1.94 1.96 1.98 2 2.02

)2

Even

ts/(

1.1

0 M

eV

/c

0

200

400

600

800

1000

1200

>0)TC (

sD

1.92 1.94 1.96 1.98 2 2.02

Pu

ll

3

0

+3

)2) (GeV/cπ

+πS

0K

+m(K

1.92 1.94 1.96 1.98 2 2.02

)2

Even

ts/(

1.1

0 M

eV

/c

0

200

400

600

800

1000

<0)TC (

sD

1.92 1.94 1.96 1.98 2 2.02

Pu

ll

3

0

+3

(b) D+s → K0S K

+ π+ π−

Figure 41: Fit to the D+(s)→ K0S K

+ π+ π− data sample. The fit has beenperformed using a model made of a double gaussian over a linear(second order polynomial) background. On the left the fit to theoverall sample is shown; on the right the projections on the foursub-samples are shown. For each plot, the distribution of the nor-malized residuals (Pull) is shown on the top.


D+s peak are significantly different from zero, while the asymmetries

on D+ are not. This effect is not present in the fit to the generic MonteCarlo sample, shown in Tab. 23. However, the BABAR events generatoris not well tuned to final state interaction effects. It has indeed beenobserved in the D0 analysis that the values of AT and AT found in thedata sample are completely different from the ones retrieved from thefit to the Monte Carlo. From Table 23, it can also be observed that theasymmetries are mainly consistent to zero, suggesting the things to besimilar in this analysis.

5.7.3 Systematics

Many checks have been applied to evaluate the systematic errors.The sources of systematic error identified are:

• events selection;

• forward-backward asymmetry;

• likelihood ratio selection;

• fit model;

• particle identification criteria.

For each source of systematic error identified a new fit on blind datawill be done little modifying the variables that are linked to that sys-tematic. The higher deviation from AT will be regarded as the errordue to that source of systematics.

To test the systematic effect of each source listed above, they havebeen studied as follows.

5.7.4 Events selection and Forward-Backward asymmetry

The signal Monte Carlo data set has been used to study the effectsof events reconstruction on these measurements. Considering thatthese events have been generated by phase space, while resonances arepresent in the real data, these effects should be somewhat included: todo so, the detector reconstruction efficiency, the resonant structure andthe forward-backward asymmetry need to be included in the MonteCarlo generated by phase space.

The reconstruction efficiency has been measured comparing the num-ber of correctly reconstructed signal events and the generated numberof signal events for each bin of the cosine of the polar angle cos θ∗, asshown in Fig. 42.

All the events in the generated Monte Carlo sample have been weightedusing this efficiency plot in order to obtain a simulation of the eventsreconstructed by the BABAR detector.

The resonant structure has been included in this simulated data setby means of relativistic Breit-Wigner distributions whose parametershave been retrieved from a fit to the data sample. The K0S π+, K0S π−,K+ π− and π+π− invariant mass spectra have been drawn into thesignal region of the data sample. These spectra, shown together with

78 D+(s)→ K0SK

+π+π− analysis

Table 23: Results of the fits to the generic Monte Carlo sample requiringLD+

(s)> 1.50.

(a) D+ → K0S K+ π+ π−


AT D+ (0.61± 1.61)× 10−2

AT bkg (3.40± 4.76)× 10−3AT D

+ (−2.98± 1.63)× 10−2AT bkg (1.04± 4.81)× 10−3

N(D+) 8631± 205N(D+) bkg 53024± 294N(D−) 8438± 198N(D−) bkg 51973± 288

mean D+ (1870.0± 0.1)MeV/c2

σ1 (3.30± 0.11)MeV/c2

σ2/σ1 2.69± 0.35fG1 (74.21± 4.39)%

p0 (1.09± 0.05)× 10−1

(b) D+s → K0S K

+ π+ π−


AT D+s (−0.95± 1.54)× 10−2

AT bkg (5.11± 4.86)× 10−3AT D

+s (−0.46± 1.53)× 10−2

AT bkg (−0.17± 4.91)× 10−3

N(D+s ) 8770± 228

N(D+s ) bkg 50531± 306

N(D−s ) 8829± 229

N(D−s ) bkg 49380± 305

mean D+s (1969.8± 0.1)MeV/c2

σ1 (3.47± 0.35)MeV/c2

σ2/σ1 1.78± 0.31MeV/c2

fG1 (65.18± 21.90)%

p0 (1.43± 0.06)× 10−1p1 (1.83± 0.80)× 10−2


*θcos1 0.8 0.6 0.4 0.2 0 0.2 0.4 0.6 0.8 1

Eff

icie

ncy

0

0.05

0.1

0.15

0.2

0.25

0.3

Figure 42: Reconstruction efficiency in bins of the cosine of the cc productionangle.

the fits in Fig. 43, indicate the presence of the resonances K∗−→ K0Sπ−, K∗0 → K+ π− and ρ→ π+π−. The results of the fits are shownin Tab. 24 and are reasonably according to the PDG values [Nakamuraet al., 2010]. The structure observed in the K0S π+ invariant mass hasnot been considered significant.

Table 24: Results of the fits shown in Fig. 43. All the resonances are fitted toa relativistic Breit-Wigner shape. The resulting masses and widthsare shown in MeV/c2.

Resonance Mass Width

K∗−→ K0S π−

886.74 55.50

K∗0 → K+ π− 894.80 42.64

ρ→ π+π− 730.65 144.41

The Monte Carlo events have been weighted making use of a func-tion that depends on m(K0Sπ

−), m(K+π−) and m(π+π−). This func-tion is made of normalized relativistic Breit-Wigner functions havingthe mass and widths shown in Table 24.

Finally the effect of the forward-backward asymmetry has been in-cluded into this data set. Forward-backward asymmetry is an effectdue to the interference between the electromagnetic and the weak cur-rents in the e+e− → cc process. A detailed study of this effect can befound in Appendix A.

Given the boost of the e+e− Center of Mass System (CMS) in PEP-IIbeam and the construction asymmetry of BABAR detector, the net effectof this interference is that the ratio c/c is not constant over the cosineof the polar angle θ∗, the angle formed by the c quark momentum andthe e− momentum.

80 D+(s)→ K0SK

+π+π− analysis

)2) (GeV/c+π

S

0m(K

0.7 0.8 0.9 1 1.1

)2

Ev

en

ts /

( 0

.00

5 G

eV

/c

0

100

200

300

400

500

)2) (GeV/c+π

S

0m(K

0.7 0.8 0.9 1 1.1

)2

Ev

en

ts /

( 0

.00

5 G

eV

/c

0

100

200

300

400

500

Pu

ll

3

0

+3

Pu

ll

)2) (GeV/cπ

S

0m(K

0.8 0.9 1

)2

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ll

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+3

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) (GeV/cπ

+m(K

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+πm(

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ll

Figure 43: Fits to the two-body invariant mass distributions for D+ signalevents. From left to right, top to down: K0S π+, K∗−→ K0S π

−,K∗0 → K+ π− and ρ→ π+π−.


This effect has been included weighting the simulated events by thefunction (shown in Fig. 44):

wFB(cos θ∗) = 1+8

3aFB

cos θ∗

1+ cos2 θ∗, (5.6)

where aFB = −2.49% has been retrieved, together with the function,from an internal note of the BABAR Collaboration [Chen et al., 2010].

*θcos1 0.8 0.6 0.4 0.2 0 0.2 0.4 0.6 0.8 1

FB

w

0.95

0.96

0.97

0.98

0.99

1

1.01

1.02

1.03

1.04

1.05

Figure 44: Distribution of the weights used to simulate the forward-backwardasymmetry effect.

The asymmetry parameters are then compared in the plots shownin Fig. 45. In these plots, the original value of the asymmetry with

eff eff+res eff+res+FB

TA

0.004

0.002

0

0.002

0.004


TA

0.004

0.002

0

0.002

0.004


Tv

A

0.004

0.002

0

0.002

0.004


TA

0.004

0.002

0

0.002

0.004


TA

0.004

0.002

0

0.002

0.004


Tv

A

0.004

0.002

0

0.002

0.004

Figure 45: The asymmetry parameters AT (left), AT (center) and AT (right)are compared with their value before the simulation (grey shadedarea) and after the introduction of the efficiency, the resonant struc-ture and the forward-backward asymmetry. On top, the results onD+ peaks, in the bottom, the D+

s .

its error is represented by the grey shaded area, while the value ob-

82 D+(s)→ K0SK

+π+π− analysis

tained after each step of the weighting described into this section isrepresented with its error by the graph points.

Some considerations can be retrieved from these plots:

• the reconstruction efficiency and the resonant structures intro-duce a bias of about 3× 10−3 into the AT , that reflects into AT ,just in the D+ sample;

• the introduction of a weighting factor depending from the forward-backward asymmetry does not affect much the asymmetry pa-rameters.

Following these considerations, a systematics error should be in-cluded related to the reconstruction bias in the D+ asymmetries, thatis the deviation from the generated value:

σrecosyst (AT ,D+) = −2.84× 10−3,

σrecosyst (AT ,D+) = +1.26× 10−3,

σrecosyst (AT ,D+) = −2.05× 10−3.

Since all the deviations in the D+s measurements are within the sta-

tistical fluctuations, a minimum bias of 1× 10−3 has been assumed foreach asymmetry parameter:

σrecosyst (AT ,D+s ) = +1.00× 10−3,

σrecosyst (AT ,D+s ) = +1.27× 10−3,

σrecosyst (AT ,D+s ) = +1.00× 10−3.

5.7.5 Likelihood ratio selection

Tighter and looser cuts on likelihood ratio have been applied andthe difference of AT respect to the optimal condition (LD+

(s)> 1.5) has

been measured. The result of this study is shown in Tab. 25.

Table 25: Statistical error (σ) on AT , AT and AT and their deviation (∆) fromthe best LRD+

(s)cut. All the values are multiples of ×10−3.

LR cut σAT ∆AT σAT ∆AT σAT ∆AT

D+1.30 10.09 -0.80 14.21 +1.34 14.32 +2.95

1.50 10.04 − 14.13 − 14.26 −1.70 10.04 +1.08 14.16 -3.41 14.24 -5.58

D+s

1.30 7.44 +2.46 10.43 +0.96 10.62 -3.95

1.50 7.67 − 10.73 − 10.93 −1.70 7.95 +0.21 11.13 -7.77 11.36 -8.16

Assuming the larger deviation as the systematic error to be assigned,one gets

σLsyst(AT [D+]) = ±1.10× 10−3,

σLsyst(AT [D+s ]) = ±2.41× 10−3.


The same procedure applied to AT and AT gives

σLsyst(AT [D+]) = ±3.41× 10−3,

σLsyst(AT [D+]) = ±5.58× 10−3,

σLsyst(AT [D+s ]) = ±7.77× 10−3,

σLsyst(AT [D+s ]) = ±8.16× 10−3.

5.7.6 Fit model

The fit model has been changed in many ways and the differenceof AT respect to the model chosen in Sec. 5.6: a double gaussian hasbeen used for both peaks of for the D+ peak only; a second order poly-nomial or a third order polynomial have been used for backgrounddescription. The results of these tests are shown in Tabs. 26, 27.

Table 26: Deviation of AT , AT and AT from the best model to fit the distribu-tion. All the values are multiples of ×10−3.

Fit Model (sig + bkg) ∆AT ∆AT ∆AT

D+double gaussian + line − − −

double gaussian + 2nd ord. poly -1.30 -1.14 +1.46

three gaussians + 2nd ord. poly -0.53 -0.44 +0.62

three gaussians + line +0.19 +0.22 -0.16

sum two gaussians + line +0.05 +0.00 -0.01

D+s

double gaussian + 2nd ord. poly − − −

sum two gaussians + 2nd ord. poly +0.04 -0.11 -0.11

single gaussian + 2nd ord. poly -0.04 -0.72 -0.63

single gaussian + 3nd ord. poly -0.03 -0.78 -0.70

double gaussian + 3nd ord. poly +0.02 +0.11 +0.10

three gaussians + 2nd ord. poly -0.01 +0.06 +0.11

Table 27: Statistical error of AT , AT and AT depending on the model used tofit the distribution. All the values are multiples of ×10−3.

Fit Model (sig + bkg) σAT σAT σAT

D+double gaussian + line 10.04 14.13 14.26

double gaussian + 2nd ord. poly 10.27 14.46 14.59

three gaussians + 2nd ord. poly 10.15 14.29 14.42

three gaussians + line 10.04 14.13 14.25

sum two gaussians + line 10.06 14.13 14.26

D+s


sum two gaussians + 2nd ord. poly 7.67 10.76 10.93

single gaussian + 2nd ord. poly 7.74 10.84 11.05

single gaussian + 3nd ord. poly 7.75 10.85 11.06


three gaussians + 2nd ord. poly 7.66 10.72 10.93

84 D+(s)→ K0SK

+π+π− analysis


σmodelsyst (AT [D+]) = ±1.30× 10−3,

σmodelsyst (AT [D+s ]) = ±0.04× 10−3.

The same procedure applied on AT and AT gives

σmodelsyst (AT [D+]) = ±1.14× 10−3,

σmodelsyst (AT [D+]) = ±1.46× 10−3,

σmodelsyst (AT [D+s ]) = ±0.78× 10−3,

σmodesyst (AT [D+s ]) = ±0.70× 10−3.

5.7.7 Particle identification criteria

Particle identification criteria have been modified to looser or tighterconditions and the difference of AT has been measured respect to thechosen selection. The results are shown in Tabs. 28, 29.


σPIDsyst (AT [D+]) = ±3.70× 10−3,

σPIDsyst (AT [D+s ]) = ±2.14× 10−3.

The same procedure applied on AT and AT gives

σPIDsyst (AT [D+]) = ±3.33× 10−3,

σPIDsyst (AT [D+]) = ±4.08× 10−3,

σPIDsyst (AT [D+s ]) = ±2.47× 10−3,

σPIDsyst (AT [D+s ]) = ±6.73× 10−3.

5.7.8 Summary of systematic errors

The systematic errors assigned to each identified source are listedin Tab. 30. The final systematic error is represented by the sum inquadrature of all the contributions.

5.8 final resultThe final results for the CP asymmetry measured through T -odd

correlation in D+(s)

decays are:

AT (D+) = (−11.96± 10.04stat ± 4.81syst)× 10−3,

AT (D+s ) = (−13.57± 7.67stat ± 4.82syst)× 10−3.

5.8 final result 85

Table 28: Deviation of AT , AT and AT from the used particle identificationcriteria. All the values are multiples of ×10−3.

PID ∆AT ∆AT ∆AT

D+kaonBDTTight + piKMLoose − − −kaonBDTLoose + piKMLoose -1.08 -1.86 +0.30

kaonBDTVeryTight + piKMLoose -3.70 -3.33 +4.08

kaonBDTTight + piKMTight +1.56 +3.76 +0.65

kaonBDTTight + piKMVeryTight +0.58 -0.43 -1.58

D+s

kaonBDTTight + piKMLoose − − −kaonBDTLoose + piKMLoose +1.09 +0.60 -1.57

kaonBDTVeryTight + piKMLoose +0.27 +0.33 -0.19

kaonBDTTight + piKMTight +1.07 -0.56 -2.68

kaonBDTTight + piKMVeryTight +2.14 -2.47 -6.73

Table 29: Statistical error of AT , AT and AT using different particle identifica-tion criteria. All the values are multiples of ×10−3.

PID σAT σAT σAT

D+kaonBDTTight + piKMLoose 10.04 14.13 14.26

kaonBDTLoose + piKMLoose 10.06 14.17 14.28

kaonBDTVeryTight + piKMLoose 10.04 14.15 14.26

kaonBDTTight + piKMTight 10.24 14.37 14.54

kaonBDTTight + piKMVeryTight 10.65 14.95 15.15

D+s

kaonBDTTight + piKMLoose 7.66 10.73 10.93

kaonBDTLoose + piKMLoose 7.67 10.74 10.94

kaonBDTVeryTight + piKMLoose 7.66 10.73 10.94

kaonBDTTight + piKMTight 7.80 10.93 11.12

kaonBDTTight + piKMVeryTight 8.14 11.43 11.59

Table 30: Summary of the contributions to systematic error. All the values aremultiples of ×10−3.

D+ D+s

Source σ(AT ) σ(AT ) σ(AT ) σ(AT ) σ(AT ) σ(AT )

Fit Bias 1.52 0.92 3.97 3.52 2.94 4.10

Reconstruction 2.05 2.84 1.26 1.00 1.00 1.27

Likelihood ratio 1.10 3.41 5.58 2.41 7.77 8.16

Fit model 1.30 1.14 1.46 0.11 0.78 0.70

PID 3.70 3.33 4.08 2.22 2.47 6.73

Total 4.81 5.74 8.20 4.82 8.76 11.41

86 D+(s)→ K0SK

+π+π− analysis

These values are obtained uncovering the central values of AT andAT :

AT (D+) = (+11.22± 14.13stat ± 5.74syst)× 10−3,

AT (D+) = (+35.13± 14.26stat ± 8.20syst)× 10−3,

AT (D+s ) = (−99.24± 10.73stat ± 8.48syst)× 10−3,

AT (D+s ) = (−72.09± 10.93stat ± 12.43syst)× 10−3.

In conclusion, this search for CP violation using T -odd correlations inthe high statistics sample ofD+ andD+

(s)decays to K+ K0S π

+ π− givesa T -violating asymmetry that is consistent to zero with a sensitivity ofthe order of 1% for D+ and 0.8% for D+

s .

6 C O N C L U S I O N S

The work outlined in this thesis has allowed to measure the observ-ables for CP violation in four-body D decays using T -odd correlations.Three decay modes have been considered:

• D0 → K+ K− π+ π− ;

• D+ → K+ K0S π+ π−;

• D+s → K+ K0S π

+ π−.

Among them, the first two are Cabibbo suppressed, while the D+s one

is Cabibbo favored.The analysis of the D0 decays showed that AT and AT are signifi-

cantly different from zero:

AT (D0) = (−68.5± 7.3(stat) ± 5.8(syst))× 10−3,

AT (D0) = (−70.5± 7.3(stat) ± 3.9(syst))× 10−3.

indicating the effects of final state interaction. Although this two asym-metries are different from zero, their difference is not

AT (D0) = (1.0± 5.1(stat) ± 4.4(syst))× 10−3.

CP violation is then not found in this decay mode, according to theStandard Model. Furthermore, the high sensitivity of this result con-strains the possible effects of new physics in this observable. In Fig-ure 46 the comparison of this result to the other results for CP violationin D0 decays is shown.

The search for CP violation in D+ → K+ K0S π+ π− decays showed

that the AT and AT asymmetries are consistent to zero

AT (D+) = (+11.2± 14.1(stat) ± 5.7(syst))× 10−3,

AT (D+) = (+35.1± 14.3(stat) ± 8.2(syst))× 10−3.

This is an interesting result, since the same asymmetries are found dif-ferent from zero in the D0 and D+

s analysis. The resulting T -violatingasymmetry is

AT (D+) = (−12.0± 10.0(stat) ± 4.8(syst))× 10−3,

consistent to zero with a sensitivity of 1%.The similar search in D+

s → K+ K0S π+ π− decays gave

AT (D+s ) = (−99.2± 10.7(stat) ± 8.5(syst))× 10−3,

AT (D+s ) = (−72.1± 10.9(stat) ± 12.4(syst))× 10−3,

87

88 conclusions

resulting into a T -violating asymmetry of

AT (D+s ) = (−13.6± 7.7(stat) ± 4.8(syst))× 10−3,

consistent to zero with a sensitivity of 0.8%.The results are expected to be published in the first half of 2011 and

look competitive to what has been previously obtained in the D+ andD+s decays, as well as shown in Figures 47 and 48. In particular for

D+s , the measurement is among the ones having the best sensitivity.All the measurements are consistent to zero as well as expected by

the Standard Model. Nevertheless the results on the AT and AT asym-metries are quite interesting: while these asymmetries are differentfrom zero in the D0 and D+

s decays studied, they are consistent tozero in the D+ decays, indicating a smaller contribution from finalstate interactions.

In conclusion, this search for CP violation showed that the T -oddcorrelations are a powerful tool to measure the CP violating observableAT . The relative simplicity of an analysis based on T -odd correlationsand the high quality results that can be obtained, allow to consider thistool as fundamental to search for CP violation in four-body decays.

Even if the CP violation has not been found, excluding any NewPhysics effect to the sensitivity of about 0.5%, it is still worth to searchfor CP violation in D decays. The high statistics that can be obtainedat the LHC or by the proposed high luminosity B-factories, makethis topic to be considered in high consideration by experiments suchas LHCb, SuperB or SuperBelle. The results outlined in this thesisstrongly suggest to include a similar analysis into the Physics programof these experiments.

conclusions 89

)2 10× (CPA

6 4 2 0 2 4 6

Belle(2007) π

+π →

0D

Belle(2007) K+ K→

0D

BaBar(2008) π

+π →

0D

BaBar(2008) K+ K→

0D

BaBar(2008) π

+π →

0D

BaBar(2008) K+ K→

0D

Belle(2008) π

+π →

0D

Belle(2008) K+ K→

0D

Belle(2008) 0π

π

+π →

0D

BaBar(2008) 0π

π

+π →

0D

BaBar(2008) 0π

K+ K→

0D

BaBar(2010) π

+π

K+ K→

0D

Figure 46: Comparison of the best recent results for CP violation in D0 decays.The result of the analysis outlined in this thesis is highlighted intoa red box.

)2 10× (CPA

10 5 0 5 10

E791(1997) +π

K

+ K→

+D

E791(1997) +π

π

+π →

+D

FOCUS(2000) +π

K

+ K→

+D

FOCUS(2002) +π

S

0 K→ +D

BaBar(2005) +π

K

+ K→

+D

CLEOc(2007) +π

S

0 K→ +D

CLEOc(2007) +π

+π

K→

+D

CLEOc(2007) 0π

+π

S

0 K→ +D

CLEOc(2007) 0π

+π

+π

K→

+D

CLEOc(2008) +π

K

+ K→

+D

Belle(2010) +π

S

0 K→ +D

Belle(2010) +KS

0 K→ +D

BaBar(2011) +π

S

0 K→ +D

BaBar(2011) π

+πS

0K+ K→ +D

Figure 47: Comparison of the best recent results for CP violation inD+ decays.The result of the analysis outlined in this thesis is highlighted intoa red box.

)2 10× (CPA

30 20 10 0 10 20 30

FOCUS(2005) π+π

+KS

0 K→ +

sD

CLEOc(2007) 0π

+ K→ +sD

CLEOc(2008) η+π → +sD

CLEOc(2008) ’η+π → +sD

CLEOc(2008)S

0K+ K→ +

sD

CLEOc(2008) π+π+π → +

sD

CLEOc(2008) π+π

+ K→ +sD

CLEOc(2008) +π

K+ K→ +sD

CLEOc(2008) +π+π

KS

0 K→ +

sD

CLEOc(2008) 0π+π

K+ K→ +

sD

Belle(2010) +πS

0 K→ +

sD

Belle(2010) +KS

0 K→ +

sD

BaBar(2011) π+πS

0K+ K→ +D

Figure 48: Comparison of the best recent results for CP violation inD+s decays.

The result of the analysis outlined in this thesis is highlighted intoa red box.

A T H E c c A S Y M M E T R I C P R O D U C -T I O N I N BABAR A N D B E L L E

The production of cc pairs in e+e− collisions at 10.58 GeV/c2 centerof mass energy is mainly mediated by the electromagnetic process

e+e− → γ→ cc, (A.1)

but e+e− could also produce cc pairs by the neutral weak currentprocess [Halzen e Martin, 1984]

e+e− → Z0 → cc. (A.2)

Let’s see how this process can interfere in the analyses made at asym-metric detectors, such as BABAR and Belle. The electromagnetic processamplitude is

MEM ≈ e2

k2, (A.3)

where k2 = s = E2CM. The weak process interfere with the electromag-netic one at the level

|MEMMNC|

|MEM|2≈ G

e2/k2≈ 10

−5k2

m2N. (A.4)

Assuming the mass of the neutron mN ≈ 1GeV/c2 and k2 ≈ E2CM ≈100(GeV/c2)2, one gets a 1% interference effect.

The differential cross section of the interference process, calculatedusing Feynman rules, is

dq

dΩ(e+L e

−R → c−L c

+L ) =

3α2

4s(1+ cos θ)2|2/3+ rccLc

eL|2, (A.5)

with

r =

√2GM2Z

s−M2Z + iMZΓZ

( se2

). (A.6)

The result is that the final production ratio of D and D differs from 1

depending on θ, the quarks production angle.BABAR and Belle are asymmetric detectors and the center of mass

frame is boosted to enhance separation of B’s vertices, so that the finalyield of D and D events has an intrinsic asymmetry [Aubert et al.,2008].

91

B S TAT I S T I C A L T E C H N I Q U E S U S E DB Y BABAR S E L E C TO R S

contentsb.1 Likelihood Ratio 93b.2 Error Correcting Output Code 94b.3 Boosted Decision Tree 96

The BABAR collaboration developed many statistical techniques to testthe identification of the particles from the detector. A brief introduc-tion to the techniques that are used for the selectors related to theanalysis shown in this thesis are outlined in the following.

b.1 likelihood ratioThe technique of the likelihood ratio is based on the probability dis-

tribution that an event is signal or background depending upon a vari-able. Let suppose that an event is represented by n variables

~x = x1, x2, ..., xn. (B.1)

Using signal and background control samples, for each one of thesevariables a probability density function can be retrieved:

Si(xi),Bi(xi), for i = 1, ..,n. (B.2)

The likelihood ratio is defined as the product of the signal distribu-tion of each variable, divided by the product of the relative backgrounddistributions:

L(~x) =

n∏i=1

Si(xi)

Bi(xi). (B.3)

This technique allows to maximize the number of signal events re-spect to the background by a selection on a single variable. Usuallythe selection is chosen in order to maximize this ratio.

The advantage of this technique is that there are not developed asmany selections as the number of variables studied, but there is onlyone selection, limiting the number of contributions to the systematicserror.

This technique is widely used in this work, not only for the particleidentification, but even for reducing the background in the D+

(s)data

sample and to find the model that best fits the resulting distributions,both for D0 and D+

(s)analysis.

93

94 statistical techniques used by BABAR selectors

b.2 error correcting output codeError Correcting Output Code (ECOC) [Dietterich e Bakiri, 1995] is

an algorithm for making a multi-class classifier from binary classifiers.It was invented around 1995 by T. Dietterich and G. Bakiri.

Let’s consider a simple example to understand how it works. Sup-pose the need to classify the data in four classes

A,B,C,D (B.4)

by means of two binary classifiers

α that separates A,B from C,D, (B.5)β that separates A,C from B,D. (B.6)

At first, the indicator matrix can be obtained. The rows and columns

Table 31: Indicator matrix of a multi-class classifier from the combination oftwo binary classifiers. tα and tβ represent how the given class istreated in training a sample for classifier α and β respectively. 1

means signal and 0 means background.

Class tα tβ

A 1 1

B 1 0

C 0 1

D 0 0

of the indicator matrix shown in Table 31 can be interpreted as follows:

• each row represents the ideal output from each classifier for agiven class. That is the template to compare the output from theclassifier.

• Each column represents the ideal output for each class for a givenclassifier. That is the way the analyst should train each classifier.

Let’s now suppose that an event d needs to be classified into one ofthe four classes defined in Equation B.4: the output of each classifiercan be 0 or 1. In the case that

Oα = 1 Oβ = 0, (B.7)

the total output can be written as O = 10.To determine which class is the more likely to identify the event,

the Hamming distance can be defined: this is the number of bits thatare different between the output and the corresponding row in theindicator matrix. The lower the Hamming distance, the more likely theclass. In Table 32 the Hamming distance for the output of Equation B.7together with the indicator matrix. The lowest Hamming distance isrelated to the class B, which would have returned the both the rightanswers from the two indicators if the event belonged to it. But what ifan indicator had failed? In this hypothesis, the classes A and C become

b.2 error correcting output code 95

Table 32: Hamming distance obtained comparing the output in Equation B.7with the indicator matrix of Table 31.

Class tα tβ Hamming distance

A 1 1 1

B 1 0 0

C 0 1 2

D 0 0 1

the most likely. If both the two indicators are failing, then the class Dis the more likely to be the right one.

The multi-class classified built from only 2 binary classifiers wouldthen mis-classify the event if one or both the classifiers make a mistake.In order to fix this problem, one can add more classifiers and try tomake sure that when one of them is failing, their sum can still recoverthe correct answer.

Let’s first count how many different classifiers can be built for a fixednumber n of classes. Each classifier can be represented by a binarystring of length n, returning the ideal output for each one of the classes.Considering that there are no permutations among the elements of thestring and that each element is a binary number, the total number ofclassifiers is 2n. All these classifiers are shown in Table 33, that canalso be followed to understand the next few paragraphs.

Table 33: All possible classifiers for a four-classes problem. Among them,there are only 7 valid classifiers.

A 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0

B 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0

C 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0

D 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0

d all 1 Good Ones | Complement

However, some classifiers are doubly accounted this way: the classi-fiers that are complement to each other actually are the same classifier.See for example 1100 and 0011, they are both trained to separate A,Bfrom C,D, . The number of valid classifiers is then 2n−1.

Among these, there is also the “all 1” classifier (1111): this classi-fier does not add any separating power to the technique, since all theclasses are the same for it. It can then be removed.

The final number of valid classifiers is 2n−1 − 1 and they are shownin Table 34 for a four-classes problem. The indicator matrix made of all

Table 34: Exhaustive Matrix for a four-classes problem.

Class t0 t1 t2 t3 t4 t5 t6

A 1 1 1 1 1 1 1

B 0 1 0 1 0 1 0

C 1 0 0 1 1 0 0

D 1 1 1 0 0 0 0


the valid combinations of classifiers is called the “exhaustive matrix”.Let’s draw an example to understand the power of this technique. If

the event belongs to the class A, the ideal output is

O = 1111111. (B.8)

Let’s suppose that one, two or three classifiers are failing. The resultingHamming distance for each one of the three cases is shown in Tables 35-37.

It can be observed that the class indication is correct up to two classi-fiers failing. The reason for this property is the row hamming distance.For this four-class exhaustive matrix, the hamming distance betweenany two rows is 4. That means classifiers can make two mistakes, inthe worst case, at the bits that are not the same between two rows andthere is still the chance to recover the correct answer.

As shown in Table 37, there is the chance to run into a tie situation.In the actual BABAR implementation, the problem is avoided by usingreal numbers for the classifiers output and generalize the hammingdistance to the sum of the squared differences between each bit.

The drawback of this technique, is that the exhaustive matrix con-tains all the possible classifiers, and their number grows exponentiallywith the number of classes. This technique then cannot be easily de-veloped for a large number of classes. However, a discussion aboutthe feasibility of this technique into a many-classes case is outlined inSection 3 of [Dietterich e Bakiri, 1995].

In the BABAR implementation of the technique, a real output in [−1, 1]is assigned to each classifier in place of the binary one. The four classesof events are related to the particle identification and are K, π, p, e. Theexhaustive matrix is shown in Table 38.

b.3 boosted decision treeBoosted Decision Tree (BDT) [Breiman et al., 1984] is a technique

of multi-variate analysis. This kind of technique is useful when theLikelihood ratio is failing due to the large correlations between theinput variables or to the complexity of a probability density functioninto a multi-variate space.

In Boosted Decision Trees, the selection is done on a majority voteon the result of several decision trees, which are all derived from thesame training sample by supplying different event weights during thetraining.

The decision trees are made of successive decision nodes that areused to categorize the events out of the sample as either signal or back-ground. Each node is associated to a single discriminating variable todecide if the event is signal-like or background-like. This forms a treelike structure with “baskets” at the end (leave nodes), and an event isclassified as either signal or background according to whether the bas-ket where it ends up has been classified signal or background duringthe training.

During the training, the “cut criteria” for each node are defined.Starting from the root node, the full training event sample is taken and

b.3 boosted decision tree 97

Table 35: Hamming distance for the exhaustive matrix of a four-classes prob-lem when there is one classifier failing (O=0111111).

Class t0 t1 t2 t3 t4 t5 t6 Hamming distance

A 1 1 1 1 1 1 1 1

B 0 1 0 1 0 1 0 3

C 1 0 0 1 1 0 0 5

D 1 1 1 0 0 0 0 5

Table 36: Hamming distance for the exhaustive matrix of a four-classes prob-lem when there are two classifiers failing (O=0011111).


A 1 1 1 1 1 1 1 2

B 0 1 0 1 0 1 0 4

C 1 0 0 1 1 0 0 4

D 1 1 1 0 0 0 0 6

Table 37: Hamming distance for the exhaustive matrix of a four-classes prob-lem when there are three classifiers failing (O=0001111).


A 1 1 1 1 1 1 1 3

B 0 1 0 1 0 1 0 3

C 1 0 0 1 1 0 0 3

D 1 1 1 0 0 0 0 7

Table 38: Exhaustive Matrix for the BABAR particle identification.

Class t0 t1 t2 t3 t4 t5 t6

K 1 1 1 1 1 1 1

π -1 1 -1 1 -1 1 -1p 1 -1 -1 1 1 -1 -1e 1 1 1 -1 -1 -1 -1


the variables and the corresponding cut values that give the best sepa-ration between signal and background are selected. Using this cut cri-terion, the sample is then divided into two sub-samples, a signal-likeand a background-like sample. Two new nodes are then created foreach of the two sub-samples and they are constructed using the samemechanism as described for the root node. The division is stoppedonce a certain node has reached either a minimum number of events,or a minimum or maximum signal purity. These leave nodes are thencalled “signal” or “background” if they contain more signal respectivebackground events from the training sample.

The decision tree is boosted by giving a weight to signal events in thetraining sample that end up into a background node (and vice versa)larger than the events falling into the correct leave node. This resultsin a re-weighted training event sample, with which a new decision treecan be developed. The boosting can be applied several times (typically100-500 times) and one ends up with a set of decision trees (a forest).The boosting stabilizes the response of the decision trees respect tofluctuations in the training sample and is able to considerably enhancethe performance with respect to a single tree. As a drawback, there isthe problem of the over training of the decision tree, that can fake theresults.

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