july, 2006 selected topics on open charm physics from cleo-c 1 selected topics on open charm physics...

July, 2006 Selected Topics on Open Charm Physics from CLEO-c 1

Selected Topics on Open Charm Physics at CLEO-c

Batbold SanghiPurdue University

(CLEO Collaboration)

K-

-

e+

K+

(3770)D0 D0

D0K+-, D0K-e+ Main topics:

Overview the CLEO-c experiment and its physics program

Absolute Hadronic D0 and D+ Branching Fractions

Preliminary Results for Absolute Branching Fractions and Form Factor Measurements in and eKD /0 eKD 00

/


CLEO-c and the CKM Matrix

Recent status

Status withtheory errors reduced)

The CKM matrix provides the only mechanism for CP violation in the SM

An important goal of flavor physics is to measure and (over)constrain the parameters in the CKM matrix (4 parameters) to test the SM

Non-perturbative hadronic effects limit our ability to extract fundamental parameters from experimental measurements

CLEO-c provides unique measurements in the charm sector that test theory and help reduce hadronic uncertainties

CLEO-c tested theory can then be applied to B decay processes to extractCKM matrix elements (especially Vub and Vtd)


An example of a test of Lattice QCD

Measure form factors in D l at CLEO-c

Theories of Strong Interactions (LQCD)

validate LQCD calculations for form factors

use LQCD to extract Vub from Bl

222

2)(~

)(qfV

dq

lDdcd

222

2)(~

)(qfV

dq

lBdub


An example of a test of Lattice QCD

m is well measured

But |Vtd| from m has a large uncertainties from fB

measure fD in D l

validate theoretical calculations

fB ~fB (LQCD)/ fD (LQCD) fD

Use fB to extract |Vtd|

Theories of Strong Interactions (LQCD)


CLEO-c impact

CLEO-c + Lattice QCD +B factories

CLEO-c CLEO-c + Lattice QCD +B factories + ppbar

Vub/Vub 15%lB

lD

Vcd/Vcd 7%lD

Vcs/Vcs =16%l

B D

Vcb/Vcb 5%

Bd Bd

Vtd/Vtd =36%

Bs Bs

Vts/Vts 39% Vtb/Vtb 29%

Vus/Vus =1%

l

Vud/Vud 0.1%ep

n

tb

W

D hadronic branching fractions(Analysis by Cornell, Purdue and CMU)Including: and

D semileptonic B’s and form factors in

(Analysis by Purdue and SMU, my main thesis topic)

I will focus on two CLEO-c analyses that have impact on Vcd, Vcs, Vub and Vcd:

D and Ds leptonic branching fraction

eKD / KD0 KD


The CLEO-c detector

Over 20 years of data taking at

Y(4S)

An event taken at (4S)

KDKD

DDee

,

,)3770(

The main components of the CLEO-c detector were developed for B physics at the Y(4S).

Minor modifications Replaced silicon with 6 layer inner drift chamber B field 1.5 T 1.0 T

P/P = 0.6% at 1GeV

E/E = 2% at 1GeV

= 5% at 100MeV

Excelent electron and hadron ID

Advantages at (3770) Pure DD, no additional particle Low multiplicity High tagging efficiency

)3770(

Started data taking in the fall of 2003

Note

: Log

S

cale


Three generations of CLEO-c analyses at the (3770):

Oct-03 through Jan-04: Luminosity = 56 pb 1

all results are published(D hadronic branching fraction)

Sep-04 through Apr-05: Luminosity = 225 pb1

most analyses are on-going(D semileptonic B’s and form factors)

Future running: projected total Luminosity = 750 pb1

CLEO-c is also collecting data above the DsDsbar

productionthreshold (goal 750 pb1) and lower energies at the (2S).

CLEO-c data samples


Absolute Hadronic D0 and D+ Branching Fractions

Introduction and Overview of the Analysis Measurements of Absolute Hadronic Branching Fractions Summary


Overview of Technique

ijjiDDij BBND 2

2

42 i

ii

ii

iDD

ji

ij

ij

jiDD D

SNor

D

SSN

e+ e

0D

0D

K+

+

K-

iiDDi BNS 2

XSingle tagged D

Double tagged D

e+ e

0D

0D

K+

ii

i

i

iii

ij

j

j

iji S

DBor

S

DB

2

Use 3 D0 modes and 6 D+ modes

K-+, K-+,0, K-+ ,+ -

K-+ +, K-+ +0, Ks+ , Ks+ 0, Ks+ 0, Ks++ + , K-K+ +

Reference modes D K+ and K++ normalize many B measurements from other experiments.


Overview of Technique

22candidatebeambc PEM

Determine separately the and yields 18=2(3+6) single tags(ST) and 45(=32 + 62) double tag yields(DT)

In a combined 2 fitter (physics/0503050), we extract 9 branching ratios and and yields : Include both statistical and systematic errors (with correlations): All experimental inputs treated consistently. Efficiency, cross-feed, background corrections performed directly in fit. Some systematic errors for and completely cancelled

Branching fractions are independent of L and cross-sections. The main variables used in the reconstruction are:

DD

00 DDN DD

N

1/ jiij ijjiDD DSSN /~

00 DDN

DDN

candidatebeam EEE


Yield Fits Unbinned ML fits to MBC (1D for ST, 2D for DT)

Signal function includes ISR, (3770) line shape, beam energy smearing, and detector resolution.

Signal parameters from DT fits, then apply to ST. Background: phase space (“ARGUS function”).

D and D yields and efficiencies separated.c

MBC (log scale) for ST modes:

ISR &

bea

m e

nergy

DT signal shape

Detectorresolution

All D0 DT

2484±51

All D+ DT1650±42

Two dimensional fit allows to separate ISR and beam energy spread (causes correlated

shifts in the mass of the two D’s) Detector resolution (uncorrelated among these

D’s )


Systematic uncertainties

Dominant error: MC simulation of tracking, K0

S, and 0 finding efficiencies: Correlated errors among all particles of

a given type add up quickly. Missing mass technique measure syst

errors by comparing data and MC: Fully reconstruct entire event, but

deliberately leave out one particle. Fraction of MM peak where the last

particle is found = efficiency.

Example: K efficiency from D0 K+

≈ 91% in fiducial volume

K found (MC)

K not found (MC)

K-+0, etc.

Source Uncertainty (%)

Tracking/K0s/0 0.7/3.0/2.0

Particle ID 0.3 /1.3 K

Trigger < 0.2

E cut 1.0—2.5 per D

FSR 0.5 ST / 1.0 DT

(3770) width 0.6

Resonant substructure

0.4—1.5

Event environment 0.0—1.3

Yield fit functions 0.5

Data processing 0.3

Double DCSD 0.8


Fit Results (PRL 95,121801) Precision comparable to PDG-04.

Statistical errors: ~2.0% neutral, ~2.5% charged from total DT yields.

(systematic) ~ (statistical). Many systematic errors are

measured in data and will be improved with time.

Our MC simulation includes FSR Using efficiencies without FSR

would lead to lower B.

NDD includes continuum and resonant production.

The CLEO-c measurement is the single most precise measurement for every

mode


Comparisons with other measurementsB

(D0 K

-+)

B(D

+ K-

++)

Other direct meas.

Overall C.L

25.9%

Reasonable agreement with PDG for all modes Measurements and errors normalized to PDG.

PDG numbers are correlated among modes PDG global fit includes ratios to K-+ or K-++.

No FSR corrections in PDG measurements Our measurements are also correlated (through statistics

and efficiency systematics).


Results for D cross sections Using a measurement of the luminosity of the data sample (55.8/pb), we obtain

nbDDee )07.007.060.3(00 nbDDee )10.007.079.2(

nbDDee )10.039.6( 17.008.0

)024.0776.0( 014.0

006.000

DDee

DDee

CLEO-c inclusive: nbhadronee )08.038.6()3770( 41.030.0

PRL 96, 092002

Our cross sections are in good agreement with BES [Phys.Lett. B 241, 278(1990) ] and higher than those of MARKIII [Phys.Rev.Lett. 60, 89 (1988) ]


Absolute Branching Fractions and Form Factor Measurements in

and

Introduction and Overview of the Analysis Measurements of Absolute Branching Fractions Measurements of Form Factors Summary

eKD /0 eKD 00/


Introduction Semileptonic decays are an excellent laboratory to study

Weak physics QCD physics

Gold-plated modes are P P semileptonic transitions as they are the simplest modes for both theory and experiment: Cabibbo favored : Cabibbo suppressed :

Main goals of the analysis: Measure efficiency-corrected absolutely-normalized decay rate distributions and

form factors Measure form factor parameters to test LQCD and model predictions

We analyze both D0 and D+ decays. By isospin invariance .

.

This is a nice cross check and adds statistics to improve statistical precision.

eDeDeKDeKD

00

00

,,

eDeD

eKDeKD00

00

2

)(

,)(24

)((

22

222

3)(

2

)(2

2

eMqwhere

qfPVG

dq

eKDd KcdcsF


Overview of the analysis Reconstruct one of the two D’s in a hadronic

decay channel. It is called a tagging D or a tag. Two key variables in the tagging D reconstruction are:

Reconstruct from the remaining tracks and showers the observable particles in the final state of a semileptonic decay.

Define an observable that can be used to separate signal and background as

where Emiss and Pmiss are the missing energy and momentum in the event, approximating the neutrino E and P. The signal peaks at zero in U.

Branching fractions are obtained as

22candidatebeambc PEM

candidatebeam EEE

K-

-

e+

K+

(3770)D0 D0

D0K+-, D0K-e+

tagMsemilep

semilepU

tagtagM

signalsemilep

Usemilep

bcbcN

N

N

NB

/

/

missmiss PEU

Obtained from Fits to U

Obtained from Fits to Mbc


D0 and D+ tag yields in 281/pb of DATA

~30% event tagging efficiency

~20% event tagging efficiency

Examples of Mbc for tag modes in the data

)281(/163~

:1

pbK

tagsDAll

)281(/308~

:1

0

pbK

tagsDAll

eventsK

KD

51~

0

eventsK

KD

98~

00

eventsK

KD

23~

000 eventsK

KD

80~

eventsK

KD

24~

0

eventsK

KD

16~

0

Tagging provides a beam of D mesons allowing semileptonic decays to be

reconstructed with no kinematic ambiguity


Measurements of

Absolute Semileptonic Branching Fractions


Fits to U in 281 pb-1 of Data for

Main backgrounds for


Electron fakes from kaons

eDeKKD

0

0*0 )( eKD0

eD0

eDeKD

)( 00

0

eKD /0

eKD 0

N~7000

eD 0

N~700

missmiss PEU


Fits to U in 281 pb-1 of Data for

eKD 0

eKD 00 /


Main Backgrounds for

eKKD )( 000*

eKKD )(0*

eKD 0

eKKD )( 000*

eD 0

N~2900

eKD 0

N~290 eD 0


Preliminary Results for BFs

)(024.0024.1)(

)(0

0

stateKD

eKD

)0.075(stat0.975 )(2

)(0

0

eD

eD

eKD 0 eD 0

eKD 0 eD 0


eKD 0 eD 0

Reasonable agreement

Systematically limitedStatistically limited

Comparisons with other experiments and projections for 750 pb-1


Measurements of

Semileptonic Form Factors


Two Fitting Methods: Fit A and Fit B

Fit A is a fit to efficiency-corrected and absolutely-normalized d/dq2 distributions. This fit is a good match for CLEO-c data as the q2 resolution is excellent. Fit A is our primary fit as the main goal of our analysis is to obtain d/dq2 and f+(q2).

Fit B is a fit to the observed decay rate according to a procedure described in D.M.Schmidt, R.J.Morrison and M.S.Witherell in Nucl. Instr. and Meth. A328 547(1993). The technique makes possible a (multidimensional) fit to variables modified by experimental acceptance and resolution. This method has been used by CLEO several times before, for example, to measure form factor ratios in ce and BD*l.

Both fitting methods were tested using large Monte Carlo samples. Two fits provide cross-checks.

The observed decay rate is related to the true decay rate in the following way:

in terms of Acceptance and Smearing functions. The fit has to take into account both effects. We have developed and tested two types of fits.


2q

d

d

D0→K-e+ν

2q

d

d

D0→π-e+ν

700 eventsS/B ~40/1

CLEOIII(Y(4S): q2 ~ 0.4 GeV2

CLEO-c((3770)): q2 ~ 0.012GeV2

q2 ~ 0.012GeV2

q2 ~ 0.011GeV2

Raw q2 distributionq2 resolution

q2 resolutions and Raw q2 distributions

Note the background in blue

7000 eventsS/B > 300/1

D0→π-e+ν

D0→K-e+ν


Efficiency corrected and absolutely normalized decay rates (DATA)

D0→K-e+ν D+→Kse+ν

D0→π-e+ν D+→π0e+ν

Subtracting background and applying efficiency corrections (matrices) we find absolute decay rates in bins of q2 (The bin width is equal q2

max/10, the last bins for D0e+

and D+0 e+ are 2 and 3 times wider):


Efficiency corrected and absolutely normalized decay rates (DATA)

These rates can be fit to any form factor model w/o knowing CLEO acceptance and resolution

The spectra on the last slide are tabulated here:


Form Factor Models

Simple pole model :

Modified pole model (BK) [Phys.Lett.B 52, 478,417(2000) ] :

Series parameterization [.Becher and R.Hill, hep-ph/0509090]

ISGW2 [Phys.Rev.D 52,2783,(1985) ] :

;

/1

022

2

poleMq

fqf

;/1

1

/1

02

)*(22

)*(2

2

sDsD MqMq

fqf

2

22max

22

121

qq

rqf

)()(

)0(/11

0

2

22)(

2

2

k

q

KD aFdq

qdf

f

mm

k

kk qza

qqPqf )0,(

0,

1 222

2


D0 K- e+ 7000 events

D0 - e+ 700 events

C-R Prediction Our Fits

anddqMqFM

MqFI

whereNI

M

polepole

pole

pole

212

22

,,

,1

The efficiency of fits is tested using the Cramer-Rao inequality:

The fitter is consistent with being fully efficient.

The fitter is consistent with being unbiased.

Mpole (GeV)

datastat0.1

Example:

The fitting techniques were tested by making ensembles of fits to mock data samples with the number of signal events equal to the expected number of events in the data. We have tested:

Fits for all 4 form factor models simultaneous fits to isospin conjugate modes fit with two free parameters [f+(0)Vcs and a form factor shape parameter]

Tests of Fit A and B


Example of a fit (DATA)



Modified Pole (BK) Model:


By isospin invariance:

eDeD

eKDeKD00

00

2

)()(

)()(22

22

00

00

qfqf

qfqfeDeD

eKDeKD

2/1

3)(2

2)( /

))((~)(

iKi

icdcs P

q

eKDqfV

The q2 spectra for isospin conjugate modes are consistent.

The plots show:

f +(q

2)V

cd D0→πe+ν

D+→π0e+ν

q2 (GeV2)

D+→KSe+ν

D0→Ke+ν

f +(q

2)V

cs

q2 (GeV2)

DATA Cross Check 1


Cross check 2: Hadron & Electron Spectra & W Helicity

D0→K-e+ν D+→Kse+ν D0→π-e+ν D+→π0e+ν

HadronMomentum

ElectronMomentum

cosW

Quantities that are not constrained in the fit are well described


Systematic Uncertainties for Form Factor Shape Parameters

PK(G

eV)

Systematic uncertainties that are independent of q2 (ex: tag Mbc fit function) do not change the decay rate shape and hence have a negligible contribution to the shape parameter uncertainty

Pe(

GeV

)

eff

Lepton momentum vs q2

q2 (GeV)

q2 (GeV)

Kaon ID efficiency

PK ~ 100MeV Few events

This correlation is not as strong as the hadron momentum correlation

Kaon momentum vs q2

Systematic effects correlated with the hadron (K/KS//0) momentum, change the decay rate distribution and lead to modest systematic uncertainties

Our studies indicate that the total systematic uncertainty is much smaller than the statistical uncertainty for each semileptonic mode


Fit results with two parameters The shape parameters for modified pole, simple pole model and series

parameterization with two parameters :

The normalization parameter for modified pole model and series parameterization with two parameters :


First measurements of form factors for the D+ modes;

CLEO-c is the most precise for D→πe+

D → K e+ νD → π e+

ν

Comparison with Other Measurements

GeVMsD

112.2* GeVM

D010.2*


First measurements of form factors for the D+ modes;

CLEO-c is the most precise for D→πe+

D → K e+

νD → π e+ ν

Comparison with Other Measurements


Confidence levels for fits results with 2 parameters

The confidence levels for fits with 2 parameters :

Which parameterization does the data prefer? The confidence levels for all parameterizations are comparable, as the functional forms for the parameterization are similar and the shape parameters are not fixed. However, the CLEO-c data exclude the ISGW2 (K/) , pole (K) and modified pole (K) parameterizations when the shape parameters are fixed to the physical values.


Data vs. physical basis for shape parameters

#1: ISGW2 Output Physical value for ISGW2

D0 K- e+ 1.567 ± 0.045 1.131

D0 - e+ 1.997 ± 0.114 1.410

D+ K0 e+ 1.476 ± 0.070 1.131

D+ -0e+ 1.806 ± 0.209 1.410

Form factor shape parameters in the data for ISGW2 are inconsistent with the model predictions

#2: Pole

#3: Modified Pole

Output Physical value for pole

D0 K- e+ 1.94 ± 0.04 2.112

Output Physical Value for effective pole

D0 K- e+ 0.26 ± 0.06 ~1.75

Because the data do not support the physical interpretation of these three parameterizations we use the series parameterization


Fit results with 3 parameters Our main form factor shape and intercept results are for the series parameterization :

)0,()0,(10,

222

2122

02 qzbqzbqqP

bqf

The series is expected to converge rapidly, so only the 1st few terms are expected to be measurable: we test for three


The fit results for 2 and 3 parameters are consistent with each other;

Noticeable improvement for 2 for D→Ke+ν with 3 parameters;

The modes do not show this trend as they lack the statistics to probe the third term in the expansion;

For D → Ke+ν the 3rd term b2 is a order of magnitude larger than b1. This cannot be interpreted as a lack of convergence if the series because both are consistent with zero indicating that the data does not yet have the sensitivity to determine three parameters simultaneously.

Interpretation


Comparison Between Parameterizations



--- Simple pole

--- Modified Pole --- Series with 2 par Series with 3 par Data

Data and Fit results are normalized to the fit results for the series parameterization with 3 parameters.


Plotted LQCD results (blue) are recent results of FNAL+MILC unquenched three flavor LQCD [C. Aubin et al., PRL 94 011601 (2005)] Lattice systematic uncertainties

dominate:

The green lines are our fits to CLEO-c data

The dashed lines show 1 (stat+syst) regions

.07.004.050.0;07.003.073.0)0(

:)(

f

KeDLQCD

.07.004.044.0;06.003.064.0)0(

:)(

f

eDLQCD

DATA FIT

LQCD

DATA FIT

LQCD

Form Factors as a Stringent Test of LQCDVcd = 0.22380.0029(CKM unitarity, i.e Vcd = Vus)

Vcs = 0.97450.0008(CKM unitarity)

eKD0

eD0


In these plots, the central values for our projections are equal to the central

values from the LQCD results

The anticipated precision for a larger 750 pb1 data sample to be collected in the future

D0→K-e+ν

D0→π-e+ν

Projections for and f+(0)


Vcs(d) and f+(0) determination Using

Vcs = 0.97450.0008 (CKM unitarity)

Vcd = 0.22380.0029 (CKM unitarity, i.e Vcd = Vus)

eD0

Using LQCD results [C. Aubin et al., PRL 94 011601 (2005)]: eKD0


Summary for D semileptonic studies

I have shown preliminary results for DK/ e+ branching fractions and form factor measurements from the 280/pb data sample collected at (3770). Results of this analysis include: the most precise branching fraction measurements for these decays

the most precise or first measurements of form factors for these modes

the most precise or first measurements of the efficiency corrected and absolutely normalized decay rates

a stringent test of LQCD calculations of semileptonic form factors


Thank you

In summary, CLEO-c provides:

unique input to test LQCD, the theory capable of solving strongly couple field theory equations, and

input to other experiments that help improve their measurements


Fit A: a 2 fit to efficiency corrected d/dq2

A brief description of the procedure for making Fit A:

Create an N x N efficiency matrix, where N is the number of q2 bins Invert the efficiency matrix Measure raw background subtracted q2 distributions Use the inverted efficiency matrix to obtain efficiency-corrected and absolutely-normalized d/dq2 (or the form

factor)

We make fits for form factor parameters to efficiency-corrected and absolutely-normalized d/dq2 (or the form factor), using the 2 fitter which includes both statistical and systematic errors (with correlations) :

bin migrations, background uncertainty, and efficiency corrections.

The low number of events in the high q2 bins can lead to biases in 2 fits, we find that the

- the decay rate

ij

jest

jcorreffij

iest

icorreff NNVNN 12

jcorreffN j

estN ijV

Bias, if any, is SMALL [~0.10(stat. data) ]

- the decay rate estimated from a form factor

- the correlation matrix


Efficiency Matrices

eKD0

eKD 0

eD0

eD 0

Full efficiency matrix for

Efficiency matrices in a truncated form for

10 bins

10 bins

9 bins

8 bins

We use 10 q2 bins for and . For and we use 9 and 8 bins, respectively. The last bin for these two modes are two or three times wider than other bins.

eKD0 eKD 0 eD0

eD 0

Do not need to read these tables

july, 2006 selected topics on open charm physics from cleo-c 1 selected topics on open charm physics...

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