strong phase measurements – towards g at cleo-c andrew powell (university of oxford) on behalf of...

Strong Phase Measurements –

Towards at CLEO-c

Andrew Powell (University of Oxford)Andrew Powell (University of Oxford)On behalf of the CLEO-c collaborationOn behalf of the CLEO-c collaboration

D measurements relevant to determining via B± DK±

• D K, K, K0 (ADS)

• D KS (Binned Dalitz)

2 Andrew Powell, University of Oxford 7th-11th September 2009, Beauty ‘09, Heidelberg

• is unique: only CP violation parameter than can be measured via both ‘tree’ and ‘loop’ B decays

• Tree-level: SM

• Loop-level: SM + NP

• Comparison of these measurements sensitive to New Physics (NP)

• Tree-level measurement currently poorly constrained

Why Measure Tree-Level ?

[CKM Fitter, Summer 2009]

1


• Rates dependent on the B-specific parameters:• rB

• B

• • …and D-specific parameters (analogous to those of B):

• rD

• D

from B± DK±

2

• Methodology and formalism given in previous talk (S. Ricciardi)

• Strong-phases, D, directly accessible in Quantum-Correlated D-decays


Introduction to CLEO-c• Detector at the Cornell Electron Storage Ring (CESR)

• Operated at energies equal to and above cc threshold

• Relevant data sets for precision CKM measurements:• ECM = 4170 MeV int ~ 600 pb-1

Determination of form factor fDs at CLEO-c, a critical test of LQCD and sensitive to New Physics [see talks by Rademacker & Spradlin]

• (3770) int = 818 pb-1

Important for analyses discussed in this talk

3

Cornell University,Ithaca, NY, USA


Introduction to CLEO-c• Detector at the Cornell Electron Storage Ring (CESR)

• Operated at energies equal to and above cc threshold

• Relevant data sets for precision CKM measurements:• ECM = 4170 MeV int ~ 600 pb-1

Determination of form factor fDs at CLEO-c, a critical test of LQCD and sensitive to New Physics [see talks by Rademacker & Spradlin]

• (3770) int = 818 pb-1

Important for analyses discussed in this talk

( = -1)• (3770)

• e+e- (3770) D0D0

• Quantum-Correlated System, conserving = -1

• Enables ‘-tagging’• Reconstructing one D-meson in a -eigenstate, can infer the ‘opposite-side’ D-meson to be of opposite

• Perks to threshold running:• Very clean – no fragmentation particles• Allows for reconstruction of unseen particles (KL) (3770) D0(K)D0()

3

Cornell University,Ithaca, NY, USA

‘ADS’ Type Measurements


2-Body ADS

f(D) = non- eigenstate (e.g. K)

• Defining strong-phase difference:

• Generalised matrix element:

4

[Phys Rev Lett 78, 3257 (1997)]


2-Body ADS




• Generalised rate (trivial phase space):

• Four charge combinations 2 suppressed (high sens.) + 2 favoured rates (low sens.)

• What about multi-body, non- eigenstates of the D-meson?

[Phys Rev Lett 78, 3257 (1997)]

4


Multi-Body ADSf(D) = non- eigenstate (e.g. K)



5

Must now consider the amplitudes at each point in multi-body phase space (x)

[Phys Rev. D 68, 033003 (2003)]

10

Andrew Powell, University of Oxford 7th-11th September 2009, Beauty ‘09, Heidelberg

Multi-Body ADS

Must now consider the amplitudes at each point in multi-body phase space (x)



• Generalised rate (integrating over ALL multi-body phase space):

The “Coherence Factor”

5

[Phys Rev. D 68, 033003 (2003)]


11


Quantum Correlations at (3770)

6

e+ e-

’’

D ()

D () • Generalised double-tagged (DT) rate:

QM = 1 – (x2 – y2)/2 RM = (x2 + y2)/2

• To access K, consider K tagged against a eigenstate :

[ Need info on rD – see later]

12


Quantum Correlations at (3770)

6

e+ e-

’’

D ()

D () • Generalised double-tagged (DT) rate:

QM = 1 – (x2 – y2)/2 RM = (x2 + y2)/2

• To access K, consider K tagged against a eigenstate :

[ Need info on rD – see later]

• To access K, consider K0 tagged against a eigenstate :

• To access R, consider K0 tagged against itself, like-charge Kaons:

13


Quantum Correlations clearly seen!

7

K Measurement [Phys Rev. D 78, 012002 (2008)]

[Phys Rev. Lett. 100, 221801 (2008)]

• Extensive K and charm-mixing (x, y) measurement• Consider both double- (DT) and single-tags (ST)• Compare coherent/incoherent ’s

[Phys Rev. D 73, 034024 (2006)]

QC rateincoherent rate

K e

K RM / RWS

K 1+2RWS - 4rcos(rcos+ y)

e 1- r(ycos+ xcos) 1

1- (2rcos+ y) / (1 + RWS) 1+ y 0

1+ (2rcos+ y) / (1 + RWS) 1+ y 2 0

ST 1 1 1 1

RWS = r2 + ry’ + RM

Avg.(Yield / No-QC prediction)

Single Tags

• Combine inputs + errors matrices in a 2 fit

• External inputs:• RWS & RM (to determine rD and extract cosD)• ’s (K, -eigenstates) 0 1 2

14


K Result (281 pb-1) [Phys Rev. D 78, 012002 (2008)]

[Phys Rev. Lett. 100, 221801 (2008)]

8

[Phys Rev. D 73, 034024 (2006)]

• Extended fit with a likelihood scan of the physically allowed region leads to a measurement of:

• Fit result important component in average of charm mixing

• Result to be updated using full 818 pb-1 and with additional tags

15


Rf & f Measurements[Phys Rev. D 80, 031105(R) (2009)]

9

K K

K

(OS)[NDD]

K

(LS)

K

(OS)[NDD]

[rec.(D )]

'2

2

.)(

1

1

KKD

KππK

D

M

K

yrR

rR

R

'2

'2'

.1

)(1

)cos(2)(1

KKD

KD

M

KKKDD

yrr

RRrr

)cos(1 KK

KDCP Rry


• Multi-body ADS modes considered:• f = K0 & K+

NEW

yf’ = ycosf - xsinf rD’ = (rK/rK)

• DTs using full 818 pb-1 dataset• f tagged against , f, f• Also, K tagged against (Normaliastion)

Double-Tag

DK3vs

DKL

Bkg

16


Rf & f Measurements[Phys Rev. D 80, 031105(R) (2009)]

9

• Multi-body ADS modes considered:• f = K0 & K+

NEW

K: K:

• DTs using full 818 pb-1 dataset• f tagged against , f, f• Also, K tagged against (Normaliastion)

Double-Tag

DK3vs

DKL

Bkg

yf’ = ycosf - xsinf rD’ = (rK/rK)

K K

K

(OS)[NDD]

K

(LS)

K

(OS)[NDD]

[rec.(D )]

'2

2

.)(

1

1

KKD

KππK

D

M

K

yrR

rR

R

'2

'2'

.1

)(1

)cos(2)(1

KKD

KD

M

KKKDD

yrr

RRrr

)cos(1 KK

KDCP Rry


17


RK & K Results

10

[Phys Rev. D 80, 031105(R) (2009)]

NEW

RK = 0.84

K= (227 )1417

• Very coherent!• Almost at ‘2-body’ limit

• Good news for ADS measurement

• Interference term will be large• High sensitivity to

18


RK3 & K3 Results

11

[Phys Rev. D 80, 031105(R) (2009)]

NEW

RK3 = 0.33

K3= (114 ) 2623

0.260.23

• Low coherence preferred• Low direct sensitivity to

• Paradoxically, also good news for ‘global’ measurement

• B D(K3)K rates will therefore be highly sensitive to rB, which is a very valuable constraint for sister B DK analyses

Poorly know

19


Impact of CLEO-c at LHCb[LHCb-2008-31]

12

• Expected precision at LHCb with 2 fb-1 of data (1 year) for ADS modes alone:

• Significant improvements in sensitivity when using CLEO-c results• Using RK3 & K3 results - equivalent to a doubling of LHCb data!

• Precision including K0 yet to be studied

‘Dalitz’ Type Measurements

21


from BD(KS)K Dalitz

• Three ingredients to measurement:

Dflavour

AmplitudeModel

+ +

• Current best constraints on from Dalitz plot analyses at BABAR & Belle

Belle

: arX

iv:0

804.

2089

• With enough statistics (LHCb), measurement becomes systematically limited• Need an alternative, model-free, method…

BABAR (383M bb)

BELLE (657M bb)

D0KS

BD(KS)K

13

22


Model-Independent Method[Phys Rev. D 68, 054018 (2003)]

[Euro. Phys. J. C 55 (2008) 51][Euro. Phys. J. C 47 (2006) 347]

14

• i known from flavour-tagged D sample (D*)

• D = strong phase-difference between D & D

• ci = < cos(D) >i

• si = < sin(D) >i

• Counting experiment proposed by Giri et al., developed by Bondar & Poluektov

• Consider Bevents in bin i of Dalitz plot:

23




s12 [GeV2]

s 13 [G

eV2 ]

Bin Num

ber

14



• Choosing bins of ‘expected’ similar D maximises statistical precision to

• Small loss in statistical sensitivity w.r.t. unbinned method… but no model error!

[Model = BABAR PRL 95 121802 (2005)]

D = 180° D = 0°

• ci = < cos(D) >i

• si = < sin(D) >i



24






s12 [GeV2]

s 13 [G

eV2 ]

D = 180° D = 0°

Bin Num

berCan be measured directly in quantum correlated

decays at (3770)

14



• Choosing bins of ‘expected’ similar D maximises statistical precision to

• Small loss in statistical sensitivity w.r.t. unbinned method… but no model error!

[Model = BABAR PRL 95 121802 (2005)]

• ci = < cos(D) >i

• si = < sin(D) >i

25


CLEO-c KS,LAnalysis

15

• As shown previously, cos() accessible from -tagged decays:•

• sin() accessible from ‘double-Dalitz’ plot:•

• Use all 818 pb-1 of (3770)

• Flavour Tags (i): ~20k

• Tags (ci): ~1,600

• Double K0ci & si: ~1,300

[Phys Rev. D 80, 032002 (2009)]

NEW

• S/B ~ 10 – 100 depending on tag mode

26


On Using KL [Phys Rev. D 80, 032002 (2009)]

NEW

16

• KS + KL• Source of additional statistics!• Approx. equality seen in data

• However, a correction term:

• (tan2C)• ci ci’

ci, si from KSci’ si’ from KL

Even

ts /

0.0

5 G

eV2

Even

ts /

0.0

5 G

eV2

M2() [GeV2]

Even

ts /

0.0

5 G

eV2

M2() [GeV2]

M2() [GeV2]

Even

ts /

0.0

5 G

eV2

M2() [GeV2]

KL KS

tags

tagstags

tags

• Determine ci = ci-ci’, si = si-si’• Introduces small model dep.

• ci/ si floated as a 2 term in fit

27


On Using KL [Phys Rev. D 80, 032002 (2009)]

NEW

16

M2(KL) [GeV2]

M2 (K

L) [

GeV

2 ]

M2(KS) [GeV2]

M2 (K

S )

[GeV

2 ]

M2 (K

L) [

GeV

2 ]

M2(KL) [GeV2]

M2 (K

S )

[GeV

2 ]

M2(KS) [GeV2]

• KS + KL• Source of additional statistics!• Approx. equality seen in data

• However, a correction term:

• (tan2C)• ci ci’

ci, si from KSci’ si’ from KL

• Determine ci = ci-ci’, si = si-si’• Introduces small model dep.

• ci/ si floated as a 2 term in fit

KL

tags

KS

tags

tagstags

28


CLEO-c Results: ci & si[Phys Rev. D 80, 032002 (2009)]

NEW

17

• Result stat sys (KL KS syst)

• Statistical uncertainties dominant• ci better determined than si

• Results also available for ci’ & si’ • Broad agreement with model predictions

[Model = BABAR PRL 95 121802 (2005)]

• Uncertainty: CLEO-input() = 1.7 (recall model error = 7)

29


Conclusions & Outlook

18

• Several CLEO-c results available applicable to -type analyses• D Kstrong phase difference [~1/3 of total (3770) data used]

• D Kocoherence factors & strong phase differences

• D KS(L)ci(‘) & si(‘) in 8 bins of equal D widthAll (3770) data used

• These results provide invaluable input to the measurement• See LHCb- talk [S. Ricciardi]

• More yet to come!• D Kfull 818 pb-1 result• D KS(L)optimal binning for maximal -sensitivity • D KS(L)ci(‘) & si(‘) measurements

• D KS(L)possible analysis

Backup

31


External Inputs to Fit[Phys Rev. D 78, 012002 (2008)]

[Phys Rev. Lett. 100, 221801 (2008)][Phys Rev. D 73, 034024 (2006)]

• External inputs improve y and K precision

• All correlations amongst measurements included in fit

• Standard fit includes:• Info needed to obtain cos:

• RWS = r2 + ry’ + RM

• RM = (x2 + y2)/2• xsin = 0 y’~ ycos

• K and -eigenstate s

• Extended fit averages y and y’• lifetimes (y)• KSDalitz analysis (x, y) • K -conserving fits (y, r2, RM):

32


External Fit Likelihoods[Phys Rev. D 78, 012002 (2008)]

[Phys Rev. Lett. 100, 221801 (2008)][Phys Rev. D 73, 034024 (2006)]

33


-Observable Results[Phys Rev. D 80, 031105(R) (2009)]

NEW

• Systematic for dominated by internal uncertainty associated w/ the

rec x (D ) normalisation• Finite -tagged K statistics

• Systematic for all other observables are small, and dominated by knowledge of s

• Extracted from PDG

• Observables dependent on x, y, K, rD in addition to parameters of interest

• Perform 2 fit, placing external constraints on x, y, K parameters

• Constraints taken from HFAG• Correlations included

34


K0 Likelihood Scans[Phys Rev. D 80, 031105(R) (2009)]

NEW

LS

LSAllConstraints

35


K3 Likelihood Scans[Phys Rev. D 80, 031105(R) (2009)]

NEW

LS

LSAllConstraints

36


Colour Suppressed

rB ~ 0.1

• Extraction through interference between b u and b c transitions

• Comparison of B- and B+ rates allow to be extracted

• D0 specific parameters also contribute to B- and B+ rates • e.g. strong-phase differences, D

• Can be accessed via Quantum-Correlated D-decays

rD & D analogous to rB & B. For multi-body final states these

parameters vary over phase space

from B± DK±

• Require both D0 and D0 to decay to a common final state, f(D)

• f(D) = K, K, K0, KS, …

37


CLEO-c Detector

strong phase measurements – towards g at cleo-c andrew powell (university of oxford) on behalf of...

Documents

r d d d g

d meson

r b d b g

b dk d

heidelberg g

cornell university

e e y3770 d

high g