1

Charm Mixing and Strong Phases Using Quantum Correlations at

CLEO-c

Werner Sun, Cornell University5-8 August 2007, Charm07 Workshop, Ithaca, NY

MotivationTechnique

Results

5-8 August 2007, Charm07 Workshop, Ithaca, NYWerner Sun, Cornell University 2

Charm Mixing So Far

H12,H210 flavor eigenstates mass eigenstates.

Previous studies: Direct lifetime measurements:

Compare KK and with K.

Time-dependent Dalitz analysis of K0S :

Intermediate CP-eigenstates give y. Interference between CP+ and CP gives x.

Time-dependent wrong-sign rate D0 K: Interfering DCS and mixing amplitudes modulate

exponential decay time. Ambiguity from strong phase: y’ = y cosx sin

Time-dependence gives 1st-order x/y sensitivity: Need boosted D mesons to resolve decay time.

11 12 1111 11

21 22

where etc...2H HD D

i H M iH HD Dt

and

2

M

x y

( )1

( )

D K

yD KK

<KD0> / <KD0> = rei

Pre-winter 2007

2

00

2,1

DDD

5-8 August 2007, Charm07 Workshop, Ithaca, NYWerner Sun, Cornell University 3

Quantum Correlations at CLEO-c

At CLEO-c, interference comes for free. Appears in time-integrated yields.

1st-order sensitivity to y: Reconstruct KK (CP+) decay

other side must be D1 (CP) Inclusive KK rate probes y.

First measurement of cos: Reconstruct KK with K

K must come from D1 (CP).

ee * D0D0

C = 1

Forbidden byCP conservation

CP+ CP+

CP CP

Maximal enhancement CP+ CP

Forbidden if no mixing K K

Interference ofCF with DCS

K CP±

CP± K

Unaffected X Kl

200002 |||| DiDjDjDiM ij

KKDD

KK

KKKKKK

BN

ny

yBBn

1

21

)1(22 1

Effective Bat (3770)

)cos21(

1

||rate

2

2

200

rrB

reB

DKDK

K

iK

(3770)

5-8 August 2007, Charm07 Workshop, Ithaca, NYWerner Sun, Cornell University 4

Coherent vs. Incoherent Decay

We use yields for single tags (one D reconstructed) double tags (D and D reconstructed)

Compare QC effective B with incoherent B to give y and cos.

Sources of incoherent B: Externally measured Bs. Semileptonic tags at (3770) (immune to

QC). CP violation neglected.

DT K e+ CP+ CP

K RM/r2

K 1+2r2(12cos2

)

e 1 1

CP+

1 + 2rcos+ r2 1 0

CP 1 2rcos+ r2 1 2 0

ST1 + 2yrcos+

r2 11

y1 + y

quantum-correlated rateincoherent rate

D DX i

D Dj i

Yield / No-QC prediction0 1 2

Quantum correlationsare seen in data!

ST

DT

5-8 August 2007, Charm07 Workshop, Ithaca, NYWerner Sun, Cornell University 5

Analysis Overview

Dataset: 281 pb-1 = 106 C-odd D0D0. Combine inputs + error matrix in a 2 fit.

ST and DT yields Efficiencies (signal and background) Crossfeed/background estimates Systematic errors (small compared to

stat.) External B and y(‘) measurements

Single tag yields (8):

Fully-reconstructed DT yields (24):

Inclusive e or e vs. hadronic (14):

K0L0 (=CP+) vs. hadronic (5):

K 1 + 2yrcos+ r2

K 1 + 2yrcos+ r2

KK 1 y

1 y

K0S00 1 y

K0S0 1 y

K0S 1 y

K0S 1 y

K K (1)1+2r2(1-2cos2)

+r4

K K (1) (x2 + y2)/2

K K (1) (x2 + y2)/2

K CP+

(3) 1 + 2rcos+ r2

K CP (3) 1 2rcos+ r2

CP+ CP (9) 2

e K (1) 1

e K (1) 1

e/e CP+

(6) 1

e/e CP (6) 1

K0L0 K (2) 1 + 2rcos+ r2

K0L0 CP (3) 2

CP+

CP

5-8 August 2007, Charm07 Workshop, Ithaca, NYWerner Sun, Cornell University 6

Yield Measurements

Fully-reconstructed single tags: Fit beam-constrained mass

distribution.

Fully-reconstructed double tags: Two fully-reconstructed STs Count events in 2D MBC plane.

Inclusive semileptonic DTs: One fully-reconstructed ST Plus one electron candidate Fit e± momentum spectrum

K0L0 double tags:

One fully-reconstructed ST Plus one 0 candidate Compute missing mass-squared

Signal peaks at M2(K0).

22 || DbeamBC pEM

5-8 August 2007, Charm07 Workshop, Ithaca, NYWerner Sun, Cornell University 7

External Measurements

External inputs dramatically improve y and cosprecision.

All correlations among measurements included in fit.

Standard fit includes: Info on r needed to obtain cos:

RWS = r2 + ry’ + RM

RM = (x2 + y2)/2 Assume xsin = 0 y’~=

ycos CP-eigenstate Bs:

Also K because correlated in PDG

Extended fit averages y and y’: CP+ lifetimes (y) K0

S Dalitz analysis (x, y)

K CP-conserving fits (y’, r2, RM) Includes covariance matrices

from Belle, BABAR, CLEO (thanks!)

5-8 August 2007, Charm07 Workshop, Ithaca, NYWerner Sun, Cornell University 8

Fit Results

Likelihood curves +95% CL ULs

Standard fit:

cos > 0.54 |sin| < 0.72

Extended fit:

cos > 0.38 |sin| < 0.84

Parameter Standard Fit Extended Fit

NDD106 1.046±0.019±0.013

1.044±0.019±0.012

y (10-3) 33 ± 16 ± 10 [4.3 ± 1.3 ± 0.7]

r2 (10-3) [6.6 ± 1.9 ± 0.8][3.39 ± 0.08 ±

0.00]

cos 1.03 ± 0.19 ± 0.08

0.93 ± 0.32 ± 0.04

x2 (10-3) [0.6 ± 1.3 ± 0.7][0.05 ± 0.05 ±

0.00]

B(K) (%)[3.77 ± 0.07 ±

0.03][3.77 ± 0.07 ±

0.03]

B(KK) (10-3)[3.81 ± 0.09 ±

0.03][3.88 ± 0.08 ±

0.03]

B() (10-3)[1.35 ± 0.03 ±

0.01][1.36 ± 0.03 ±

0.01]

B(K0S00)

(10-3)8.08 ± 0.34 ±

0.518.35 ± 0.32 ±

0.52

B(K0S0) (%) [1.18 ± 0.03 ±

0.03][1.14 ± 0.03 ±

0.03]

B(K0S) (10-3) [4.56 ± 0.21 ±

0.25][4.41 ± 0.19 ±

0.25]

B(K0S) (%) [1.16 ± 0.04 ±

0.06][1.11 ± 0.03 ±

0.05]

B(Xe) (%)6.55 ± 0.16 ±

0.176.59 ± 0.16 ±

0.17

B(K0L0) (%) [0.98 ± 0.03 ±

0.02][1.02 ± 0.03 ±

0.02]

2/ndof 27.8/46 58.1/58

B measurements do not supersede other CLEO-c results!

[ ] = with external input

CLEO PRELIMINARY

5-8 August 2007, Charm07 Workshop, Ithaca, NYWerner Sun, Cornell University 9

Comments on Results Information in inputs: observe change in parameter

errors when removed from fit. y: [Info: 50% KK ST+Bext, 20% ST+Bext, 15% e±/CP

DTs] 2.1 discrepancy between CLEO-c and world average. Checked extensively for bias; none found

statistical fluctuation. cos: [Info: 45% K/CP+ DTs, 45% K/CP DTs]

Strong nonlinearity introduced by RWS ~= r2 + 2yrcos:

1- likelihood contoursin y vs. cos

(excludes xsin error)

Extended fit

Error on cosdepends onvalue of y

Standard fit

y’ not incl.

Standard fit

5-8 August 2007, Charm07 Workshop, Ithaca, NYWerner Sun, Cornell University 10

Other Systematic Effects (I)

C+ contamination of initial state (not expected, cf. A. Petrov): ee D0D0 is C+, but photon must be radiated from D0 or D0,

or from (3770) itself. ISR, FSR, bremsstrahlung photons do not flip C eigenvalue.

Allow fit to determine C+ fraction. Include same-CP double tags (CP±/CP±).

Allowed decay only for C+. All yields consistent with zero.

Fit each yield to sum of C and C+ contributions. Results: C+/C = 0.003 ± 0.023.

No evidence for C+. Other results unchanged.

5-8 August 2007, Charm07 Workshop, Ithaca, NYWerner Sun, Cornell University 11

Other Systematic Effects (II)

Standard fit, for (xsin) = ±0.0034: cos = 1.03 ± 0.19 (stat) ± 0.08 (syst) ± 0.02 (xsin) y = 0.033 ± 0.016 (stat) ± 0.10 (syst) ± 0.00 (xsin)

Extended fit, (xsin) still under investigation: cos = 0.93 ± 0.32 (stat) ± 0.04 (syst) ± 0.?? (xsin) y = +0.0043 ± 0.0013 (stat) ± 0.0007 (syst) ± 0.00?? (xsin) Alternative: fit for xsin by sacrificing improvement in y precision.

Variation of cos and y with xsin—include additional systematic error:

CLEO PRELIMINARY

Standard fit Extended fit

5-8 August 2007, Charm07 Workshop, Ithaca, NYWerner Sun, Cornell University 12

Summary

First measurement of cos(needed to interpret other D mixing results). Allows y’ to be added to world-average y, but with the assumption xsin = 0.

Can measure xsin using C+ D0D0 pairs from ee D0D0 at Ecm = 4170 MeV.

Demonstrated new technique for charm mixing studies. Time-independent 1st-order sensitivity to mixing parameters and phases. Different systematics from other experiments. With full CLEO-c dataset (Ecm = 3770 & 4170 MeV) expect:

(cos)~±0.1—0.2 (y)~±0.01 (xsin)~±0.03

Extended fit: cos = 0.93 ± 0.32 (stat) ± 0.04 (syst) ± 0.?? (xsin) y = +0.0043 ± 0.0013 (stat) ± 0.0007 (syst) ± 0.00??

(xsin)

Standard fit: cos = 1.03 ± 0.19 (stat) ± 0.08 (syst) ± 0.02 (xsin) y = 0.033 ± 0.016 (stat) ± 0.10 (syst) ± 0.00 (xsin)

CLEO PRELIMINARY

5-8 August 2007, Charm07 Workshop, Ithaca, NYWerner Sun, Cornell University 13

BACKUP SLIDES

5-8 August 2007, Charm07 Workshop, Ithaca, NYWerner Sun, Cornell University 14

Previous Results (Oct 2005)

PANIC’05 prelim. results: 281 pb-1. No systematics. Only one CP mode. With r2 constrained to world

average, cos = 1.08 ± 0.66. No other external

measurements. Now:

Added 70% more CP K0

SK0S

Added K0L0.

Param. ValuePDG04 or CLEO-c

NDD(1.09 ±

0.04)x106

(1.01 ± 0.02)x106

y -0.057 ± 0.066 0.008 ± 0.005

r2 -0.028 ± 0.069

(3.74 ± 0.18)x10-3

PDG + Belle + FOCUS

rz 0.130 ± 0.082

RM(1.74 ±

1.47)x10-3 < ~1x10-3

B(K) (3.80 ± 0.29)% (3.91 ± 0.12)%

B(KK)(0.357 ± 0.029)%

(0.389 ± 0.012)%

B()(0.125 ± 0.011)%

(0.138 ± 0.005)%

B(K0S00

)(0.932 ± 0.087)%

(0.89 ± 0.41)%

B(K0S0) (1.27 ± 0.09)% (1.55 ± 0.12)%

B(Xe) (6.21 ± 0.42)% (6.87 ± 0.28)%

5-8 August 2007, Charm07 Workshop, Ithaca, NYWerner Sun, Cornell University 15

Mode-dependent correlated uncertainties cancel in y and cos, but only if external measurements are not included. Tracking, 0, , K0

S, PID, EID efficiency, FSR systematics: use DHad.

E cut, mass cut, K0S mass cut, K0

S flight significance cut, K0S

PID. Peaking background BFs: values and errors from PDG. Multiple candidates, SL form factor. Event selection variations:

dominates y and cosd syst error.

Uncorrelated uncertainties: Fit function variations.

Systematic Uncertainties