1. 1 Charm Mixing and Strong Phases Using Quantum Correlations at CLEO-c Werner Sun, Cornell University 5-8 August 2007, Charm07 Workshop, Ithaca, NY (Revised 19 November 2007) Motivation Technique Results

2. 5-8 August 2007, Charm07 Workshop, Ithaca, NYWerner Sun, Cornell University 2 Charm Mixing So Far  H 12,H 21  0  flavor eigenstates  mass eigenstates.  Previous studies:  Direct lifetime measurements:  Compare K  K  and     with K   .  Time-dependent Dalitz analysis of K 0 S     :  Intermediate CP-eigenstates give y.  Interference between CP+ and CP  gives x.  Time-dependent wrong-sign rate D 0  K    :  Interfering DCS and mixing amplitudes modulate exponential decay time.  Ambiguity from strong phase: y’ = y cos  x sin   Time-dependence gives 1 st -order x/y sensitivity:  Need boosted D mesons to resolve decay time. / =  re  i  Pre-winter 2007

3. 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.  1 st -order sensitivity to y:  Reconstruct K  K  (CP+) with SL  SL must be D 1 (CP  ).  SL width indep. of CP, but total width depends on CP, so effective branching fraction probes y.  First measurement of cos  :  Reconstruct K  K  with K     K    must come from D 1 (CP  ). e  e    *  D 0 D 0 C =  1 Forbidden by CP conservation CP+ CP  Maximal enhancement CP+ CP  Forbidden if no mixing KK KK Interference of CF with DCS KK CP± KK Inclusive unaffected X K   , CP, K  l  Effective B at  (3770)  (3770) semileptonic

4. 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 B s.  Single tags at  (3770) (immune to QC).  CP violation neglected. DT KK e+e+ CP  CP  KK R M / R WS KK 1  2R WS  4rcos  (rcos  y) ee 1  r (ycos  xsin  ) 1 CP  1  (2rcos  y) / (1  R WS )1  y 0 CP  1  (2rcos  y) / (1  R WS )1  y 20 ST1111 quantum-correlated rate incoherent rate DD Xi DD ji Yield / No-QC prediction 012 Quantum correlations are seen in data! ST DT R M = (x 2 + y 2 )/2 R WS = r 2 + ry’ + R M

5. 5-8 August 2007, Charm07 Workshop, Ithaca, NYWerner Sun, Cornell University 5 Analysis Overview  Dataset: 281 pb -1 = 10 6 C-odd D 0 D 0.  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):  K 0 L  0 (=CP+) vs. hadronic (5): KK 1 KK 1 KKKK 1  1 K0S00K0S00 1 K0S0K0S0 1 K0SK0S 1 K0SK0S 1 KK KK (1) 1  2R WS  4rcos  (rcos  y) KK KK (1)(x 2 + y 2 )/2R WS KK KK (1)(x 2 + y 2 )/2R WS KK CP+(3) 1  (2rcos  y) / (1  R WS ) KK CP  (3) 1  (2rcos  y) / (1  R WS ) CP+ CP  (9)2 ee KK (1) 1  r (ycos  xsin  ) ee KK (1) 1  r (ycos  xsin  ) e  /e  CP+(6) 1  y e  /e  CP  (6) 1  y K0L0K0L0 KK (2) 1  (2rcos  y) / (1  R WS ) K0L0K0L0 CP  (3)2 CP+ CP 

6. 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 M BC plane.  Inclusive semileptonic DTs:  One fully-reconstructed ST  Plus one electron candidate  Fit e ± momentum spectrum  K 0 L  0 double tags:  One fully-reconstructed ST  Plus one  0 candidate  Compute missing mass-squared  Signal peaks at M 2 (K 0 ).

7. 5-8 August 2007, Charm07 Workshop, Ithaca, NYWerner Sun, Cornell University 7 External Measurements  External inputs improve y and cos  precision.  All correlations among measurements included in fit.  Standard fit includes:  Info on r needed to obtain cos  :  R WS = r 2 + ry’ + R M  R M = (x 2 + y 2 )/2  Assume xsin  = 0  y’~= ycos   CP-eigenstate B s:  Also K  because correlated in PDG  Extended fit averages y and y’:  CP+ lifetimes (y)  K 0 S     Dalitz analysis (x, y)  K  CP-conserving fits (y’, r 2, R M )  Includes covariance matrices from Belle, BABAR, CLEO (thanks!)

8. 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 ParameterStandard FitExtended Fit N D  D   10 6  1.046±0.019±0.0131.044±0.019±0.012 cos  1.03 ± 0.19 ± 0.080.93 ± 0.32 ± 0.04 y (10 -3 ) Still under study r 2 (10 -3 ) x 2 (10 -3 ) B (K    ) (%) [3.77 ± 0.07 ± 0.03] B (K  K  ) (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 (K 0 S  0  0 )(10 -3 ) 8.08 ± 0.34 ± 0.518.35 ± 0.32 ± 0.52 B (K 0 S  0 ) (%) [1.18 ± 0.03 ± 0.03][1.14 ± 0.03 ± 0.03] B (K 0 S  ) (10 -3 ) [4.56 ± 0.21 ± 0.25][4.41 ± 0.19 ± 0.25] B (K 0 S  ) (%) [1.16 ± 0.04 ± 0.06][1.11 ± 0.03 ± 0.05] B (X  e  ) (%) 6.55 ± 0.16 ± 0.176.59 ± 0.16 ± 0.17 B (K 0 L  0 ) (%) [0.98 ± 0.03 ± 0.02][1.02 ± 0.03 ± 0.02]  2 /ndof 27.8/4658.1/58 B measurements do not supersede other CLEO-c results! [ ] = with external input CLEO PRELIMINARY

9. 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: 90% e ± /CP DTs, 10% e ± /K  DTs]  cos  : [Info: 50% K  /CP+ DTs, 50% K  /CP  DTs]  Strong nonlinearity introduced by R WS ~= r 2 + 2yrcos  : 1-  likelihood contours in y vs. cos  (excludes xsin  error) Extended fit Error on cos  depends on value of y Standard fit

10. 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):  e  e    D 0 D 0 is C+, but photon must be radiated from D 0 or D 0, 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.

11. 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  )  Extended fit,  (xsin  ) still under investigation:  cos  = 0.93 ± 0.32 (stat) ± 0.04 (syst) ± 0.?? (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 xsin 

12. 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+ D 0 D 0 pairs from e  e    D 0 D 0 at E cm = 4170 MeV.  Demonstrated new technique for charm mixing studies.  Time-independent 1 st -order sensitivity to mixing parameters and phases.  Different systematics from other experiments.  With full CLEO-c dataset (E cm = 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  )  Standard fit:  cos  = 1.03 ± 0.19 (stat) ± 0.08 (syst) ± 0.02 (xsin  ) CLEO PRELIMINARY

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

14. 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 r 2 constrained to world average, cos  = 1.08 ± 0.66.  No other external measurements.  Now:  Added 70% more CP   K 0 S  K 0 S   Added K 0 L  0. Param.ValuePDG04 or CLEO-c NDDNDD (1.09 ± 0.04)x10 6 (1.01 ± 0.02)x10 6 y-0.057 ± 0.0660.008 ± 0.005 r2r2 -0.028 ± 0.069 (3.74 ± 0.18)x10 -3 PDG + Belle + FOCUS rz0.130 ± 0.082 RMRM (1.74 ± 1.47)x10 -3 < ~1x10 -3 B (K    ) (3.80 ± 0.29)%(3.91 ± 0.12)% B(KK)B(KK)(0.357 ± 0.029)%(0.389 ± 0.012)% B()B() (0.125 ± 0.011)%(0.138 ± 0.005)% B(K0S00)B(K0S00) (0.932 ± 0.087)%(0.89 ± 0.41)% B(K0S0)B(K0S0) (1.27 ± 0.09)%(1.55 ± 0.12)% B (X  e  ) (6.21 ± 0.42)%(6.87 ± 0.28)%

15. 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, , K 0 S, PID, EID efficiency, FSR systematics: use DHad.   E cut,  mass cut, K 0 S mass cut, K 0 S flight significance cut, K 0 S 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