From the Collaboration of Dmd, CP, CPT Results Sep. 11, 2008 CKM2008: WG4 Rome, Italy

Contents Introduction Dmd measurements Indirect CP violation measurements. CPT violation measurements – dilepton mode CPT violation measurements – hadronic mode (including Belle’s status and prospect on this issue) Summary

Analysis Procedure The analysis procedure of the Dmd and CPT is quite compatible to the standard mixing-induced CP one. e- e+ Brec Recon. (4S) Btag Flavor tag Dz Fully / partially reconstruct B decays Measure proper-time difference: Dt Determine Btag flavor and its ambiguity: q and w Evaluate Dmd / CPT asymmetry from the Dt and q

Master Equation for the Dt Predefinition of decay amplitudes Predefinition of intermediate parameters The most generic equation of the Dt distribution In BaBar’s paper h = a z: CPT-violating parameter.

Dmd Measurement Derivation from the master equation Opposite flavor Same flavor

Dmd Measurements Belle (latest) BaBar (latest) _ 152M BB pairs: D(*)-h+, D*ln # of total neutral B used in the fit = 122349. K.Abe et al., Phys. Rev. D71, 072003 (2005). BaBar (latest) 50k partially reconstructed D*ln events B.Aubert et al., Phys. Rev. D73, 012004 (2006). _

Dmd Measurement by Belle Event reconstruction Vertex reconstruction, Flavor tagging, then Maximum likelihood fit log lin For D*ln events N=37,562 cos qB,D*l: D*ln Mbc: D(*)+h- OF/SF asymmetry distribution

Dmd Measurement by Belle Systematic uncertainty Syst. and stat. errors get comparable. This item may be improved if the track selection criteria tuned more… Due to uncertainty of component fractions categorized in D**ln decay.

Dmd Measurement by BaBar Opposite flavor Same flavor Event reconstruction Vertex reconstruction, Flavor tagging, then Extended maximum likelihood fit 50k signal events in total. Binomial factor to account for the expected SF/(OF+SF) fraction to the observed one.

Dmd Measurement by BaBar Systematic uncertainty Syst. and stat. errors get comparable as well. Quoted as “possible fit bias” In the Belle’s analysis. Similar amount. Both Belle and BaBar results indicate we need technical break through to proceed further precise Dmd measurement.

Dmd Average PDG2008 average Dmd = 0.5070.005 ps-1  

Indirect CP Violation _ B0 B0 Mixing (1) _ B0 B0 Mixing (1) = Mixing (2) ? … yes: CP conservation … no: CP violation _ Mixing (2) B0 B0 Measurement or equivalently where p and q are defined in

Indirect CP Violation – Cont’d Belle 78 fb-1: 92k same-charge dilepton events. E.Nakano et al., Phys. Rev. D73, 112002 (2006). BaBar 200.8 fb-1: Dilepton and/or dipion events from D*ln decay. B.Aubert et al., hep-ex/0607091 (2006). DØ 3M dilepton events. E.Cheu et al., Nucl. Phys. Proc. Suppl. 170, 153 (2007).

CPT Violation in Mixing CPT violating parameter z in mixing Different notations of the z CPT violation In BB mixing _ The z is a complex number. Non-zero z indicates the CPT violation in mixing. BaBar (z, q/p) Belle (q, f) 

Master Equation of CPT Study Applications of the master equation CP eigenstate Flavor specific final state (e.g.: B0  D-p+, B0  D+p- case) Let ‘1’ for fully reconstructed side B, and ‘2’ for tag side B. TSI is ignored. _ _ DCSD and TSI are ignored. If DCSD is accounted for.

Examples of Dt Distribution (log(y)) Brec  fCP (hCP = -1), Basc  flavor specific Brec  flavor specific, Basc  flavor specific default Re(z) = +0.2 Im(z) = +0.2 DG/G = +0.2 DG/G = +0.2 Im(z) = +0.2 default Re(z) = +0.2 Im(z) = +0.2

CPT Measurements – Dilepton Belle (latest) 32 fb-1: 281k dilepton events. N. Hastings et al., Phys. Rev. D67, 052004 (2003). BaBar (latest) 232M BB pairs: 11M dilepton event candidates. B. Aubert et al., Phys. Rev. Lett. 96, 251802 (2006). _

Dilepton Event Analysis B1 D Interaction point profile Y B2 D Dz l2 n Lepton charge determines B flavor. Lepton is primarily decayed from B  B decay positions can be determined from the lepton track and an IP profile. Detector response can be precisely determined from J/yll events (with no secondary particle effect).

CPT Measurements – Hadronic Belle 535M BB pairs: D(*)-h+, D*ln, J/yK0 Not completed yet; Belle people are working on this issue now. BaBar 88M BB pairs: D(*)-h+, J/yK*(K+p-), J/yK0, J/yKL, y(2S)KS, cc1KS B. Aubert et al., Phys. Rev. Lett. 92, 181801 (2004). _ _

Status of Belle CPT – Hadronic Data set 535M BB pairs Decay modes (# of events including background) D-p+(39,366), D*-p+(46,292), D*-r+(45,913) D*ln(383,818) J/yKS(7,713), J/yKL(10,966) Monte Carlo data sets Parameterized simulation (“toy MC”) – for linearity study. GEANT full simulation – for detector response study, etc. 3 times of the data set, 81 input parameter variations for each 3-sets. _ Same sample as K.-F.Chen et al., PRL 98 031802.

Status of Belle CPT – Hadronic Extraction of CPT violating parameters CPT fitter w/ event-by-event maximum likelihood method. Parameters to be floated in the final fit: Re(z), Im(z), |q/p|, arg(q/p), DGd/Gd, Dmd, 10 wrong-flavor-tag probabilities, and ~15 detector response parameters. Linearity test with “Toy MC” “Toy MC” indicates Im(z) and arg(q/p) cannot be determined simultaneously unless both CP-even and CP-odd are used. Mathematically, this is due to the coefficient for a sin-term. This effect causes biased output from the likelihood fit. Correlations btw. Im(z) and arg(q/p) J/yKS J/yKS+J/yKL

Status of Belle CPT – Hadronic 270 “toy MC” sets with DGd/Gd=0 and variant arg(q/p) and z. Pull  (output-input)/fit_error J/yKS Mean shift observed arg(q/p) Im(z) J/yKS + J/yKL Mean shift canceled Beside them, the linearity of DGd/Gd and Re(z) are found OK.

Status of Belle CPT – Hadronic Linearity test with GEANT full simulation Going on; very preliminarily, no serious non-linearity is observed up to now. Expected statistical error e(Re(z)) < 0.027 e(Im(z)) < 0.006 Prospects The Belle tries to obtain central values within this month. ~ ~

Summary Both Dmd measurements by Belle and BaBar show the statistical uncertainties are comparable to the systematic ones. We need technical break through to access more precise measurement. Indirect CP violation measurements by Belle, BaBar, and DØ indicate the |q/p| is consistent to unity. CPT-violating parameter measurements with dilepton events by Belle and BaBar are reviewed. The one with hadronic event is only available by BaBar. Belle is making effort to update the numbers with 535M BB pairs. _

Backup

Mixing-Induced CP Violation Belle (latest) BaBar (latest) K.-F.Chen et al., Phys. Rev. Lett. 98, 031802 (2007). 535M BB pairs. _ B.Aubert et al., Phys. Rev. Lett. 99, 171803 (2007). 383M BB pairs. _ (hCP is CP eigenvalue.)