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

2. 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

3. 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

4. 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.

5. Dmd Measurement Derivation from the master equation Opposite flavor
Same flavor

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

7. 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

8. 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.

9. 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.

10. 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.

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

12. 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

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

14. 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) 

15. 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.

16. 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

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

18. Dilepton Event AnalysisB1 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).

19. 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, (2004). _ _

20. 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

21. 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

22. 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.

23. 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)) <
e(Im(z)) <
Prospects
The Belle tries to obtain central values within this month. ~ ~

24. 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. _

25. Backup

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