1. Search for Time-integrated CP Violation in 3-body Cabibbo-suppressed D0 Decays
G. Mancinelli, B.T. Meadows, K. Mishra, M.D. Sokoloff
University of Cincinnati
BaBar Collaboration Meeting, December 2007

2. CP Violation in Charm Decays
SM predictions O(0.01%).
New Physics must be playing a role if an asymmetry is observed with present experimental sensitivity [O(1%)].
The CP violation can be of any of the three types:
- in decay
- in mixing between D0 and D0
- in interference of decay with mixing
Indirect CPV is universal.
Direct CPV is localized => different parts of phase-space might have different asymmetries (and may even cancel each other out when integrated over the whole phase-space).
 CPV in charm decays highly suppressed.
 direct CPV. –
 indirect CPV.
Kalanand Mishra
BaBar Coll. Meeting, December 2007

3. New Physics Scenarios For details:
CPV ~ 1% will be a strong evidence for non-SM processes
Most SUSY models predict enhancement of CP asymmetry in charm decays:
- Minimal flavor violation models predict tiny, unobservable effects.
- Squark alignment models predict large indirect and large direct CPV.
- Models with squark degeneracy predict small indirect and large direct CPV.
If direct CPV is at 1% level, its likely source is new physics in loop diagrams.
SCS D0 decays are unique in the sense that they are sensitive to the effects of “gluonic penguin” SUSY operators. Both CF and DCS decays have vanishing contributions from these operators.
Y. Grossman, A.L. Kagan, and Y. Nir, Phys. Rev. D75, (2007).
I.I. Bigi, hep-ph/ (2001).
For details:
Kalanand Mishra
BaBar Coll. Meeting, December 2007

4. Why 3-body SCS D0 Decays ?
3-body decays permit the measurement of phase differences which are required to create CP violation in the interference between SM and non-SM processes.
Access to both CP eigen states (0π0, f0π0, π0 ) and flavor states (π-+, K*K-+). Therefore, can probe diverse possibilities of CPV.
Also, these are relatively high statistics modes (84 k D0/D0πππ0 and 15 k D0/D0KKπ0 events). – –
Kalanand Mishra
BaBar Coll. Meeting, December 2007

5. What is Known ? PDG 2006  BaBar 2007 
CLEO measures ACP in D0-+0 decays
ACP =  0.05
No ACP measurements available for D0K-K+π0
Asymmetry in the Dalitz-Plot-integrated coherent sum of all amplitudes in the Dalitz Plot for D0 and D0 events.
+0.07 –
-0.05
ACP(K+K-) = ± 0.010
ACP(π+π-) = ± 0.012
ACP(π0π0) = 0.00 ± 0.05
ACP(K+K-π+π-) = ± 0.07
PDG 2006 
ACP(K+K-) = (0.00 ± 0.34 ± 0.13)%
ACP(π+π-) = (-0.24 ± 0.52 ± 0.22)%
BaBar 2007 
Kalanand Mishra
BaBar Coll. Meeting, December 2007

6. Methodology to Measure CP Asymmetry
Perform a blind analysis to search for direct CPV
Use 4 independent methods to measure CP asymmetry:
- directly compare Dalitz plot distributions for D0/D0 events. (Model independent, calculate 2/ and compare w/ null hypothesis).
- compare angular moments of the cosine of helicity angle (Model independent, calculate 2/ and compare w/ null hypothesis).
- fit the D0 and D0 Dalitz plots separately and extract asymmetry in amplitudes and phases. (Model Dependent).
- asymmetry in the total number of signal events. – –
The model independent methods would help establish asymmetry, while the model fit can help interpret measured asymmetry in data.
Kalanand Mishra
BaBar Coll. Meeting, December 2007

7. Definition of 2 for Model Indep. Methods
Dalitz Plot Comparison: Calculate normalized residual in each bin
R = ND /NDbar
Then 2 =  2
bins
Angular Moments Comparison: Calculate normalized residual in each bin for first eight moments ( l = )
where ij is the correlation between moments of order i and j in a bin
Then 2 =    Xi ij Xj
bins i j
Kalanand Mishra
BaBar Coll. Meeting, December 2007

8. arXiv: 0711.1544 HADRON-07 Proceeding
What I am NOT Going to Talk about ?
D0-+0, K-K+0 Signal Reconstruction:
Phys. Rev. D74, (2006)
D0-+0 Dalitz Plot Parametrization:
hep-ex / , accepted PRL
D0K-K+0 Dalitz Plot Parametrization:
Phys. Rev. D 76, (2007)
Distribution of Angular Moments in
D0-+0, K-K+0 and their Interpretation:
arXiv: HADRON-07 Proceeding
I have a brief summary on these in later slides.
Kalanand Mishra
BaBar Coll. Meeting, December 2007

9. Quick Review I: SM D0-+0 DP
hep-ex/ , accepted in PRL
r-r destructive
interference
KS veto
Event selection described in:
Phys. Rev. D74, (2006)
Kalanand Mishra
BaBar Coll. Meeting, December 2007

10. Quick Review II: D0-+0 Ang. Moments
Each event is weighted by the spherical harmonic
functions (l=0,1,2,…..).
Good agreement between data & model.
Large interference between S and P waves. P0 P1 P0 P1 P3 P2 P3 P2
m(-+) (GeV/c2)
m(+0) (GeV/c2)
m(+0) (GeV/c2)
m(-+) (GeV/c2)
Higher moments above 1.1 GeV are mostly coming from cross channels.
P-wave dominates in all channels.
S-wave contribution small.
-0 moments show similar behavior as +0moments.
arXiv:
Kalanand Mishra
BaBar Coll. Meeting, December 2007

11. Quick Review III: SM D0K-K+0 DP
 (1020)
±1 region:
≈ events,
purity ≈ 98 % 
m2(K+0) (GeV2/c4)
Events used
to obtain bkg
shape
K*+
K*-
m2(K-0) (GeV2/c4)
Event Selection K-
Define amplitude for the D0K-K+0 decay as:  
PCM ( D0) > 2.77 GeV/c
|mD* - m D |
< 0.6 MeV/c2 K+ 0 D0
+soft
PDF for signal events = | f |2
D*+
Phys. Rev. D 76, (2007)
Phys. Rev. D74, (2006)
Kalanand Mishra
BaBar Coll. Meeting, December 2007

12. Quick Review IV: D0K-K+0 Amplitudes
: 19 %
f0/a0: 7-10%   
Ambiguity between a large K+0 S-wave & K*(1410),f2’(1525).
2 Prob = 62 %
2 Prob = 48 %
Kalanand Mishra
BaBar Coll. Meeting, December 2007

13. Quick Review V: D0K-K+0 Ang. Moments
Excellent agreement between data & models.
Each event is weighted by the spherical harmonic
functions (l=0,1,2,…..).
Large interference between S and P waves. 
m(K-K+) (GeV/c2)
m(K+0) (GeV/c2)
m(K-K+) (GeV/c2)
m(K+0) (GeV/c2)
Higher moments above 1.1 GeV are coming from cross channels.
For S- and P- waves only, in the absence of cross-feeds from other channels, the amplitudes and the relative phase are given by:
We solve these equations for the K-K+ system in a limited mass range (where the above conditions are satisfied) to extract |S|, |P|, and cos SP.
arXiv:
Kalanand Mishra
BaBar Coll. Meeting, December 2007

14. Sensitivity to CPV: Toy MC Studies
Plot the difference in the Dalitz plot
distributions of D0 and D0 events
(in number of standard deviations).
no asymmetry –
Clear signal of asymmetry
in expected places. – –
D000 amp changed by -5%, phase by -5o
D0-+ amp changed by -5%, phase by -5o
D0-+0, 25 times larger statistics
Kalanand Mishra
BaBar Coll. Meeting, December 2007

15. Sensitivity to CPV: Toy MC Studies continued …
D0K-K+0, 25 times larger statistics –
no asymmetry
Asymmetry: 5%, 5o in D00 – –
Generate asymmetry in amplitude, phase of either D000 [D00] or
D0-+ [D0K*-K+]. Then fit the resulting Dalitz plot to see with what
sensitivity we get the original parameters back. – –
Find that, with the present data sample, we are sensitive to asymmetry of the order O(1%) in amplitude and O(1o) in phase in the main decay channels. Sensitivity is higher in D0-+0 decay compared to D0K-K+0.
Kalanand Mishra
BaBar Coll. Meeting, December 2007

16. 2/ from Dalitz Plot for No CPV
Will use these to evaluate Gaussian
confidence level for results from Data
D0-+0
D0K-K+0
Ploted the 2/ distribution for Dalitz plot distribution from CP symmetric 500 toy MC samples ( = number of bins in the Dalitz plot)
- Use the same number of events in each experimental sample as the number of events in our real Data sample.
- These plots give an estimate of the scale and spread in 2/ values.
Kalanand Mishra
BaBar Coll. Meeting, December 2007

17. Sensitivity to CPV in Monte Carlo
Only 4 moments shown here, but 2/ comes from first 8 moments. Also take correlation among the moments into account in each bin.
Plot the difference of moments between D0 and D0 events –
(i) When there is no asymmetry (i.e., “noise level”)
D0-+0 –
(ii) When D000 amplitude is changed by -5% and its phase changed by -5o
Kalanand Mishra
BaBar Coll. Meeting, December 2007

18. 2/ from Ang. Moments for No CPV
+–
+0
Will use these to evaluate Gaussian
confidence level for results from Data
K+0
K+K–
Kalanand Mishra
BaBar Coll. Meeting, December 2007

19. Study of Systematic Uncertainties–
D0 and D0 may have slightly different coefficients
Experimental:
efficiency parametrization
PID corrections
MC statistics
background shape ….
Similar to the ones in the original DP analysis
Model dependent:
form factors
inclusion / exclusion of some resonant states
uncertainty in the shape of component amplitudes
….. –
D0 / D0 cross-feed:
Tabulate the systematic uncertainty for different levels of cross-feed
Take into account the correlations among Legendre polynomial moments of different orders in each bin
Plus:
There are some discrete ambiguities in the asymmetry measurement. Fortunately, this can be resolved in a straightforward way in most cases.
Also:
Kalanand Mishra
BaBar Coll. Meeting, December 2007

20. Decouple Localized vs DP-integrated ACP
CP asymmetry can be:
either localized in some specific part of the Dalitz plot
(as predicted by most new physics models)
or integrated over the whole phase-space (a la 2-body decay)
Best way is to decouple the two:
- For obtaining asymmetry in the Dalitz plot distribution, normalize D0 and D0 events to the same number:
2/ = nD - R. nDbar / Poisson error –
R = ND /NDbar
- obtain the phase-space integrated asymmetry after applying the soft pion efficiency corrections as done in the 2-body D0KK,  decays.
Kalanand Mishra
BaBar Coll. Meeting, December 2007

21. Validation Studies
Validation studies on toy Monte Carlo treated as data
Analysis on CP-symmetric D–+0, K–K+0 samples
Analysis on asymmetric samples
Validation studies on signal Monte Carlo treated as data
Repeat the above steps
Validation studies on data
We are still ‘blind’.
Divide the data sample randomly into two disjoint samples of equal size (without looking into the flavor of the D meson)
Perform the whole analysis
Repeat the procedure several times
Summary: We find consistent results and get the input parameters back.
Kalanand Mishra
BaBar Coll. Meeting, December 2007

22. Asymmetry in Data: Dalitz Plot
D0K-K+0
Consistency with No CPV
32.8 %
Use one sided Gaussian
confidence level
Consistency with No CPV
16.6 %
Conclusion: no hint of CP violation in direct comparison of DPs.
Kalanand Mishra
BaBar Coll. Meeting, December 2007

23.  Consistency with No CPV: 28.2 %
Asymmetry in Data: Angular Moments
+– channel moments
 Consistency with No CPV: 28.2 %
Only 3 moments shown here, but 2/ comes from first 8 moments
 Consistency with No CPV: 28.4 %
+0 channel moments
Kalanand Mishra
BaBar Coll. Meeting, December 2007

24.  Consistency with No CPV: 63.1 %
Asymmetry in Data: Angular Moments
K+K– channel moments
 Consistency with No CPV: 63.1 %
Only 3 moments shown here, but 2/ comes from first 8 moments
 Consistency with No CPV: 23.8 %
K+0 channel moments
Kalanand Mishra
BaBar Coll. Meeting, December 2007

25. Angular Moments: Consistency with No CPV
+–
+0
Consistency with No CPV
28.2 %
Consistency with No CPV
28.4 %
Use one sided Gaussian
confidence level
K+0
K+K–
Consistency with No CPV
63.1 %
Consistency with No CPV
23.8 %
Kalanand Mishra
BaBar Coll. Meeting, December 2007

26. Asymmetry in Data: Model Fit
DK-K+0
Conclusion: No evidence for CPV in any CP eigen or flavor state in either decay mode.
Kalanand Mishra
BaBar Coll. Meeting, December 2007

27. Phase-space-integrated Asymmetry
–+0: aCP = [ ± 0.41 (stat) ± 0.17 (syst) ] %
K–K+0: aCP = [ 1.00 ± 1.67 (stat) ± 0.25 (syst) ] %
Conclusion: consistent with no integrated asymmetry.
Kalanand Mishra
BaBar Coll. Meeting, December 2007

28. Status of Analysis In the Review Committee.
Expect to go to CWR soon - hopefully in a week.
Plan to upload to the PRL server by the end of the year.
Support BAD:
Journal draft BAD: 1833
Kalanand Mishra
BaBar Coll. Meeting, December 2007

29. Summary
Direct CP violation at present experimental sensitivity would be a signature of new physics.
D0-+0, K-K+0 sensitive to asymmetry in amplitude and phase for both CP eigen and flavor states.
Model Independent methods show no evidence of CPV in either decay modes.
Model Dependent measurements of asymmetry in the amplitudes and phases of CP eigen and flavor states show no compelling evidence of CPV either.
Phase-space-integrated asymmetry consistent with 0.
These results are consistent with SM.
CPV in charm decays is suppressed below 1 %.
Can provide constraints on some theories beyond SM.
Kalanand Mishra
BaBar Coll. Meeting, December 2007

30. Backup Slides
Kalanand Mishra
BaBar Coll. Meeting, December 2007

31. CP Violation in D0 Decays- -
Where f is: p+p-p0 [π, f0π0, …] or K+K-p0 [K*K, π0 , f0π0, …].
direct CPV
need interference between diagrams with different strong (i) and
weak phases (i).
New physics can provide additional amplitudes and phases.
Kalanand Mishra
BaBar Coll. Meeting, December 2007

32. D0-+0, K-K+0 Reconstruction
D0h-h+0 Reconstruction
Background Sources
Charged track combinatoric
Mis-reconstructed 0
Real D0, fake s
K0 reflection in 0
and KK0 modes
h- and h+ tracks are fit to a vertex
Mass of 0 candidate is constrained
to m0 at h-h+ vertex
PCM ( D0 ) > GeV/c
D* Reconstruction
D*+ candidate is made by fitting the D0 and the s+ to a vertex constrained in x and y to the measured beam-spot for the run.
|mD* - m D | < 0.6 MeV/c2
Vertex 2 probability > 0.01
Choose a single best candidate with smallest 2 for the whole decay chain ( multiplicity = 1.03 ).
Kalanand Mishra
BaBar Coll. Meeting, December 2007

33. Model-dependent fit: including non-SM amplitudes
SM D0 decay three-body amplitude
With additional non-SM amplitudes 
A = 
For D0 :
ar, δr : Free parameters of fit  –
For D0 :
Angular distribution
Form factors
[ See D. Asner, hep-ex/ ]
Relativistic
Breit-Wigner
br = non-SM amplitude coeff.
r = strong phase
r = weak phase
Flatte: f0 / a0
Kalanand Mishra
BaBar Coll. Meeting, December 2007