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

2. Methodology to Measure CP Asymmetry
Use three independent methods to measure CP asymmetry:
- directly compare Dalitz plot intensity distribution for D0/D0 events. (Model independent, calculate 2/ and compare w/ null hypothesis).
- compare Legendre polynomial moments of the cosine of helicity angle in two-body channels (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). – –
The first two methods (Model Independent) would help establish asymmetry, while the third method can enable us to interpret any measured asymmetry in data in terms of new physics parameters.
Kalanand Mishra
BaBar Coll. Meeting, September 2007

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

4. 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, September 2007

5. Sensitivity to CPV in Monte Carlo–
Plot the difference of moments between D0 and D0 events
D0-+0
(i) When there is no asymmetry (i.e., “noise level”) –
(ii) When D000 amplitude is changed by -5% and its phase changed by -5o
Kalanand Mishra
BaBar Coll. Meeting, September 2007

6. 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
Do not forget to take into account the correlations among Legendre polynomial moments of different orders in each bin
Plus:
There are some discrete ambiguities between between the asymmetry in one channel and the corresponding cross-channel. Fortunately, this ambiguity can be resolved in a straightforward way in most cases.
Also:
Kalanand Mishra
BaBar Coll. Meeting, September 2007

7. Decouple Localized vs DP-integrated ACP
Direct 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 in the usual way, i.e., as done in the branching ratio analysis and applying the soft pion efficiency corrections as done in the 2-body D0KK,  decays.
Kalanand Mishra
BaBar Coll. Meeting, September 2007

8. Status of Analysis All necessary ground works completed:
- Parametrization for the SM amplitudes established.
- methodology to extract CP asymmetry being finalized.
Sensitivity and validation studies on MC completed.
Most important sources of systematic uncertainties identified and studied in detail.
The first version of BAD 1531, detailing the sensitivity and validation studies, was released in August. Initial feedback from AWG received.
We have acted on the suggestions and have performed several additional validation studies. The second version is almost ready to go. We are also working on PRL draft.
After feedback from AWG and then from Review Committee, we’ll proceed to unblind the data.
Kalanand Mishra
BaBar Coll. Meeting, September 2007

9. Summary
Direct CP violation at present level of experimental sensitivity would be a signature of new physics. D0-+0, K-K+0 are directly sensitive to asymmetry in amplitude and phase for both CP eigen and non-CP eigen intermediate states.
Sensitivity studies using Monte Carlo events indicate:
- with the present data sample we are sensitive to asymmetry of O(1%) in amplitude, O(1o) in phase.
- asymmetry in more than one intermediate states will increase our sensitivity in general.
Use three independent methods to measure asymmetry:
The two Model Independent methods will help establish the asymmetry, while the third method will enable us to interpret any measured asymmetry in data in terms of new physics parameters.
Validation studies completed. A new version of support BAD soon. Ready to unblind once OKed by the AWG and RC.
Kalanand Mishra
BaBar Coll. Meeting, September 2007

10. Backup Slides
Kalanand Mishra
BaBar Coll. Meeting, September 2007

11. 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 ( ad)
- in mixing between D0 and D0 (am)
- in the interference of decays with and without mixing (ai).
In case of indirect CPV ( aindirect = am + ai ) and final CP eigen states, the time integrated CP asym and time-dependent CP asym are universal (and equal to each other).
In contrast, for direct CPV, the time-integrated asymmetries are not expected to be universal => 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. –
Kalanand Mishra
BaBar Coll. Meeting, September 2007

12. New Physics Scenarios
CPV ~ 1% will be a strong evidence for non-SM processes
Most of the SUSY models predict enhancement of CP asymmetry in charm decays:
- Minimal flavor violation models predict tiny, unobservable effects.
- Alignment models predict large indirect CPV and large direct CPV.
- Models with squark degeneracy predict small indirect CPV but, depending on the model, large direct CPV.
If direct CPV is at 1% level, its likely source is new physics that contributes to the decay via loop diagrams rather than via tree diagrams.
SCS D 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.
See for details: Y. Grossman, A.L. Kagan, and Y. Nir, Phys. Rev. D75, (2007).
I.I. Bigi, hep-ph/ (2001). Also, talk in the Mixing workshop in May.
A.L. Kagan, talk given in a special Charm AWG session in March.
Kalanand Mishra
BaBar Coll. Meeting, September 2007

13. 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, September 2007

14. Why 3-body SCS D0 Decays ?
3-body decays permit the measurement of phase differences which are required to create direct CP violation in the interference between SM and non-SM processes.
Access to both CP eigen states (0π0, f0π0, π0 ) and non-CP eigen states (π-+, K*K-+). Therefore, can probe more diverse possibilities of direct CPV.
Since we can normalize measurements relative to the whole phase space (Dalitz plot), the dependence on πs tagging efficiency is negligibly small.
Also, these are relatively high statistics modes (80 k D0/D0πππ0 and 12k D0/D0KKπ0 events). – –
Kalanand Mishra
BaBar Coll. Meeting, September 2007

15. What is Known ? PDG 2006  CLEO measures ACP in D0-+0 decays
No ACP measurements available for D0K-K+π0
Other analysis is under way to measure CP asymmetry in D0K-K+, π-π+ modes
Measures the difference in the integrated coherent sum of all amplitudes across the Dalitz Plot between 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 
Kalanand Mishra
BaBar Coll. Meeting, September 2007

16. Parametrization of SM D0-+0 Amplitudes
hep-ex/ , submitted to PRL
r-r destructive
interference
KS veto
Event selection described in:
Phys. Rev. D74, (2006)
Kalanand Mishra
BaBar Coll. Meeting, September 2007

17. SM D0-+0 Amplitudes continued ….
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.
Kalanand Mishra
BaBar Coll. Meeting, September 2007

18. Parametrization of SM D0K-K+0 Amplitudes
 (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*+
arXiv: , accepted for pub. in PRD-RC
Phys. Rev. D74, (2006)
Kalanand Mishra
BaBar Coll. Meeting, September 2007

19. SM D0K-K+0 Amplitudes continued ….
: 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, September 2007

20. Excellent agreement between data & models.
Analysis of Angular 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.
Kalanand Mishra
BaBar Coll. Meeting, September 2007

21. 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, September 2007