1. D0 mixing and charm CP violation
Moriond EW, 2010 La Thuile, March 8th 2010
Jordi Garra Ticó
Universitat de Barcelona
BaBar collaboration

2. Outline Introduction to mixing and CP violation.
Standard model predictions and new physics.
Recent results on D0 mixing. State of the art.
Dalitz time dependent analysis of Ks + - and Ks K+ K- decays.
Recent results on D0 CPV.
Summary.

3. Introduction to mixing and CPV
Mixing has been well measured in K, Bs and Bd systems.
The and mesons are produced as flavor eigenstates, but evolve and decay as mixtures of the effective Hamiltonian eigenstates, and
Mixing can occur because flavor eigenstates differ from the effective Hamiltonian eigenstates.
The change of base is
If there was no CP violation, is defined to be CP even, and CP odd.
The mixing parameters are defined as
The amplitudes of a or meson into a final CP eigenstate can be written as ,
3 types of CPV:

4. Standard model predictions and new physics
Short distance contributions
Mixing box diagrams.
SM predicts small mixing effects.
b quarks are CKM suppressed, and s and d quarks are GIM suppressed.
They mainly contribute to the x mixing parameter.
Long distance contributions
Hadronic intermediate states.
Expected to be dominant, but still small.
Hard to estimate, since they are not perturbative.
Predictions give x and y in the range [0.001, 0.01], and |x| < |y|.
NP through new particles in loops
If |x| >> |y| this could be a hint of NP.
Not expected to find SM CPV (~10-3) with current sensitivity. Larger CPV would be evidence of NP.
A. Falk et al., PRD 69, (2004)
E. Golowich et al., PRD 76, (2007)
Y. Grossman et al., PRD 75, (2007)

5. D0 production and selection
Tagging at production:
Inclusive D* production. Using D*±  D0 s± decays.
The flavor of the D0 is determined by the charge of the s.
Tagging at decay:
The flavor can be determined by the wrong sign (WS) or right sign (RS) D0 decay products. ~
Selection:
e+e-  cc events have high D0 momentum in the CM frame.
Use momentum to reject BB events (pD0CMF > 2.5 GeV)
Beam spot constraint determines t and t.
It also improves mD and m = m(D0 s) – m(D0) resolutions.
D0 decay vertex
Beam spot
x ~ 100 m
y ~ 6 m
D0 production vertex

6. Recent D0 mixing and CPV analyses
References in the first backup slide

7. Mixing searches

8. Life time ratio D0  h+ h- / D0  K- +
D0 mixing and CPV alter the lifetime distributions of CP eigenstates h+h-.
A good approximation are effective lifetimes ±,
Measured magnitudes
Mixing and CP observables are
Lifetime average and asymmetry

9. Life time ratio D0  h+ h- / D0  K- +
540 fb-1
PRL 98, (2007)
yCP = ( 1.31 ± 0.32 (stat) ± 0.25 (syst) )·10-2
A = ( 0.01 ± 0.30 (stat) ± 0.15 (syst) )·10-2
Mixing evidence at 3.2
PRD 78, (R) (2008)
384 fb-1
Tagged:
yCP = ( 1.03 ± 0.33 (stat) ± 0.19 (syst) )·10-2
y = ( ± 0.36 (stat) ± 0.08 (syst) )·10-2
Mixing evidence at 3
PRD 80, (R) (2009)
Combined tagged + untagged:
yCP = ( 1.13 ± 0.22 (stat) ± 0.18 (syst) )·10-2
Tagged
Mixing evidence at 4.1

10. HFAG averages (measurements of yCP)

11. Time dependent Dalitz plot analyses
D0 Dalitz decays (D0  Ks + -, Ks K+ K-)
Since evolution of mass eigenstates is known, the time dependent amplitude is
Where
May implement CP violation in the mixing
May implement CP violation in the decay
Sensitivity to mixing arises from the lifetime dependence on the point in the Dalitz plot.
This provides sensitivity to the mixing parameters x and y, directly, if CP conservation in the decay is assumed.
Phase space and life time dependences do not factorize.
An accurate phenomenological decay model for the variation of the amplitude over the Dalitz plot is needed in order to have sensitivity to x and y.

12. Variables for time dependent Dalitz analysis (Ks h+ h-)
Generic variables of the method:
mD: The mass of the D0, obtained from the 4-momenta of the 4 charged particles of the decay channel.
m: The mass difference between the D* and the D0, obtained from the 4-momenta of the charged particles of the decay channel, plus that of the soft pion.
t: The life time of the D0, obtained from its flight length.
t: The error on the life time (per event).
The Dalitz variables m2AB, m2AC, m2BC.
Each variable has been characterized, as well as the background.
Several categories have been introduced in order to describe the signal and background.

13. Signal and bkg characterization for TD Dalitz analysis
Definitions:
True D0: it means that the 4 charged particles of the signal channel have been reconstructed and matched correctly.
True s: it means that its mother is a D*± and has a D0 sister.
Categories:
For each category, the kinematic variables have been characterized separately, i.e., functions have been found to describe well their distributions.
D0  Ks  
BaBar
Preliminary

14. BaBar model for time dependent Dalitz analysis (Ks h+ h-)
Model taken from PRD 78, (2008) (BaBar).
Z describe the angular distribution of the decay products.
B,r are the form factors, usually parameterized using the Blatt- Weisskopf penetration factors. It accounts for the effect of the angular momentum of the resonance on the decay rate.
Gr is a propagator that describes the resonance.
Most of them are relativistic Breit-Wigner.
Gounaris-Sakurai for 0.
K-matrix / LASS for a better description of overlapping BW resonances ( and K S waves).

15. BaBar model for time dependent Dalitz analysis (Ks h+ h-)
Preliminary
BaBar
Preliminary
Dalitz plot distributions for D0  Ks   (left) and D0  Ks K K (right) from D*+  D0 + events after all selection criteria are applied.

16. BaBar systematics for time dependent Dalitz analysis (Ks h+ h-)
Experimental systematic uncertainties.
Fit bias.
Signal and background yields.
Efficiency map.
Mistag.
Mixing in the background.
Dalitz background profiles.
Dalitz normalization.
D0 mass window.
Final mixing fit cuts.
SVT misalignment.
Dalitz model systematic uncertainties.
Different K-matrix solutions.
Float parameters of some resonances.
Different radii of the BW barrier factors.
Fits with more and less resonances.

17. BaBar result for time dependent Dalitz analysis (Ks h+ h-)
x = ( 0.16 ± 0.23 (stat) ± 0.12 (exp) ± 0.08 (mod) ) 10-2
y = ( 0.57 ± 0.20 (stat) ± 0.13 (exp) ± 0.07 (mod) ) 10-2
BaBar
Preliminary
Most precise direct measurement of x and y.
Mixing significance at 1.9, similar to Belle (2.2).
First combined analysis of D0  Ks   and D0  Ks K K.
BaBar measurement favors a lower value for x than for y.
Central point moves toward SM prediction.
BaBar
Preliminary

18. Previous results for time dependent Dalitz analysis (Ks h+ h-)
PRL 98, (2007)
540 fb-1
Belle
(with no CPV)
BaBar
Exclude the no-mixing hypothesis at 2.2.
It also allows to fit for CPV in the interference.
No evidence for CPV
BaBar
Preliminary
BaBar and Belle results agree at less than 1.

19. CPV searches

20. Time integrated CPV searches, D0  +-(0), K+K-(0)
CP even final states.
Single Cabibbo suppressed modes.
Standard model predicts CPV in these modes to be ~
Evidence of CPV with current experimental sensitivity is sign of physics beyond SM.
Based on the measurement of the asymmetries of the partial decay widths
It includes the 3 possible sources of CPV.
Y. Grossman et al., PRD 75, (2007)
Experimental difficulty:
Forward-backward asymmetry in e+e-  cc production.

21. Time integrated CPV searches, D0  +-(0), K+K-(0)
385.8 fb-1
PRL 100, (2008)
aCPKK = ( ± 0.34 (stat) ± 0.13 (syst) )·10-2
aCP = ( ± 0.52 (stat) ± 0.22 (syst) )·10-2
385 fb-1
PRD 78, (2008)
aCP0 = ( ± 0.41 (stat) ± 0.17 (syst) )·10-2
aCPKK0 = ( ± 1.67 (stat) ± 0.25 (syst) )·10-2
532 fb-1
No evidence of CPV
at the level of 10-2
PLB 662, (2008)
aCP0 = ( 0.43 ± 1.30 )·10-2

22. Summary
BaBar and Belle have established evidence for mixing, confirmed by CDF.
No single mixing measurement exceeds 5, but combined measurements exclude the no-mixing hypothesis at more than 10.2.
No evidence of any kind of CPV (direct, mixing or interference).

23. BACKUP SLIDES

24. Recent D0 mixing and CPV analyses

25. Time dependence of suppressed hadronic decays
 is the strong phase between the D0->f (DCS) and D0-> f (CF).
Mixing is implied through non-zero values of x' or y'.
Do not allow for measurement of x and y parameters directly.
Example: D0  K+ -. Contributions from:
Doubly Cabibbo suppressed (DCS) decay D0  K+ -
Mixing and Cabibbo favoured (CF) decay D0  D0  K+ -
Interference
DCS
Interference
Mixing

26. Time dependence of suppressed hadronic decays
384 fb-1
PRL 98, (2007)
x'2 = ( ± 0.30 ± 0.21 ) · 10-3
y' = ( 9.7 ± 4.4 ± 3.1 ) · 10-3
Mixing evidence at 3.9
PRL 100, (2008)
1.5 fb-1
400 fb-1
PRL 96, (2006)
x'2 = ( ± 0.35 ) · 10-3
y' = ( 8.5 ± 7.6 ) · 10-3
RD = ( ± )·10⁻2
x'2 < 0.72· @ 95 % CL
y' ∈ ( -9.9·10-3, 6.8· % CL
RD = ( ± ± )·10⁻2
Mixing evidence at 3.8
No-mixing excluded at 2.0

27. The BaBar experiment 5 layered silicon vertex tracker (SVT)
40 layered drift chamber (DCH)
Cerenkov detector for PID (DIRC)

28. Dalitz time dependent analysis of D0  Ks + - and D0  Ks K+ K-

29. Selection criteria for Ks h+ h-
Reject true D0 from B decays
Selection efficiency:
14.2 % for Ks   = events
12.6 % for Ks K K = events
Purity:
97.8 % for Ks  
99.8 % for Ks K K
Reduce contamination of fake Ks, specifically in
D0  4  and D0    K K events.

30. Signal and background characterization
Example: signal pdfs.

31. The Dalitz model
 S wave: Scattering part expressed as the K-matrix, and production part expressed as the production vector.
K S wave: The LASS parameterization is used to describe this component.
P wave: The vector contribution is represented by the  0(770), (782) and the Cabibbo allowed and DCS K*(892). RBW is used for them all, except GS for the 0(770).
D wave: The tensor part of the amplitude is given by the K*2(1430)± and the f2(1270)
Efficiency over the Dalitz plot is also taken into account.

32. The Dalitz model for D0

33. Fit strategy Step 1: Fit for the parameters of {mD, m, t, t}.
Dalitz integrated.
Step 2:
Time integrated Dalitz fit (amplitudes, phases, masses and widths of the resonances).
Shapes for {mD, m, t, t} are taken from step 1.
Neglect mixing.
Step 3:
Time dependent Dalitz fit.
Shapes for {mD, m, t, t} are taken from step 1, but float category yields.
Extract mixing parameters and CPV.

34. Data – MC comparison
Ks  
Ks K K