1. CP Violation in B Decays Lecture III
Vivek Sharma
University of California at San Diego

2. Outline of Lecture 3 Reminder: Requirement for CP Violation
Three types of CP violation in B Decays
General strategy for time-dependent CP asymmetry measurement
Effect of Detector imperfections on CP Asymmetry
Calibration measurements using data
Calibrating the Detector clock
Calibrating B flavor mis-identification rate
Experimental measurement of sin2 in B (cc) s final states
Babar & Belle
Perspective from first observation of CP violation in B decays

3. Conditions for CP violation
Two amplitudes, A1 and A2, with a relative CP-violating phase (f2) only
No CP violation since magnitudes of A and A are the same!
Two amplitudes, A1 and A2, with both a relative CP-violating phase 2 and CP-conserving phase (d2)
Now have CP violation!

4. CP Violation in B Meson System
Identify B final states which are arrived at by two paths
B Meson is heavy  many final states, multiple “paths.”
2 classes of B decays come into play: “Tree”  spectator decay like
“Penguin”  FCNC loop diagrams with u,c,t

5. CP Violating Effects in B decay Processes
CP violation in the interference between two decay amplitudes (“Direct CP violation”)
Decay amplitudes must have different CP violating and CP conserving phases.
CP conserving phase from strong, final-state interaction, so difficult to interpret results in terms of CKM parameters
Can measure in both B0/B0 and B+/B- decays (time-independent)
CP violation in B mixing
Interference is between bundle of amplitudes with on-shell (real) intermediate states and bundle of amplitudes for off-shell (virtual) intermediate states.
CP violating in the interference between mixing and decay amplitudes
Occurs in B0 system , one set of CP phases from mixing
If only one direct B decay amplitude  has clean CKM interpretation

6. Reminder: CPV Phase in CKM Matrix

7. Experimental Results on CP Violation in B Meson system

8. CPV in Decay aka Direct CP Violation2  B f

9. Observation of Direct CPV in B0K- +
Loop diagrams from New Physics (e.g. SUSY) can modify SM asymmetry via P
Clean mode with “large” rate :
Measure charge asymmetry, reject large B background with Particle ID
B background
signal
E (GeV)
K separation
K separation()

10. BaBar: First Observation of Direct CPV in B decay !
B0K+
B0K+
BABAR
4.2, syst. included
BABAR
background subtracted
signal enhanced

11. Confirmation of Direct CPV by Belle at ICHEP04
ACP =   0.005
3.9s significance _
B0 K-p+
B0 K+p-
274M BB
Signal=2139 53
Establishes CPV not just due to phase of B Mixing (M12)
Rules out superweak model of CP violation
Non-Pert QCD uncertainties large, SM CPV not precisely predictable
 insufficient to prove or rule out contribution from New Physics Amp.

12. CPV in B0 Mixing 2  B0 f
Occurs when Mass eigenstates CP eigenstates
(|q/p|1 and<BH|BL> 0)
The Box diagrams provide the required 2 phases
Strong phases depend on quark masses and
non-perturbative physics.
Asymmetries are small and hard to calculate precisely (QCD)
off-shell states f
on-shell states f

13. CPV in B0 Mixing
Time-dependent CP Asymmetry:

14. Measurement region > 200mm
CPV in B0 Mixing
Time dependent measurement, time measured from Z
BABAR
20.7 fb-1
Sample backgrounds B(Dt): 4.3% continuum 24% direct+cascade 12% direct+fake
Measurement region > 200mm

15. CPV in B0 Mixing BABAR So far, no experimental evidence
20.7 fb-1
So far, no experimental evidence
of large CP violation in B0 mixing
To a good approximation:

16. CPV In Interference Between Mixing and Decay+ 2  B0
fcp
CP asymm. can be very large and can be cleanly related to CKM angles

17. Tree
Penguin:: u,c,t loops 

18. CPV In Interference Between Mixing and Decay: B0 J/K0
for J/y K0S(L)
Same is true for a variety of B (cc) s final states

19. CPV In Interference Between Mixing and Decay
Requires measurement of proper time difference t=t between the
decay of Btag and BCP. S C
Asymmetry

20. Time-Dependent CP Asymmetry with a Perfect Detector
Perfect measurement of time interval t=t
Perfect tagging of B0 and B0 meson flavors
For a B decay mode such as B0Ks with |f|=1
sin 2b B0
Asymmetry ACP
CPV

21. Consequences of Detector Imperfections
Acp(Dt)
F(Dt)
Dt(ps)
sin2b
D sin2b
True Dt, Perfect tagging:
True Dt, Imperfect tagging:
Measured Dt, Imperfect tagging:
Must measure flavor tag Dilution.
D = (1-2w) where w is mistag fraction.
Must measure Dt resolution properties.

22. Time Dependent CPV Measurement Technique
Since the techniques of time-dependent analysis is common to many modes, I will now describe this in detail using the “platinum” mode B0 (cc) K0 from which CP violation in B0 decays was first established.
The analysis (from 2002) based on 88 fb-1 is “old” but forms basis for all other time-dependent CPV results that I will present later

23. CP Violation in Picturez
Separate
B0 and B0 m- K-
bgU(4S) = 0.55
Coherent BB pair B0
B0  J/y Ks
Vivek Sharma , UCSD

24. Time-Dependent CPV Analysis Strategy
Factorize the Time Dependent analysis into building blocks
Obtain ALL analysis ingredients from DATA (avoid MC)
Measurements
B±/B0 Lifetimes
B0 B0-Mixing
CP-Asymmetries
Analysis Ingredient
Reconstruction of B mesons in flavor specific states
B vertex reconstruction
Flavor Tagging + a + b
Reconstruction of neutral B mesons in CP eigenstates + a + b + c
Increasing complexity
Higher precision
Vivek Sharma , UCSD

25. Calibrating The BaBar Clock: B Meson Lifetime Measurement

26. Measurement of the B0 and B+ Lifetime
U(4s)
bg = 0.55
Tag B
sz ~ 110 mm
Reco B
sz ~ 65 mm p+ Dz
Dz/gbc K0 g D- p- K+
3. Reconstruct Inclusively the vertex of the “other” B meson (BTAG)
Fully reconstruct one B meson in flavor eigenstate (BREC)
Reconstruct the decay vertex
4. compute the proper time difference Dt
5. Fit the Dt spectra
Vivek Sharma , UCSD

27. Fully-Reconstructed B sample
Flavor eigenstates Bflav : for lifetime and mixing measurements
Cabibbo-favored hadronic decays
“Open Charm” decays
Neutral B Mesons
~21000 signal Purity: 85%
Charged B Mesons
Hadronic decays into final states
with Charmonium
~20000 signal Purity: 85%
[GeV]
Vivek Sharma , UCSD

28. Vertex and Dt Reconstruction
Beam spot
Interaction Point
BREC Vertex
BREC daughters
BREC direction
BTAG direction
TAG Vertex
TAG tracks, V0s z
Reconstruct Brec vertex from
charged Brec daughters
Determine BTag vertex from
charged tracks not belonging to Brec
Brec vertex and momentum
beam spot and U(4S) momentum
High efficiency (97%)
Average Dz resolution is 180 mm (<|Dz|> ~ bgct = 260 mm)
Dt resolution function measured from data
Vivek Sharma , UCSD

29. tB Measurement: Unusual Situation at (4S)
e-t/t
true Dt
B production point known eg. from beam spot
LEP/SLD
Dt resolution
measured Dt
Resolution
function
lifetime  =
e-|Dt|/t
Either Brec or Btag can decay first (this analysis)
BaBar
Resolution Function Lifetime  =
Need to disentangle resolution function from physics !
Vivek Sharma , UCSD

30. Dt Resolution Function
sDz
event-by-event s(Dt) from vertex errors
Lifetime-like bias to
Small correlation between lifetime and Resolution Function parameters
~0.6 ps
Signal MC (B0)
tracks from long-lived D’s in tag vertex asymmetric Resolution Function
Dt (meas-true)/sDt
Vivek Sharma , UCSD

31. Lifetime Likelihood Fit
Simultaneous unbinned maximum likelihood fit to B0/B+ samples
Use data to extract the properties of background events
Mass distribution provides the signal probability
Use the events in the sideband (mES < 5.27) to determine the Dt structure of the background events under the signal peak
19 free parameters
t(B+) and t(B0) 2
Dt signal resolution 5
empirical background 12 description
B0 mES
B0 Bkg Dt
Vivek Sharma , UCSD

32. B Lifetime Fit Results B0/ B0 B
World’s best measurement
2 % statistical error
1.5% systematic error
Main source of systematic error
Parameterization of the Dt resolution function
Description of events with large measured Dt (outliers)
20 fb-1
B0/ B0
Detector Clock precisely calibrated B
signal + bkg
PRL 87, (2001)
t0 =   ps PDG:  ps
t =   ps
PDG:  ps
t/t0 =   0.011
PDG:  0.029
background
Dt (ps)
Vivek Sharma , UCSD

33. B Flavor (Mis)Identification (Mistag Knowledge From Data)

34. Using B Mixing to Measure Flavor Mistag Rate
B0 B0
B Lifetime
Start with a B0 beam, slowly (compared to B lifetime) a B0 component builds up
But no “Mixed” events at t=0. If the detector measures some “mixed” events, it must be because it has measured the flavor of the B incorrectly ( mistag)

35. Analysis Strategy (II)
Measurements
B±/B0 Lifetimes
B0 B0-Mixing
CP-Asymmetries
Analysis Ingredient
Reconstruction of B mesons in flavor eigenstates
B vertex reconstruction
Flavor Tagging + a + b
Reconstruction of neutral B mesons in CP eigenstates + a + b + c ü
Vivek Sharma , UCSD

36. Measurement of B0B0 Mixing rate Vs t
U(4s)
bg = 0.55
Tag B
sz ~ 110 mm
Reco B
sz ~ 65 mm p+ Dz
Dz/gbc K0 g D- p- K+
3. Reconstruct Inclusively the vertex of the “other” B meson (BTAG) ü
4. Determine flavor of BTAG to separate Mixed and Unmixed events
1. Fully reconstruct one B meson in flavor eigenstate (BREC) ü
2. Reconstruct the decay vertex ü
5. compute the proper time difference Dt ü
6. Fit the Dt spectra of mixed and unmixed events
Vivek Sharma , UCSD

37. Dt Spectrum of Mixed and Unmixed Events
perfect
flavor tagging & time resolution
Decay time diff (t) in ps _ +
w: the fraction of wrongly tagged events
Dmd: oscillation frequency
realistic
mis-tagging & finite time resolution
Decay time diff (t) in ps
Vivek Sharma , UCSD

38. B Flavor Tagging Methods
Hierarchical Tagging Categories
For electrons, muons and Kaons use the charge correlation b c d l- n B0
D, D* W-
Lepton Tag b d B0 W- W+ c s
K*0
Kaon Tag
NN output
Not Used
Multivariate analysis exploiting the other kinematic information of the event, e.g.,
Momentum spectrum of the charged particles
Information from non-identified leptons and kaons
Soft p from D* decay
Neural Network
Each category is characterized by the probability of giving the wrong answer (mistag fraction w)
Vivek Sharma , UCSD

39. Flavor Tagging Performance in Data
The large sample of fully reconstructed events provides the precise determination of the tagging parameters required in the CP analysis
Tagging category
Fraction of tagged events e (%)
Wrong tag fraction w (%)
Mistag fraction difference Dw (%)
Q =
e (1-2w)2 (%)
Lepton
10.9  0.3
9.0  1.4
0.9  2.2
7.4  0.5
Kaon
35.8  1.0
17.6  1.0
-1.9  1.5
15.0  0.9
NT1
7.7  0.2
22.0  2.1
5.6  3.2
2.5  0.4
NT2
13.8  0.3
35.1  1.9
-5.9  2.7
1.2  0.3
ALL
68.4  0.7
26.1  1.2
Error on sin2b and Dmd depend on the “quality factor” Q approx. as:
Highest “efficiency”
Smallest mistag fraction
BABAR
29.7 fb-1
Vivek Sharma , UCSD

40. Flavor Tagged B Meson Sample For Mixing Studies
psig,i ~ 0
psig,i ~ 0.96
Background properties from sideband events
Lepton
Lepton
Kaon
NT1
NT2
Vivek Sharma , UCSD

41. Dt (or DZ) Resolution Function
Use the event-by-event
uncertainty on Dt
B0 flavour sample
CP sample
sDt (ps)
Dt Residual (ps)
R(dDt)
Core
Tail
Outlier
Vivek Sharma , UCSD

42. Mixing Likelihood Fit on Reconstructed B0 Sample
Unbinned maximum likelihood fit to flavor-tagged neutral B sample
Fit Parameters
Dmd
Mistag fractions for B0 and B0 tags 8
Signal resolution function 2 x 8
Empirical description of background Dt
B lifetime fixed to the PDG value tB = ps
44 total free parameters
All Dt parameters extracted from data
Vivek Sharma , UCSD

43. Mixing Measurement with Fully Reconstructed B Sample
T=2/m
1-2w
Precision measurement consistent with world average
 Well calibrated detector for Flavor tagging
Vivek Sharma , UCSD

44. CP Analysis Analysis Strategy (Step III)
Measurements
B±/B0 Lifetimes
B0 B0-Mixing
CP-Asymmetries
Analysis Ingredient
Reconstruction of B mesons in flavor eigenstates
B vertex reconstruction
Flavor Tagging + a + b
Reconstruction of neutral B mesons in CP eigenstates + a + b + c ü ü
Vivek Sharma , UCSD

45. Measurement of CP Asymmetry
U(4s)
bg = 0.55
Tag B
sz ~ 110 mm
CP B
sz ~ 65 mm m+ Dz
Dz/gbc K0 g p+ p-
Ks0 m-
3. Reconstruct Inclusively the vertex of the “other” B meson (BTAG) ü
4. Determine the flavor of BTAG to separate Mixed and Unmixed events ü
1. Fully reconstruct one B meson in CP eigenstate (BCP)
2. Reconstruct the decay vertex ü
5. compute the proper time difference Dt ü
6. Fit the Dt spectra of B0 and B0 tagged events
Vivek Sharma , UCSD

46. Charmonium+K0 CP Sample for BABAR (’02)
1506 signal candidates,
purity 94%
988 signal candidates,
purity 55%
BABAR
81.3 fb-1
(after tagging & vertexing)
Vivek Sharma , UCSD

47. Dt Spectrum of CP Events
perfect
flavor tagging & time resolution
realistic
mis-tagging & finite time resolution
CP PDF
Mistag fractions w
And resolution function R
Mixing PDF
determined by flavor sample
Vivek Sharma , UCSD

48. sin2b Likelihood Fit Description
Combined unbinned maximum likelihood fit to Dt spectra of Bflav and CP samples
Fit Parameters #
Main Sample
Sin2b 1
Tagged CP sample
Mistag fractions for B0 and B0 tags 8
Tagged flavor sample
Signal resolution function
Empirical description of background Dt 17
Sidebands
B lifetime from PDG 2002
tB = ps
Mixing frequency from PDG 2002
Dmd = ps-1
Total parameters 34
Global correlation coefficient for sin2b: 13%
All Dt parameters extracted from data
Correct estimate of the error and correlations

49. Control Sample: non-CP sample with CPV=0
Final check of residual detector biases on CP=0 control sample
of fully reconstructed, flavor specific sample (BD etc)
Input Bflav sample to CP fit
No CP asymmetry expected
Measure
Sample
“sin2b”
Bflav
0.021±0.022 B+
0.017±0.025

50. BABAR Result for sin2b (July 2002)
hCP = -1
hCP = +1
sin2b =  0.074

51. Pure Gold : (Clean) Lepton Flavor Tags
BABAR
81.3 fb-1
220 lepton-tagged
hf = -1 events
98% purity
3.3% mistag rate
20% better Dt resolution
CP asymmetry
is obvious !

52. Systematic Errors on sin2b from BABAR
s[sin2b]
Description of background events
0.017
CP content of background components
Background shape uncertainties, peaking component
Composition and CP content of J/yKL background
0.015
Dt resolution and detector effects
Silicon detector residual misalignment
Dt resolution model (Gexp vs 3G, Bflav vs BCP)
Mistag differences between BCP and Bflav samples (MC)
0.012
Fit bias correction and MC statistics
0.010
Fixed lifetime and oscillation frequency
0.005
Total
0.033

53. Updated (ICHEP04) sin2b results from Charmonium Modes
BABAR
Limit on direct CPV

54. Belle Results on sin2b from Charmonium Modes
BKS Sample
Belle
2005
New Belle value lower than in ’03
but still consistent with BaBar’04

55. CP Violation in B Decays Firmly Established

56. Lessons From sin2 Measurement With B0K0
In 2001, large CP Violation in B system was observed in this mode by BaBar and Belle.
It was the first instance of CPV outside the Kaon system.
It was also the first instance of a CPV effect which was O(1) in contrast with the Kaon system and confirms the 1972 conjecture of Kobayashi & Maskawa.
It excludes models with approximate CP symmetry (small CPV).
In 2005 sin2 is a precision measurement (5%) and agrees well with the constraints in the - plane from measurements of the CKM magnitudes.
Now it appears unlikely that one will find another O(1) source of CPV and the enterprise now moves towards looking for corrections rather than alternatives to the SM/CKM picture
Focus now shifts to measurements of time-dependent asymmetries in rare B decays which are dominated by Penguin diagrams in the SM and where New Physics could contribute to the asymmetries

57. End of Lecture 3 Tomorrow: Measurements of angles  and  ++ =?
“Sin2” in bs Penguin decay
Status of Unitarity Triangle
Future Directions : Tevatron, LHC-b….

58. Direct CPV in B- K- 0 Belle Belle BaBar
Not in BK- +
Belle
ACP(Kp0 ) = 0.04  0.05  0.02
Belle
ACP(Kp0 ) = 0.06  0.06  0.01
BaBar

59. CP Violation In B Decays: SM Expectations
Group various amplitudes in B decays by the associated CKM couplings
Helpful in categorizing B Decays:
where CPV is cleanly interpretable (quantitative) in SM
Where Hadronic uncertainties pollute interpretation of measured CPV

60. Decay Amplitude Weak Phase Structure in CPV
Most B decay final states have contributions from both “Tree” and 3 “Penguin” (Pt,Pc,Pu) diagrams.
All Tree diagrams (Spectator, W-exchange, W-Annihilation, rescattering) have same weak phase
The three Pi can have different Weak and Strong phases
EW penguins “suppressed” due to EW coupling

61. B Decay Amplitude Weak Phase Structure

62. Decay Amplitude Weak Phase Structure in CPV

63. Decay Amplitude Weak Phase Structure in CPV

64. Three Major “Classes” of B Decays For CPV

65. CPV in B0 Mixing 2  B0 f
off-shell states f
on-shell states f

67. Mixing Measurement at Belle (Hadronic Modes)
Mistag rate
BELLE
29.1 fb-1
Vivek Sharma , UCSD

68. The “Platinum” Final State
dominant decay
amplitude

69. Sin2b Likelihood Fit Fit Parameters
Combined unbinned maximum likelihood fit to Dt spectra of flavor and CP sample
Fit Parameters
sin2b
Mistag fractions for B0 and B0 tags 8
Signal resolution function 8
Empirical description of background Dt 17
B lifetime fixed (PDG value) tB = ps
Mixing Frequency fixed (PDG value) Dmd = ps-1
tagged CP samples
tagged flavor sample
35 total free parameters
All Dt parameters extracted from data
Correct estimate of the error and correlations

70. Mixing Measurement with Fully Reconstructed B Sample
29.7 fb-1
Dt [ps]
Precision measurement consistent with world average
 Well calibrated detector for Flavor tagging
Vivek Sharma , UCSD

71. Dt Resolution Function
Core
Tail
Outlier
Use the event-by-event
uncertainty on Dt
Dt Residual (ps)
R(dDt)
B0 flavour sample
CP sample
sDt (ps)
Different bias scale factor
For each tagging category
Vivek Sharma , UCSD

72. B0 B0 Mixing Asymmetry with Hadronic Sample
Unfolded raw asymmetry
Folded raw asymmetry
|Dt| [ps]
Flavor mistag rate
well calibrated from
mixing measurement
Dt [ps]
BABAR
29.7 fb-1
Vivek Sharma , UCSD

73. Belle Results on sin2b from Charmonium Modes
2003

74. Dmd Measurement in Comparison With World
WA: ± ps-1
Precision Dmd measurement
3% statistical error
2% systematic error dominated by MC correction
BaBar Measurements
Well Calibrated Detector for
B flavor tagging
Vivek Sharma , UCSD