1. Lecture 3: Time-Dependent Asymmetries as a Test of the Standard Model
CP asymmetries in CP eigenstates involving b ® ccs transitions
Measuring sin2b in other channels
Asymmetries in 2-body neutral B decays
Brief word on future prospects and plans

2. Experimental Technique for B Factories
Exclusive B Meson Reconstruction
(4S) produces coherent B pair: t ® Dt
Time-integrated asymmetries are zero
B-Flavor Tagging
(flavor eigenstates) lifetime, mixing analyses
(CP eigenstates) CP analysis
Aug 5-7, 2002
D.MacFarlane at SSI 2002

3. (after tagging & vertexing)
CP Sample for BABAR
1506 signal candidates,
purity 94%
988 signal candidates,
purity 55%
BABAR
81.3 fb-1
(after tagging & vertexing)
Aug 5-7, 2002
D.MacFarlane at SSI 2002

4. Improved Tagging at BABAR
4 Physics
Categories
9 Tagging
Categories
Sub-taggers
Electron-K
Muon-K
Electrons
Muons
Kaon-psoft
Kaon 1
psoft
Kaon 2
Other
Lepton
Kaon I
Kaon II
Inclusive
Combined Tagging NN
7% improvement in Q = eD2 (DQ = 1.9%)
Aug 5-7, 2002
D.MacFarlane at SSI 2002

5. Flavor Tagging Performance in Data
The large sample of fully reconstructed events provides the precise determination of the tagging parameters required in the CP fit
Tagging category
Fraction of tagged events e (%)
Wrong tag fraction w (%)
Mistag fraction difference Dw (%)
Q =
e (1-2w)2 (%)
Lepton
9.1  0.2
3.3  0.6
-0.9  0.5
7.9  0.3
Kaon I
16.7  0.2
9.9  0.7
-0.2  0.5
10.7  0.4
Kaon II
19.8  0.3
20.9  0.8
-2.7  0.6
6.7  0.4
Inclusive
20.0  0.3
31.6  0.9
-3.2  0.6
0.9  0.2
ALL
65.6  0.5
28.1  0.7
Error on sin2b and Dmd depend on the “quality factor” Q approx. as:
Highest “efficiency”
Smallest mistag fraction
BABAR
81.3 fb-1
Aug 5-7, 2002
D.MacFarlane at SSI 2002

6. Comparison Tests with New Tagger
Test of crucial underlying assumption: tagging the same for CP & Bflav samples
BABAR
81.3 fb-1
CP vs Bflav sample
Bflav sample vs MC
Aug 5-7, 2002
D.MacFarlane at SSI 2002

7. Golden Sample: (cc)KS CP Eigenstates
BELLE
78 fb-1
1996 signal candidates,
purity 94%
Aug 5-7, 2002
D.MacFarlane at SSI 2002

8. CP Eigenstate Sample: J/yKL
BELLE
78 fb-1
1330 signal candidates,
purity 63%
Aug 5-7, 2002
D.MacFarlane at SSI 2002

9. Track level and event level look-up tables
Tagging at Belle
Track level and event level look-up tables
Quality factor r varies from
0 = low likelihood
1 = high likelihood
Data vs MC comparison
BELLE
41.8 fb-1
Aug 5-7, 2002
D.MacFarlane at SSI 2002

10. Mistag rate extracted in six bins in r from mixing fit
Measuring Mistag Rate
Mistag rate extracted in six bins in r from mixing fit
Comparison between measured (1-2w) and quality factor r obtained in 6 bins in r r1 r2 r3 r4 r5 r6
BELLE
78 fb-1
Aug 5-7, 2002
D.MacFarlane at SSI 2002

11. CP Analysis: Time Distributions
hCP = -1
perfect
flavor tagging &
time resolution
realistic
mistag probability &
finite time resolution
Aug 5-7, 2002
D.MacFarlane at SSI 2002

12. Time-Dependent CP Asymmetries
Time-dependence of
Time-dependence of
CP-violating asymmetry in
(Assuming no confusion of Brec state)
Use the large statistics Bflav data sample to determine the mistag probabilities and the parameters of the time-resolution function
Aug 5-7, 2002
D.MacFarlane at SSI 2002

13. Global correlation coefficient for sin2b: 13%
sin2b Likelihood Fit
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
Aug 5-7, 2002
D.MacFarlane at SSI 2002

14. BABAR Result for sin2b hCP = -1 hCP = +1 sin2b = 0.755  0.074
Aug 5-7, 2002
D.MacFarlane at SSI 2002

15. Checks with control samples where no asymmetry expected
Belle Result for sin2b
BELLE
78 fb-1
Checks with control samples where no asymmetry expected
Sample
“sin2b”
B0 ®D*+p-
0.035±0.032
B0 ®J/yK*
-0.021±0.093
B0 ®D*ln
0.004±0.017
Aug 5-7, 2002
D.MacFarlane at SSI 2002

16. Belle Result for sin2b hCP = -1 hCP = +1 BELLE 78 fb-1 Aug 5-7, 2002
D.MacFarlane at SSI 2002

17. Pure Gold: Lepton Tags Alone
BABAR
81.3 fb-1
220 lepton-tagged
hf = -1 events
98% purity
3.3% mistag rate
20% better Dt resolution
Aug 5-7, 2002
D.MacFarlane at SSI 2002

18. Check “null” Control Sample at BABAR
Input Bflav sample to CP fit
No asymmetry expected
Sample
“sin2b”
Bflav
0.021±0.022 B+
0.017±0.025
Aug 5-7, 2002
D.MacFarlane at SSI 2002

19. 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
Aug 5-7, 2002
D.MacFarlane at SSI 2002

20. Monte Carlo Correction
Potential bias on sin2b evaluated by fitting full MC in 2 ways:
Fitting data-sized signal MC samples with mistag fractions and Dt resolution fixed to the MC truth values (see plot)
Average bias =  0.005
Same as above except mistag fractions and Dt resolution from Breco MC
Average bias =  0.005
One possible source of bias comes from neglecting the known correlation between the mistag fractions and s(Dt)
Estimates from toy and full MC indicate a bias at the level of
We correct the fitted sin2b by subtracting and assign a systematic error of to this correction
Aug 5-7, 2002
D.MacFarlane at SSI 2002

21. Comparison of Resolution Functions
Aug 5-7, 2002
D.MacFarlane at SSI 2002

22. Subsample Checks
Aug 5-7, 2002
D.MacFarlane at SSI 2002

23. World Average sin2b BABAR BELLE CDF ALEPH OPAL World average
Aug 5-7, 2002
D.MacFarlane at SSI 2002

24. Standard Model Constraints
Aug 5-7, 2002
D.MacFarlane at SSI 2002

25. Summary of sin2b from ccs modes
Precision measurements of sin2b from charmonium modes now available
World average
Results have been improving by more than just luminosity gain
Million BB pairs
July 00
Feb 01
July 01
Mar 02
July 02
sin2b = ± (stat) ± (syst)
BABAR-PUB-02/008, hep-ex/ ,
submitted to PRL
sin2b = ± (stat) ± (syst)
BELLE-CONF-0201, hep-ex/ ,
submitted to ICHEP2002
sin2b = ± (stat+sys)
The Standard Model remains unscathed, but the high statistics future of B Factories will provide further opportunities to challenge the theory
Aug 5-7, 2002
D.MacFarlane at SSI 2002

26. CP Violation in the B System
CPV through interference of decay amplitudes
Aug 5-7, 2002
D.MacFarlane at SSI 2002

27. CP Violation in the B System
off-shell states f
on-shell states f
CPV through interference of decay amplitudes
CPV through interference of mixing diagram
Expected to be very small
Aug 5-7, 2002
D.MacFarlane at SSI 2002

28. Formalism for CP Violation in Mixing
Time-dependent CP Asymmetry:
constant
with
time
See for instance Bañuls & Bernabéu hep-ph/
Aug 5-7, 2002
D.MacFarlane at SSI 2002

29. Characterizing the Dilepton Sample
Search for asymmetry in same-sign dilepton sample containing events
BABAR
20.7 fb-1
Sample backgrounds B(Dt): 4.3% continuum 24% direct+cascade 12% direct+fake
Measurement region > 200mm
Aug 5-7, 2002
D.MacFarlane at SSI 2002

30. Determination of AT BABAR So far, no experimental evidence
20.7 fb-1
BABAR PRL 88, (2002)
So far, no experimental evidence
of large CP violation in B0 mixing
To a good approximation:
Aug 5-7, 2002
D.MacFarlane at SSI 2002

31. *Would be zero if one assumed CP invariance in cascade decays
Systematic Errors
Source
s(AT) [%]
Sample
Detection asymmetry for electrons
0.5
Direct electrons in semileptonic B decays
0.6
Direct muons in semileptonic B decays
Non-BB background asymmetry
0.7
Off-resonance data
BB background asymmetry
0.9
* On-resonance data with Dz < 100mm
Total
1.4
Statistical Error
1.2
*Would be zero if one assumed CP invariance in cascade decays
Aug 5-7, 2002
D.MacFarlane at SSI 2002

32. CP Violation in the B System
CPV through interference of decay amplitudes
CPV through interference of mixing diagram
CPV through interference between mixing and decay amplitudes
Directly related to CKM angles for single decay amplitude
Aug 5-7, 2002
D.MacFarlane at SSI 2002

33. CP Formalism Revisited
For B0 decays, allowing for more than one amplitude contributing to the decay to fCP
Amplitude
ratio
CP eigenvalue
Full time-dependent distributions and CP asymmetry:
Aug 5-7, 2002
D.MacFarlane at SSI 2002

34. Search for Direct CP in Golden Sample
Redo fits tagged time distributions of CP sample with sine and cosine terms (assuming DG = 0)
If more than one amplitude contributes |l| might be different from 1
Probing new physics: only use hCP = -1 sample (contains no mixing background)
No evidence of direct CP violation due to decay amplitude interference
Coefficient of the “sine” term unchanged
Aug 5-7, 2002
D.MacFarlane at SSI 2002

35. Other Modes for sin2b
Provide an independent measurement of CP violation
Some possible b ® sss modes
fKS is CP = -1 with Iml = -sin2b
Sensitive to new physics in b ® s loop diagram
Pure b ® s penguin process?
Other examples
h’KS is CP=+1
K+K-KS appears to be mostly CP=+1 according to Belle
Possible double-charm modes
B ® D*+D*- or B ® D*D channels
No KS mixing, but penguins?
Other charmonium modes
Aug 5-7, 2002
D.MacFarlane at SSI 2002

36. BABAR Results for fKS BABAR 81.3 fb-1 Ncand = 66 Purity = 50%
BABAR-CONF-02/016, hep-ex/
Aug 5-7, 2002
D.MacFarlane at SSI 2002

37. Belle Results for b ® sss
BELLE-CONF-0225
mbc
Aug 5-7, 2002
D.MacFarlane at SSI 2002

38. More CP channels: B ® D*+D*-
BABAR
81.3 fb-1
Tree
Penguin
Cabibbo suppressed
Ncand = 102
Purity = 82%
No KS mixing contribution
Potential for significant Penguin contamination
BABAR-CONF-02/014, hep-ex/
Aug 5-7, 2002
D.MacFarlane at SSI 2002

39. CP Composition of B0  D*+D*-
Measure small CP odd fraction (corrected for acceptance):
R = 0.07  0.06 (stat)  0.03 (syst)
Preliminary
BABAR
81.3 fb-1
Aug 5-7, 2002
D.MacFarlane at SSI 2002

40. The PDF The decay rate f+(f-) for a B tagged as a B0 (B0)
Aug 5-7, 2002
D.MacFarlane at SSI 2002

41. CP Asymmetry Fit Results
Preliminary
If Penguins are negligible
i.e., about 2.7s difference
Aug 5-7, 2002
D.MacFarlane at SSI 2002

42. Testing the Origins of CPVa g b
Aug 5-7, 2002
D.MacFarlane at SSI 2002

43. CP Violation in B0 ® π+π- Decays
Decay distributions f+(f-) when tag = B0(B0)
For single weak phase from tree diagram
Cpp = 0, Spp = sin2a
|  |  1  must fit for direct CP
Im ()  sin2  need to relate asymmetry to 
With additional weak phase from penguin diagram
Cpp  0, Spp = sin2aeff
Aug 5-7, 2002
D.MacFarlane at SSI 2002

44. Competing Amplitudes for B  h+h-
Tree diagrams
Penguin diagrams s K+ p- B0 s K+ p- B0
Penguin dominated:
Potential direct CPV and constraints on g d p+ p- B0 d p+ p- B0
|Penguin| ~ 0.3|Tree|
Complicates extraction of a from mixing induced CPV
Aug 5-7, 2002
D.MacFarlane at SSI 2002

45. Analysis Overview Analysis issues: charmless two-body B decays
Rare decays! BR ~ → need lots of data (B Factories)
Large background from e+e- → qq → need background suppression
Ambiguity between p and K → need excellent PID (DIRC or ACC)
CP analysis issues:
Need to determine vertex position of both B mesons → standard vertex separation algorithms
Need to know the flavor of “other” B → standard tagging algorithms
Analysis proceeds at BABAR in two steps:
Use kinematic, topological, and PID information in a global ML fit to extract yields for pp, Kp, and KK decays, as well as the asymmetry AKp
Exclude vertexing & tagging information to avoid systematic error
Add vertexing and tagging information to extract Spp and Cpp
Yields and AKp fixed to result of the first fit
Aug 5-7, 2002
D.MacFarlane at SSI 2002

46. Pion mass assumed for all tracks, so shift in DE for Kp and KK decays
Kinematics
Pion mass assumed for all tracks, so shift in DE for Kp and KK decays
s(mES)  2.6 MeV/c2
(DE)  26 MeV Kp KK pp
Signal Monte Carlo
Sideband
Sideband
Aug 5-7, 2002
D.MacFarlane at SSI 2002

47. Background Suppression
Background is due to light-quark production e+e- →qq (q=u,d,s,c)
Jetty topology, distinct from spherical B decays
Cut on angle qS between sphericity axes of B candidate and the remaining particles in the event:
|cos(qS)| < 0.8, removes 83% bkg, 20% signal
Define Fisher discriminant F derived from momentum flow in the event
Used directly in the ML fit
Sideband Data
Signal MC
Aug 5-7, 2002
D.MacFarlane at SSI 2002

48. Branching Fraction Fits
Projections in mES and DE
Proj eff: 52% pp pp
26070 two-prong candidates (97% background, mostly continuum)
BF Likelihood includes PDFs for: mES, DE, Fisher, qc for + & - tracks
Proj eff: 79% Kp Kp
BABAR
81.3 fb-1
Aug 5-7, 2002
D.MacFarlane at SSI 2002

49. Branching Fraction Results
Preliminary
Mode
Yield
BR [10-6]
ACP(Kp)
B0 → p+p-
157±19
4.7±0.6±0.2
B0 → K+p-
589±30
17.9±0.9±0.7
-0.102±0.050±0.016
B0 → K+K-
1±8
<0.6 [90%CL]
BABAR
81.3 fb-1
BABAR-PUB-02/009, hep-ex/
Aug 5-7, 2002
D.MacFarlane at SSI 2002

50. Two-Body Tagged Sample
Tagging efficiency is very different for signal and bkg
Strong bkg suppression in lowest mistag categories (Lepton/Kaon)
Different bkg tagging efficiencies for pp, Kp, KK
Sum of p+p-/K+p-: No particle ID used until the fit is performed
BABAR
81.3 fb-1
Untagged category also used
Aug 5-7, 2002
D.MacFarlane at SSI 2002

51. CP Asymmetry Results from BABAR
Fit projection in sample of pp-selected events
qq + Kp
For CP asymmetry add tagging and Dt measurement to likelihood but fix yields and AKp
BABAR
81.3 fb-1 m
Preliminary
Aug 5-7, 2002
D.MacFarlane at SSI 2002

52. App vs. mES in sample of pp-selected events
Crosschecks
App vs. mES in sample of pp-selected events
Inspect pp-selected sample
2-param fit consistent with full fit
Asymmetry vs. mES
Yields consistent with measured value of Cpp, which do not suggest large direct CP violation
Toy MC generated over all allowed values of Spp and Cpp
Expected errors consistent with data
No significant bias observed
Validated in large samples of signal and background MC events
Systematic errors dominated by uncertainty in PDF shapes
signal bins
Aug 5-7, 2002
D.MacFarlane at SSI 2002

53. Belle Signal for B → p+p–
Reject most of Kp feedthrough with PID systems
5.271 GeV/c2
5.287 GeV/c2
p+p– Kp qq
p+p–+Kp
|DE|<0.067 GeV
other rare decays
BELLE
41.8 fb-1
BELLE, hep-ex/
Aug 5-7, 2002
D.MacFarlane at SSI 2002

54. B → p+p– Time Distributions
162 events after vertexing and flavor tagging
|DE| < GeV
B0 tagged
– 5 5
Dt (ps)
Flavor Blind
total
qq + Kp
p+p–
Dt (ps)
p+p–
B0 tagged
– 5 5
Dt (ps)
p+p–
Aug 5-7, 2002
D.MacFarlane at SSI 2002

55. B → p+p– Fit Result BELLE p+p– sample 41.8 fb-1 (BG subtracted)
– 5 5
Dt (ps)
B0 tagged
BELLE, hep-ex/
control sample
Aug 5-7, 2002
D.MacFarlane at SSI 2002

56. Crosscheck with B → K+p- Sample
asymmetry
Dt (ps)
Events / 20 MeV
K+p–
other rare decay
pp feed across qq
DE [GeV]
Null Asymmetry
Aug 5-7, 2002
D.MacFarlane at SSI 2002

57. Comparison of Results BABAR Belle App +0.30±0.25±0.04 Spp
+0.02 ±0.34±0.05
A2pp+S2pp ≤ 1
Aug 5-7, 2002
D.MacFarlane at SSI 2002

58. Consistent with SM expectations
Interpretation?
Gronau and Rosner,
Phys. Rev. D65, (2002)
BABAR Result
Spp and Cpp are determined by a, b, |P/T|, and d.
Consistent with SM expectations
Aug 5-7, 2002
D.MacFarlane at SSI 2002

59. PEP-II Luminosity Projections
Equivalent expectation for Belle
Aug 5-7, 2002
D.MacFarlane at SSI 2002

60. Possible PEP-II upgrade
Aug 5-7, 2002
D.MacFarlane at SSI 2002

61. Projections for CP Asymmetry Measurements
Some rough estimates
Expression of Interest at KEK for 1035 machine in spring 2002
Ongoing workshops to examine this or higher luminosity options
Snowmass 2001 study of 1036 concept and physics capability
Aim to be competitive and complementary to LHCb, BTeV on time scale of end of the decade
Physics case still being explored; still very early days in the exploration of these possibilities
Requires completely new vacuum and rf system, mostly new detector (current technologies cannot handle backgrounds)
Aug 5-7, 2002
D.MacFarlane at SSI 2002

62. Future Tests of the Standard Model
Assumes |Vcb| ~ 3% and |Vub| ~ 10%
Much experimental and theoretical work underway to achieve this
New results on inclusive/exclusive semileptonic decays
Will be entering an era of very large tagged samples
Assumes Dms known to <1% from Tevatron in 2004?
ca. 2007:
s(sin2b) ~ 1%
a ~ 5o, g ~ 10o
Illustration of SM breakdown
Aug 5-7, 2002
D.MacFarlane at SSI 2002

63. World average dominated by BELLE and BABAR
Summary
Now in the era of B Factories, with a renaissance of experimental and theoretical activity in B physics
Data samples are 5 times larger than CLEO; will be 10 times larger within a few years
July 2001 saw the beginnings of this program
But…still working towards a definitive systematic test of Standard Model expectations and constraints
Motivation for these and upcoming facilities is to provide a definitive test of CP violation in the Standard Model
Unambiguous observation of CP violation in the B system
World average dominated by BELLE and BABAR
July 2002: Textbook plots!
Aug 5-7, 2002
D.MacFarlane at SSI 2002

64. Bibliography: Lecture 3
[sin2b] Belle Collab, PRL 86, 2509 (2001)
[sin2b] Belle Collab, PRL 87, (2001)
[sin2b] Belle Collab., hep-ex/ , to appear in PRD
[sin2b] Belle Collab., hep-ex/ , submitted to ICHEP2002
[sin2b] BABAR Collab., PRL 86, 2515 (2001)
[sin2b] BABAR Collab., PRL 87, (2001)
[sin2b] BABAR Collab., hep-ex/ , to appear in PRD
[sin2b] BABAR Collab., hep-ex/ , submitted to Moriond2002
[sin2b] BABAR Collab., hep-ex/ , submitted to PRL and ICHEP2002
[phi-KS] Belle Collab., BELLE-CONF-0225, submitted to ICHEP2002
[phi-KS] BABAR Collab., hep-ex/ , submitted to ICHEP2002
[D*D*] BABAR Collab., hep-ex/ , submitted to ICHEP2002
[h+h-] BABAR Collab, PRD 65, (2002)
[h+h-] Belle Collab., PRL 89, (2002)
[h+h-] BABAR Collab., hep-ex/ , submitted to PRL
Snowmass 2001, SuperBABAR Report, SLAC-PUB-8970
Belle Collab., SuperKEKB EOI,
Aug 5-7, 2002
D.MacFarlane at SSI 2002