1. Experimental Aspects of CP Violation in B Decays : Lecture IV
Vivek Sharma
University of California, San Diego

2. Outline of Lectures 3 & 4 Lecture 3
Three types of CP violation & SM expectations in B Decays
Decay amplitude Weak phase structure
Decay asymmetry prediction in SM
General strategy for time-dependent CP asymmetry measurement
Observables that probe angle 
Time dependent CP asymmetry in B -> Charmonium KS modes Step-by-Step
Other modes with subdominant or dominant Penguin
Lecture 4
Observables that probe angle
Observables that probe angle 
Summary of current measurements
Future prospects

3. CP Asymmetries and Testing  against “”

4. Confronting Loop Decays with Tree Dominance
decays are tree and penguin diagrams, with same dominant weak phases
decays are pure “internal” and “flavor-singlet” penguin diagrams
High virtual mass scales involved: believed to be sensitive to New Physics
Both decays dominated by single weak phase
Tree:
Penguin:
New Physics? 3 ?

5. bs Penguin Observables
Naive (dimensional) uncertainties on sin2
One may identify golden, silver and bronze-plated s-penguin modes:
Gold
Color-suppressed tree
Silver
Color-suppressed tree
Bronze
Note that within QCD Factorization these uncertainties turn out to be much smaller, but you must believe in QCD Factorization !

6. Results on sin2b from s-penguin modes
All new!
All new!
2.7s from s-penguin to sin2b (cc)
2.4s from s-penguin to sin2b (cc)

7. World Averages for sin2b and s-penguin modes
3.6s from s-penguin to sin2b (cc)
No significant sign of Direct CP
Beginning to look suspicious but must wait for 5/expt to get exciting

8. Comparison of Sin2 With “Sin2”
From Z. Ligeti
Upper limit
Some modes more clean for
Interpretation than others

9. Projections for Penguin Modes (BaBar)
f0KS
KSp0
jKS
h’KS
KKKS
Luminosity expectations:
2004=240 fb-1
2009=1.5 ab-1
K*g
Similar projections for Belle as well
5s discovery region if non-SM
physics is 30% effect
2004
2009
Projections are statistical errors only;
but systematic errors at few percent level

10. PEP II Luminosity Projections
0.5 ab-1
2004
2006
1.6 x 1034

11. Probing The CKM Angle 

12. Example of Class I (b u u d): B0 +-
Neglecting Penguin diagram

13. Reality in B0 +-, + -
Tree
Penguin
Ratio of amplitudes |P/T| and
strong phase difference 
can not be reliably calculated!
One can measure dapeng using isospin relation and bounds to get 

14. Measurement of  : Reality in B0 +-, + -
3 such relations (one for each polarization)
Now need
to measure 

15. Time Dependent Asymmetry Measurement: B0 +-
BABAR B0 B0

16. Time Dependent Asymmetry Measurement: B0 +-
(372  32) +- signal
152M BB
152M BB
good tag
Belle claim of direct and
Indirect CPV not supported by
BaBar data
Cpp = 0.15(stat) 0.07(syst)
Spp = 1.00 0.21(stat) 0.07(syst)

17. Comparison of Present and Past B0 +- results
Coefficients of time-dependent CP Asymmetry
With large penguins
and |P/T| ~ 0.3
With no penguins
>3s discrepancy between BABAR & Belle
3.2s
5.2s
Belle 3.2s evidence for Direct CP violation not supported by BABAR measurements
Caution When averaging!

18. “One is too few and three is too many” -Carlo Rubbia, CERN DG, Its essenstial for an independent & similarly capable experiment to verify an experiment’s claims!

19. Constraining : B-  p- p0 Rate Measurement
B-  p- p0 (I=2, I=1/2) has only tree amplitude, no penguin  Base of Isospin triangle u B- - B- 0 u
BaBar

20. Constraining  : B  p0p0 Decay Diagrams
Difficult to calculate rates for such processes,
Smaller the better for constraining 
Grossman-Quinn bound:

21. B  p0p0 : Rate and Flavor Tagged Rate Asymmetry
First measurements
B00 is large !
Measured by flavor of the other B  Btag
4.9s
BaBar
6.0s
Belle
274M BB
Average
Key ingredient for Isospin analysis
And constraints on angle 

22. Estimate of  From B Studies
Interpretation unclear because of inconsistency in B0 +-
Penguin pollution
 Not well constrained !

23. ACP(t) in B0r+r- Decays
Run1-3 data (122M BB)
314±34 Signal Events (205 tagged) fL=1.00±0.02
Events with cleanest tags
mES DE
Fit: total
Fit: bkgd
After cuts on likelihood ratio
BaBar prelim
BaBar prelim

24. ACP(t) in B0r+r- Decays
314±34 Signal Events B0+-
Distribution of ± helicity distributions in data
Clear demonstration of strong longitudinal polarization
fL=1.00±0.02

25. Results for sin2eff from B  r+ r- decays
Extraction of a similar to pp, but with advantage of larger rate ( 5) & smaller Penguin pollution because
BABAR
Time-dependent CP Asymmetry

26. Isospin Corrections for a From MeasurementsVs
Compare with 35o for pp
Can Measure 
more precisely
Geometric limit on 2dapeng:
Grossman-Quinn bound

27. B is an example of the fact that if you build a good detector and take lots of data, people (with help from nature) will find unpredictable & innovative ways to surmount difficult sticky situations! e.g: B for precise measurement of  was never seriously discussed at conferences till last year

28. Summary Of Measurements of Angle 
Confidence level =1
 Favored result

29. Towards The Angle : The phase in Vub
Look for B decays with 2 amplitudes with relative weak phase 
Direct CP Asymmetry
 Angle 

30. Angle  from B±DK±: Critical Requirement
Relative size of the 2 B decay amplitudes matters for interference
Want rb to be large to get more interference  Large CP asymmetry
Diff. between rb=0.1 and rb=0.2 substantial for precision on 
Theory cannot calculate r reliably must measure experimentally
Color suppression: Fcs  [0.2,0.5]
Left side U.T.: Ru  0.4
Expected range

31. Angle  from B±D0 K±: Current Status
Even with ~250 fb-1 data in hand for each experiment, reconstructed samples of B±DK± events are too few for a meaningful measurement of the angle  (and r, and strong phase )
E.g: Effective Br. Ratio for (B±D0 K±)(D0K+-) 10-7
The exception is the case when B±D0 K± and D0KS+- , a Cabbibo favored decay accessible to both D0 and D0. Entire resonant substructure can be used with Cabbibo-allowed and suppressed modes in D0KS + - interfering directly

32.  from B±D0 K±: D0 KS + - Dalitz Analysis2
Schematic
view of the
interference

33.  from B±D0 K±: D0 KS + - Dalitz Analysis
Sensitivity to g
A functional form (model) for f(m2+ ,m2- ) obtained from high statistics D*+D0 sample can fix phase variation dD across Dalitz plot.
Fit Dalitz distribution for B+ and B- simultaneously using A- & A+ forms to extract r,  and  simultaneously. No additional assumptions necessary
Only two-fold ambiguity in g extraction
g=75,d=180,rB=0.125
First and most precise such measurement from Belle 

34. D0 Dalitz Plot Model From High Statistics D*+ Sample
Characterize Dalitz distribution
with 15 two-body amplitudes

35. B+ D0K+ Samples B+ D(*)0K+ signal B+ D0K+ D0  Ksπ+π– B+ D*0K+
misID
146 events
112±12 signal
25% background
ΔE (GeV)
Mbc (GeV)
B+ D*0K+
D*0 D0π0
D0  Ksπ+π–
D*0K
D*0π
misID
39 events
33.6±6.2 signal
12% background
140 fb-1
ΔE (GeV)
Mbc (GeV)

36.  from B±D0 K±: D0 KS + - Dalitz Analysis
Belle
140 fb-1
M2(KSp-) [GeV2]
M2(KSp+) [GeV2]
73 events
73 events
Visible asymmetry in Dalitz plots
20 events
19 events
Large !
Good start for direct measurement of  already, 2 data in hand
Ultimate sensitivity will depend on precise value of rb

37.  from B±D0 K±: D0 KS +- Dalitz Analysis
261 19
D0K
83 11
D*0(D0p0)K
40 8
D*0(D0g)K

38. With measurement of CKM element magnitudes and Angles , ,  in hand, Lets Look at the - plane to see if all these measurements hang together in 2004 !
Courtesy: The CKMfitter Group

39. Bd mixing
+ CPV in
K mixing
(K)
Allowed region
Allowed region

40. Add
|Vub/ Vcb|

41. +
BS Mixing
constraint

42. + Sin2

43. + 
constraint

44. All measurements consistent, apex of (,) well defined
+ 
measurement

45. Summary Of Results
B factories producing data at record breaking pace !
In just 4 years of data taking, CP Violation firmly established in the B system by BaBar & Belle
CPV in interference of Decay and Mixing: sin2=0.7260.037
Direct CPV: ACP(B0K-+)= -0.110.02
Limits on CPV in B mixing
Unlike in the Kaon system, CPV in B system is O(1) effect
“sin2”=0.300.08 from bs penguin decays 3.5 from sin2K
Needs careful investigation
B+- provides the best measurement of angle 
First measurement of  from B±D0 K±, D0 + - Dalitz analysis  the most promising technique with added statistics
But precise & redundant measurements of  will be difficult
All observables yield a consistent picture. The - plane is now sharply defined

46. Limits of Future Explorations

47. PEP II Luminosity Projections
0.5 ab-1
2004
2006
1.6 x 1034
Similar projections for Belle

48. Future Prognostications
BaBar & Belle have just begun and have a long term and a rich program for B physics (>2007) [I showed only 10% of results !]
Most CP asymmetry measurements are statistics limited
S-Penguins
Alpha & Gamma measurements (multiple to be sure)
CPV in B mixing remains to be discovered
Rare decays such as Radiative and Electroweak are a very clean probe of new physics.
e.g. F-B Asymmetry in b s l+ l-
CPV in B  s  etc
Tevatron is accumulating large B samples:
They are the only current laboratory for studying Bs and b properties
Immediate focus : Bs oscillation search till xs 20
B Physics return to Europe in 2007 with LHC-B !!
Will be the ultimate instrument for precision B physics
Precise exploration of CPV in BS and Bd systems

49. LHC-b
Reduced
material
Improved
level-1 trigger

50. LHC-b: Example of CKM Physics Reach (107 s)
Reaction
Para-meter
LHC
Yield
S/B
Sensitivity†
Bop+p-
Asym
26,000
>1.4
BoJ/y KS ,
J/y l+ l-
sin(2b)
241,000
1.2
0.02
Bs Ds K-
g-2c
g
5,400
>1
14o
Bs Ds p- xS
80,000 3
<100†
B-Do (K+p-) K- g
B-Do (K+K-) K-
B0 D0(Kp)K*0
B0 D0CPbar K*0
B0 D0CP K*0bar
B-KS p-
BoK+p-
Reaction
Parameter
Bor+p- a
Boropo
BsJ/y h,
J/y l+ l-
sin(2c)
BsJ/y h,
BsJ/y f
DGS/GS

51. Thank You & Best Wishes !

52. Backup Slides

53. Strategy for CP violation study in B0  + -
Helicity Frame
Pure
CP-eigenstate
In a simultaneous fit we measure 4 quantities:
+- yield and Polarization (fraction of longitudinal events)
CLong and SLong CP parameters
The additional parameters CTran and STran are fixed to zero
(vary within (-1.0 ; 1.0) in the study of the systematics) .
Longitudinal polarization
Pure CP-eigenstate
Transverse polarization
Mix of CP-eigenstate
(not useful…) 53

54. Ingredients of +- analysis
Event selection:
As the longitudinal polarization was expected to be large (>90%) we have optimized our analysis to be able to treat the events with large values of |cos(H)|
(Longitudinal events have for the helicity distribution which is in ~cos(H)2).
See details in BAD #634, #798.
Rejection of continuum:
NN approach.
Combine discriminating variables:
L0 and L2 monomials for
charged and neutral particles
Sum of transverse momentum
Cosine of the B thrust with z axis
Cosine of the thrust of the r.o.e
with the B thrust
Cosine of the B direction with z axis.
0 angular distribution.
Choice of best candidate:
Multiplicity per event ~ 1.8
Choose one candidate per event with best 2.
transverse
longitudinal
qqbar 54

55. Likelihood Fit 4 types of events: Likelihood:
8 discriminating variables
 mES , E, NN output and t
Vector particle information (m1, m2, cos(1), cos(2)).
4 types of events:
True Signal.
Self Cross-Feed (~50% of the events
come from 0 mis-reconstruction):
Longitudinal  (SCF fraction: 49%),
Transverse  (SCF fraction: 25%).
Continuum.
floating parameters to model PDFs
B backgrounds:
Charmless B background (B0+-, B+0  +…. ).
Charm B (bc) background.
19 distinct PDFs!!!
Likelihood:
The likelihood is the sum over the types of events of the terms :
Pdf(xNN)  Pdf( E)  Pdf( mB ),  Pdf( t)  Pdf( m1)  cos(1)  Pdf(m2)  cos(2)
Minimization and Pdf modeling based on the RhoRhoTools package (RooFit technology).
Self
Cross-Feed
True
Signal
mES
mES 55

56. Angle  from B±DK± : 3 Sets Of Observables
D decays to CP eigenstates (p+p-, Ksp0, …)
Interference term small
D decays to definite flavor states (K-p+)
Interference term large
D decays to 3-body states (Dalitz analysis of D0 decay)
Interference varies in 2-D Dalitz plot
Common parameters for all analyses :

57. B±DK± : D0 Decays to CP Eigenstates
(a.k.a. GLW technique)
Babar & Belle averages
Note: rb and db different for each B mode (DK,DK*,D*K)
No sign of large direct CP violation (rb is not anomalously large)

58. B±DK± : D0 decays to Definite Flavor
(a.k.a. ADS technique)
Favored (b c)
favored
suppressed
Suppressed (b u)
Babar preliminary
Belle
Events / 10 MeV
Results for
Hints of signals
Rules out very optimistic scenario (very large rb)
Favors small rb
Belle
ICHEP 2004
Babar
hep-ex/