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

2. Outline of Lecture IV
Observables that probe angle
Observables that probe angle 
 Vs  : CPV in Penguins and Search for NP
Summary of current measurements
Future Directions

3. Probing The CKM Angle 

4. CKM Angle  From (b u u d) Process: B0 +-
Neglecting Penguin diagram T P

5. Decay Amplitudes 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 

6. Time Dependent Asymmetry Measurement: B0 +-
BABAR B0 B0
sin2 = ??

7. Estimating Penguin Pollution in B0 +-, + -
Needs lots of statistics for B  0 0 and B  0 0 rate measurements

8. 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

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

10. 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
Bad news is C  is not precise enough
and B00 is too large for useful G-Q bound

11. Angle  From B+ - : Bottomline
B+ - TD CPV
Very weak constraint on  [67o -131o]
Needs more precise C00 measurements

12. B0+ - Decay As Probe of T P
This was a surprise !
Two years ago few would
have bet that this system
would play a defining role
in  measurement !
This system seems to have
the monk’s blessings !
(Penguin contribution turns
out to be small….(why ?) )

13. B0 + - System As Probe of 
Blessing # 1
Likelihood projection
Although 2 0’s make efficiency small

14. B0 + - System As Probe of 
Blessing # 2
Blessing # 3
68%C.L.
bkgd
total
 Helicity angle

15. TD CPV Measurement in B0 + -
Shown are events from the Lepton and Kaon1 tagging categories only
total likelihood
total background
617 52 signal events
CPV not yet observed here
but measurement constrains 

16. Discerning  BaBar B0 + - Br(r+r-) (30±6) 10-6 Br(r+r0)
(26±6) 10-6
Br(r0r0)
<
B0 + -
BaBar

17. 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 hopeless situations! e.g: B for precise measurement of  was never seriously discussed at conferences till 2003 !!

18. Probing The CKM Angle 

19. CP Asymmetry In BDK Decay  
Look for B decays with 2 amplitudes with relative weak phase 
Relative strength of the two B decay amplitudes matters for interference
Want rb to be large to get more interference  Large CP asymmetry

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

21.  from B±D0 K± with D0 KS + - Dalitz Analysis
Factorized Amplitudes From Data !

22. B Samples From Belle (253 fb-1)

23. The B->D(*)0 K(*) Dalitz Distributions: Belle
Analysis is statistics limited

24. Belle ‘05

25. Measurement Of CKM Angle 
Belle ‘05

26. Angle (CPV) Measurements And The Unitarity Triangle >> Putting Them All Together <<

27. The Unitarity Triangle From Just CPV Measurements

28. Probing New Physics Contribution to CP Violation Via Penguin Loops in B Decays

29. << Testing  Vs “” >>
New Physics ?
Standard Model SM

30. Compare sin2 with “sin2” from CPV in Penguin decays of B0
Both decays dominated by single weak phase
Tree:
Penguin:
New Physics? 3 ?
Must be if one amplitude dominates

31. Ranking Penguin Modes by SM “pollution”
Naive (dimensional) uncertainties on sin2
Decay amplitude of interest
SM Pollution f f
Gold
SemiGold
Bronze
Note that within QCD Factorization these uncertainties turn out to be much smaller !

32. The « Golden » Penguin mode B0   K0
BaBar
hep-ex/
Modes with KS and KL are both reconstructed
(Opposite CP)
full background
continuum bkg
114 ± 12 signal events
98 ± 18 signal events
Plots shown are ‘signal enhanced’ through a cut on the likelihood on the dimensions that are not shown, and have a lower signal event count

33. CP analysis of ‘golden penguin mode’ B0   K0
BaBar
(Opposite CP)
S(fKS) = ± 0.31(stat)
S(fKL) = ± 0.51(stat)
Combined fit result (assuming fKL and fKS have opposite CP)
Standard Model Prediction
S(fK0) = sin2b = 0.72 ± 0.05
C(fK0) = 1-|l| = 0
0.9s
hfK0

34. The Semi-Gold penguin modes: B0  h’KS
hep-ex/
B0  h’KS
B0  h’KS
Large statistics mode
Reconstruct many modes
’   + –, 0 
    ,  + –0
KS  + – ,00
BaBar
hfK0
 sin2 3.0
819 ± 38 signal events

35. CPV Results from Penguin Modes – Summary
C Direct CP Violation

36. TD CPV Results from Penguin Modes – Summary
S = “sin2”
Averaged over Belle/BaBar
All s-Penguin modes
exhibit “sin2” consistent
with but below sin2Tree
while Theory (Beneke et al)
predicts same or higher !!
Discrepancy between
sPenguin and bc tree
modes = 2.6 ???!!

37. What Are Penguins Telling Us ?
This could be one of the greatest discoveries of the century,
depending, of course, on how far down it goes…
2.7s?
discrepancy

38. Theoretical Estimates of deviation: sin2β(bs) - sin2β(bc)
Example: QCD factorization
Expected deviation in QCDF
Always positive  opposite direction of experiment value
Generally small – in some cases extremely small
Consistent w/ estimates from SU(3)-flavor – those are unsigned and assume worst case for the strong phase
Need theory community to give robust and precise calculations of hadronic uncertainties
by consensus !
Need better experimental ACP precision, in particular in clean bs modes like
[Beneke, hep-ph/ ]
[Cheng,Chua,Soni, hep-ph/ ]
sin2β(bs) - sin2β(bc)

39. Projections of Data Sample Growth
Double data by summer 2006
Double again by Sep 2008
1 ab-1 !

40. Golden modes reach 5 sigma level 5s discovery region if non-SM
Projections: Summer 2008
f0KS
KSp0
jKS
h’KS
KKKS
Luminosity expectations:
2004=240 fb-1
2008=1.1 ab-1
K*g
Golden modes reach 5 sigma level
5s discovery region if non-SM
physics is 0.30 effect
2004
2008
Projections are statistical errors only;
but systematic errors at few percent level

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

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

43. Add
|Vub/ Vcb|

44. +
BS Mixing
constraint

45. + Sin2

46. + 
constraint

47. All measurements consistent, apex of (,) well defined
+ 
measurement
Remarkable that dozens of measurements
in Flavor Physics all agree so well and
have constrained UT apex to a tiny region!

48. 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”=0.500.06 from bs penguin decays 2.7 from sin2K
Needs careful investigation and MORE data
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. SM and CKM Picture holds (yet).

49. Limits of Future Explorations

50. Future Prognostications
BaBar & Belle are mature experiments and have a long term and a rich program for B physics (>2007) [I showed only 5% 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 clean probe of NP
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 m/ 15
B Physics returns to Europe in 2007 with LHC-B !!
Will be an instrument for precision B physics
Sensitive to Bs Oscillation over entire SM range and beyond (m68ps-1
Precise exploration of CPV in BS and Bd systems

51. LHC-b is a beautiful forward spectrometer (10–300 mrad)
Will sample L ~ 2 1032 cm-2s-1  1012 bb produced/year !
It will live or die by its trigger acceptance and S/N
Reduced
material
Improved
level-1 trigger

52. Catching Bs Oscillations And Exploring CPV
1 year datataking sensitivity
Expected (> 5) Reach
Dms = 20 ps-1 (SM preferred)
Dms < 68 ps-1 (Can exclude SM)
LHC-b will be the perfect instrument for exploring CPV in BS system

53. Thank You & Best Wishes !

54. Summary of Experimental Program for sin 2eff
snapshot May’05
Mode CP
Tot. error Belle
L ~ 253 fb–1
Tot. error BABAR
L ~ fb–1
Δ(SM)
[in ]
Error estimate at 2 ab–1
Syste-matics
Max. central value for 5 deviation at 2 ab–1
Quality
[naïve theoretical cleanliness]
K0 –1
0.34
0.26
– 1.9
0.10
small
0.22
☻☻☻
’K0
0.18
0.14
– 2.6
< 0.05
0.45
☻☻(☻)
f0(980)K0 +1
0.42
0.29
– 1.3
< 0.12
Q2B
0.12 ☻☻
KSKSK0 ±1
0.71
0.36
– 1.4
< 0.16
vertex
– 0.08
K+K–K0
~+1
0.25
– 1.1
< 0.08
0.31
☻(☻)
0KS
0.60
0.32
0.13
0.07 ☻
K0
0.66
– 0.6
< 0.15
– 0.03
(☻)
0K0 - ?
KS
Average
0.39 ± 0.11
0.45 ± 0.09
– 3.7
< 0.034 ok
0.53
Need both Theory and Experimental Errors to get more precise

55. LHC-b: CP Physics Reach (in 107s Data Taking)
Reaction
Para-meter
LHC-b
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

56. Backup Slides

57. 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…) 57

58. 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 58

59. 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 59

60. 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 :

61. 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)

62. 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/

63. sin2 From Penguin Modes: B0K0

64. CP Asymmetry In Penguin Modes: B0K0
Analysis based on 227 Million BB pairs
full background
continuum bkg
Sample orthogonal to the non-resonant BKKK0 data

65. CP Asymmetry In Penguin Modes: B0K0
B0KS
B0KL

66. CP Asymmetry In Penguin Modes: B0K0
Belle 274M BB
pB*
fKS
Nsig=139 14
fKL
purity 0.63
Nsig= 36 15
purity 0.17

67. CP Asymmetry In Penguin Modes: B0K0
Belle 274 M BB
S = 0.736
fit
f K0
Good tags
Poor tags
Good tags
fKS + fKL : S (fK0) = ±0.33 ±0.09
C (fK0) = ±0.22 ±0.09
~2.2s away from SM

68. CP Asymmetry In Penguin Modes: B0/ K0
BaBar
227 M BB
Nsig=512 27
Belle
274M BB

69. CP Asymmetry In Penguin Modes: B0/ K0
Belle 274M BB
Raw Asymmetry
Good tags
S = 0.736
fit
S =  0.18  0.04
C =  0.11  0.05
sin2 3.0

70. 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)

71. Summary of sin2eff

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

73. Projections for Penguin Modes
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

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

75. CP Asymmetries in bc cd Modes
Statistics limited, may get interesting in about 2 years !

76. CP Violation In B Decays: SM Expectations

77. 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

78. B Decay Amplitude Weak Phase Structure

79. Decay Amplitude Weak Phase Structure in CPV

80. Decay Amplitude Weak Phase Structure in CPV

81. Five “Classes” of B Decays For CPV

82. Five “Classes” of B Decays For CPV

83. Some Examples of Class I (b c c s): B0 KS

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

85. An Example of Class II (b c c d): B0 D+ D-
Ignoring Penguin Diagram (?)

86. Unused Slides

87. B0 B0bar Oscillation

88. Unitarity Triangles and B Decays
The three angles are large

89. Searching For New Physics In Penguin Decays << Testing  Vs “” >>

90. Probing Penguins Needs More Data
New Physics
Standard Model

91. Constraining Penguin PollutionVs
Compare with 35o for pp
Can Measure 
more precisely
Grossman-Quinn bound

92. How good are Standard Model predictions?
Beneke, CKM05
Present SM uncertainty
“3 sigma”