Transcript This is a test

CP Violation in B Decays
Lecture III
Vivek Sharma
University of California at San Diego
http://vsharma.ucsd.edu/marialaach05.pdf
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
•
2
Conditions for CP violation
A  A1  A2
• Two amplitudes, A1 and
A2, with a relative CPviolating phase (f2)
only
• No CP violation since
magnitudes of A and A
are the same!
A2
2
A1  A1
A2
A  A1  A2
A  A1  A2
A2
A1  A1

Two amplitudes, A1 and
A2, with both a relative
CP-violating phase f2 and
CP-conserving phase (d2)

Now have CP violation!
2 
2
d2
A2
3
CP Violation in B Meson System
Identify B final states which are arrived at by two paths
A1
B
B
A2
A1
A2
In B0 system, B0
B0 oscillation provides one path with
the other path(s) come from weak decay of B hadron
In Bsystem  no oscillation possible,
2 (or more) amplitudes must come from different weak decay of B
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
4
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
5
Reminder: CPV Phase in CKM Matrix
V
V
V 
us
ub 
 ud
V
 V
V
V 
cs
cb
CKM  cd

V
V
V 
ts
tb 
 td
 1 1 e-iγ 


V
 1 1 1 
CKM 

 e-iβ 1 1 


 V V* 
 V V* 
  arg   cd cb  ,   arg   ud ub 
 V V* 
 V V* 
 td tb 
 cd cb 
 V V* 
  arg   td tb 
 V V* 
 ud ub 
6
Experimental Results on CP Violation
in B Meson system
B
CPV in Decay aka Direct CP Violation
2
B

f
A(B f )
A1
A(B  f )
B f
i wk
( B  f )  A1  A2e
ACP 
B
f
A2e
2
e i dst
iwk id st 2
e
f
wk
A2
, ( B  f )  A1  A2e
Br  B  f   Br  B  f 
Br  B  f   Br  B  f 

Af
Af
2
 Af
2
 Af
2
B f
d st
A1
2
wk
 iwk id st 2
e
 0  Direct CPV
8
Observation of Direct CPV in B0K- +
T
P
SM amplitude   2e i T  P AK
sin   
K separation
E (GeV)
K separation()
• Loop diagrams from New Physics (e.g. SUSY) can modify SM asymmetry via P
• Clean mode with “large” rate : BF  B 0  K     18.2  0.8 106
• Measure charge asymmetry, reject large B background with Particle ID
signal
B background
9
BaBar: First Observation of Direct CPV in B decay !
n  B0  K     910
nK  1606  51
AK  0.133  0.030  0.009
B0K+
n  B 0  K     696
BABAR
4.2, syst.
included
B0K+
BABAR
background
subtracted
signal enhanced
10
Confirmation of Direct CPV by Belle at ICHEP04
ACP = -0.101  0.025  0.005
_
B0 K
3.9 significance
B0 K
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.
11
CPV in B0 Mixing
2
B0
B0
f
2

B0
A( B 0  B 0 )
B0
f
A( B0  B0 )
M 12
Occurs when Mass eigenstates CP eigenstates
B0
B0
(|q/p|1 and<BH|BL> 0)
off-shell states f
The Box diagrams provide the required 2 phases
Strong phases depend on quark masses and
on-shell
i
states f
non-perturbative physics.
12
2
Asymmetries are small and hard to calculate precisely (QCD)


B
 B
asl
0
phys
0
phys

 X   B
0
(t )   X    Bphys
(t )   X 
(t ) 

0
phys
(t )   X 


1 q / p
4
1 q / p
4
 O(104 )
12
CPV in B0 Mixing
Time-dependent CP Asymmetry:
0
0
( Bphys
(t )   X )  ( B phys
(t )   X )
AT (t ) 
0
0
( Bphys
(t )   X )  ( B phys
(t )   X )
Search for asymmetry in same-sign dilepton sample
same  sign
 
events occur in mixed events where
one B0  B0  X  ;other B0  Y   
 
one B0  B0  X  ;other B0  Y   
 
AT
obs
N(
(t ) 
N(
, t )  N (

, t )  N (
, t )
S ( t )

A

T

, t )
S ( t )  B ( t )
 
 


S ( t )  signal
B ( t )  background from B decay and continuum
13
CPV in B0 Mixing
Time dependent measurement, time measured from Z
BABAR
20.7 fb1
Sample backgrounds B(t):
4.3% continuum
24% direct+cascade
12% direct+fake
B 0B 0 , B 0B 0 signal S (t )
Measurement region > 200mm
14
CPV in B0 Mixing
BABAR
20.7 fb1
Find:  0.005  0.012(stat )  0.014(syst )
Conclude: Re( Bd ) /(1 |  Bd |2 ) 
0.0012  0.0029( stat )  0.0036(syst )
q / p  0.998  0.006(stat )  0.007(syst )
So far, no experimental evidence
of large CP violation in B0 mixing
To a good approximation:
q / p  1 and q / p  e 2i M   | M12 | / M12
15
CPV In Interference Between Mixing and Decay
B0
fcp
+
B0 B0
fcp
2
B0

B0
2
fcp
+
B
ACP e i f
B0
M 12 
0
fcp
B
ie 2i M
0
fCP
ACP e i f
Neutral B Decays into CP final state fCP accesible by both B 0 & B 0decays
This is CPV when
q
A f CP
q A f CP
 1 and
 1 and the CP parameter of interest is  fCP   fCP
p
AfCP
p AfCP
CPV Asymmetry is defined as :
a fCP 
B
B
0
phys
0
phys
(t )  fCP     B
(t )  fCP     B
0
phys
0
phys
(t )  fCP 
(t )  f CP 

2Im fCP
1   fCP
2

sin  m t  B
1   fCP
2
1   fCP
2
 cos  m t 
B
When B decay is dominated by a single diagram,  fCP  1  a fCP  Im fCP sin  mBt 
CP asymm. can be very large and can be cleanly related to CKM angles
16
B  K : The "Platinum" Final State
0
Penguin:: u,c,t loops
Tree
*
*
*
A
=V
V
P
+V
V
P
+
V
V
AT  VcbV T
P
tb ts t
cb cs c
ub us Pu
Use Unitarity relation Vtb Vts*  Vcb Vcs*  Vub Vu*s to rearrange terms
*
cs ccs

A  A T  A P  Vcb Vcs* (Tccs  Pc  Pt )  Vub Vus* (Pu  Pt )
= (Vcb Vc*s ) T +(Vub Vus* ) P
Since
*
us
*
cs
Vub V
Vcb V
1
 (Vcb Vcs* ) T is the dominant amplitude
50
A
expect -1 =10-2
A
Hence "Platinum" mode !
17
CPV In Interference Between Mixing and Decay: B0 J/K0
B0
ACP e i f
M 12 
ie 2i M
B
0
fCP
ACP e i f
e2i
q B A ψKS Vt*b Vtd Vcb Vcs* Vcs Vcd*
Vtb* Vtd Vcb Vcd*
λ ψKS =
==*
*
*
pB AψKS Vtb Vtd Vcb Vcs Vcs Vcd Vtb Vtd* Vcb* Vcd
  B 0  J / K S ,L   e t / 1  CP sin 2 sin(mt ) 
  B 0  J / K S ,L   e t / 1  CP sin 2 sin(mt ) 
 Im(λ ψKS )  sin(2β)
 λ ψKS  1
λψKL  λψKS
CP = -1 (+1)
for J/K0S(L)
Same is true for a variety of B (cc) s final states
18
CPV In Interference Between Mixing and Decay
Requires measurement of proper time difference t=t between the
decay of Btag and BCP.
F+ (t) : decay rate for a B0  f CP denoted
F- (t) : decay rate for a B0  f CP
 1  λf 2

2Im(λ f )
F (t )  exp(t ) 1
cos(mt ) 
sin(mt ) 
2
2
1  λf
 1  λ f

Asymmetry
S
C
19
Time-Dependent CP Asymmetry with a Perfect Detector
B0
sin 2
CPV
B0
Asymmetry ACP
• 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
ACP (t )  sin2β sin(ΔmΔt )
20
Consequences of Detector Imperfections
F(t)
F(t)
Acp(t)
True t, Perfect tagging:
sin2
True t, Imperfect tagging:
D sin2
D = (1-2w) where w is mistag fraction.
Must measure flavor tag Dilution.
Measured t, Imperfect tagging:
Must measure t resolution properties.
t(ps)
t(ps)
21
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
CP Violation in Picture
z
Separate
B0 and B0

m
(4S) = 0.55
e-

Btag
  4s 
K
e+
B0
μ-
Brec
K
B0
Coherent BB pair
Δz
Δt 
 βγ  c
z
Vivek Sharma , UCSD
μ
0
s
π-
+
π
+
B0  J/ Ks
23
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
Vivek Sharma , UCSD
24
Calibrating The BaBar Clock:
B Meson Lifetime Measurement
0
+
Measurement of the B and B Lifetime
Tag B
z ~ 110 mm
K+
K0

Reco B
z ~ 65 mm
(4s)
 = 0.55
3. Reconstruct Inclusively
the vertex of the “other”
B meson (BTAG)
z
-
-
D-
+
t @ z/c
1. Fully reconstruct one B meson
in flavor eigenstate (BREC)
2. Reconstruct the decay vertex
4. compute the proper time difference t
5. Fit the t spectra
Vivek Sharma , UCSD
26
Fully-Reconstructed B sample
Flavor eigenstates Bflav : for lifetime and mixing measurements
Cabibbo-favored hadronic decays
bc u d
Neutral
B Mesons
“Open Charm” decays
~21000 signal
Purity: 85%

B0  D(  ) π  /ρ /a1
B  D(  )0π 
Charged
B Mesons
Hadronic decays into final states
with Charmonium
b  (c c ) s
B0  J / K *0 ( K   )
B  J / K  ,  (2S ) K 
~20000 signal
Purity: 85%
cm
2
[GeV]
mES = (Ebeam
)2 - (pcm
)
B
Vivek Sharma , UCSD
27
Vertex and t Reconstruction
BREC direction

Reconstruct Brec vertex from


charged Brec daughters
Determine BTag vertex from



charged tracks not
belonging to Brec
Brec vertex and
momentum
beam spot and (4S)
momentum
BREC Vertex
BREC daughters
Interaction Point
Beam spot
TAG Vertex
z
BTAG direction
TAG tracks, V0s

High efficiency (97%)

Average z resolution is 180 mm (<|z|> ~ c = 260 mm)

t resolution function measured from data
Vivek Sharma , UCSD
28
B Measurement: Unusual Situation at (4S)
true t
t resolution
measured t
LEP/SLD
e-t/

B production
point known
eg. from
beam spot
BaBar
Either Brec or
Btag can decay
first (this
analysis)
e-|t|/

=
Resolution
function
=
lifetime
Resolution
Function +
Lifetime
Need to disentangle resolution function from physics !
Vivek Sharma , UCSD
29
t Resolution Function


z
event-by-event (t) from vertex errors
Lifetime-like bias to
 Small correlation between lifetime
and Resolution Function parameters
R  (1  ftail  f outlier )G ( S t , mcore  0)
 ftail G ( S t , m  0)  exp(dt / d bias t )
~0.6 ps
Signal
MC (B0)
 f outlier G ( outlier , moutlier )
tracks from long-lived D’s
in tag vertex
asymmetric Resolution
Function
Vivek Sharma , UCSD
t (meas-true)/t
30
Lifetime Likelihood Fit


Simultaneous unbinned maximum
likelihood fit to B0/B+ samples
Use data to extract the properties of
background events


B0 mES
Mass distribution provides the
signal probability
Use the events in the sideband
(mES < 5.27) to determine the
t structure of the background
events under the signal peak
B0 Bkg t

19 free parameters



(B+) and (B0)
t signal resolution
empirical background
description
2
5
12
Vivek Sharma , UCSD
31
B Lifetime Fit Results
20
B0/ B0
fb-1

World’s best measurement



2 % statistical error
1.5% systematic error
Main source of systematic
error
Parameterization of the t
resolution function
precisely
calibrated
 Description of events with large
measured t (outliers)

Detector Clock
B
signal
+ bkg
PRL 87, 201803 (2001)
0
= 1.546  0.032  0.022 ps
PDG: 1.548

background
= 1.673  0.032  0.022 ps
PDG: 1.653
t (ps)
 0.032 ps
 0.028 ps
/0 = 1.082  0.026  0.011
Vivek Sharma , UCSD
PDG: 1.062
 0.029
32
B? B?
B Flavor (Mis)Identification
(Mistag Knowledge From Data)
Using B Mixing to Measure Flavor Mistag Rate
P ( B 0  B 0 )  et 1  cos( m t ) 
0
B
0
0
BB
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)
34
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
Vivek Sharma , UCSD
35
Measurement of B0B0 Mixing rate Vs t
Tag B
z ~ 110 mm
K+
K0

Reco B
z ~ 65 mm
(4s)
 = 0.55
z
-
-
D-
+
t @ z/c
3. Reconstruct Inclusively
the vertex of the “other”
B meson (BTAG)

4. Determine flavor of BTAG to
separate Mixed and Unmixed
events
1. Fully reconstruct one B meson
in flavor eigenstate (BREC)

2. Reconstruct the decay vertex 
5. compute the proper time difference t

6. Fit the t spectra of mixed and unmixed events
Vivek Sharma , UCSD
36
t Spectrum of Mixed and Unmixed Events
perfect
flavor tagging & time resolution
realistic
mis-tagging & finite time resolution
Decay time diff (t) in ps
 | Δ t |/τ Bd
e
f Unmix (Δ t)   Unmix
4τxB
Mix
 Mi
d

f
Decay time diff (t) in ps
| Δ t |/τ Bd
4τ Bd
0
0
Unmixed: B0flav Btag
or B0flav Btag
Mixed:


cos(
t ) Δm
 1Δm
d Δcos(
Δt )
  dResolutionFunction



+
_ 1  2w
(Δ t)1 

e
0
0
B0flav Btag
or B0flav Btag

w: the fraction of wrongly tagged
events
md: oscillation frequency
Vivek Sharma , UCSD
37
B Flavor Tagging Methods
Hierarchical Tagging Categories
For electrons, muons and Kaons use the charge correlation
l

b
W-
D, D*
d

l B
d
b
c
 Q 0 B
s
K
B0
Lepton Tag
0
kaons
0
c
B0
 Q0 B
l   B0
-
d
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  from D* decay
Neural Network
*0
0
kaons
d
Kaon Tag
NN output
Each category is characterized by the probability of
giving the wrong answer (mistag fraction w)
Vivek Sharma , UCSD
38
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 (%)
Wrong tag
fraction w (%)
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
Highest “efficiency”
Mistag fraction
difference w
(%)
Q =
(1-2w)2 (%)
26.1  1.2
Error on sin2 and md depend on
the “quality factor” Q approx. as:
  sin 2 
Smallest mistag fraction
1
BABAR
Q
29.7 fb1
Vivek Sharma , UCSD
39
Flavor Tagged B Meson Sample For Mixing Studies
Lepton
Lepton
psig,i ~ 0
psig,i ~ 0.96
Kaon
Nsignal  3156  63
Purity  (84.6  0.7)%
Nsignal  1097  34
Purity  (96.0  0.7)%
Background properties
from sideband events
NT1
NT2
Nsignal  798  31
Purity  (88.9  1.2)%
Nsignal  1293  43
Purity  (79.4  1.3)%
Vivek Sharma , UCSD
40
t (or Z Resolution Function
Use the event-by-event
uncertainty on t
R(dt)
B0
flavour
sample
core  Score  evt
t
tail  Stail  evt
t
CP sample
t Residual (ps)
R  dt   1  ftail  foutl   Gcore  dt , Score , dcore,i 
 ftail  Gtail  dt , Stail , dtail 
t (ps)
Outlier
Core
Tail
 foutl  Goutl  dt , outl  0 ps, doutl  8 ps 
Vivek Sharma , UCSD
41
Mixing Likelihood Fit on Reconstructed B0 Sample
Unbinned maximum likelihood fit to flavor-tagged neutral B sample
Fit Parameters
md
Mistag fractions for B0 and B0 tags
Signal resolution function
Empirical description of background t
B lifetime fixed to the PDG value
44 total free parameters
1
8
2x8
16+3
B = 1.548 ps
All t parameters
extracted from data
Vivek Sharma , UCSD
42
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
43
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
Vivek Sharma , UCSD
44
Measurement of CP Asymmetry
Tag B
z ~ 110 mm
-
K0

CP B
z ~ 65 mm
+
Ks0
m-
(4s)
 = 0.55
3. Reconstruct Inclusively
the vertex of the “other”
B meson (BTAG)
4. Determine the flavor of
BTAG to separate Mixed and
Unmixed events
z
t @ z/c

m+
1. Fully reconstruct one B meson
in CP eigenstate (BCP)
2. Reconstruct the decay vertex 

5. compute the proper time difference t

6. Fit the t spectra of B0 and B0 tagged events
Vivek Sharma , UCSD
45
Charmonium+K0 CP Sample for BABAR (’02)
 f  1 modes
f   1 modes
1506 signal
candidates,
purity 94%
988 signal
candidates,
purity 55%
 f  1 mode
BABAR
81.3 fb1
(after tagging & vertexing)
Vivek Sharma , UCSD
46
t Spectrum of CP Events
perfect
flavor tagging & time resolution
B0tag  B 0
Mistag fractions w
And
resolution function R
determined by
flavor sample
realistic
mis-tagging & finite time resolution
B0tag  B0
B0tag  B 0
B0tag  B0
CP PDF









| Δ t |/τ
|Δt|/τ
e B Bd












d
e


(

t
)


1
η
sin
2
β
sin(
Δm
Δt
) R
f f(Δt)


1
η
sin2
β
(1

2
w
)sin
(
Δm
Δ
t
)

 
f
d
B0
f
d


4 τB4d τ B 

0
B
d
Mixing PDF







|Δt|/τBd
f mixing,(Δt)  e
4τ
Bd
Vivek Sharma , UCSD















 1 (1 2w)cos( Δmd Δt)  R
47
sin2 Likelihood Fit Description
Combined unbinned maximum likelihood fit to t spectra of Bflav
and CP samples
Fit Parameters
#
Main Sample
Sin2
1
Tagged CP sample
Mistag fractions for B0 and B0 tags
8
Tagged flavor sample
Signal resolution function
8
Tagged flavor sample
Empirical description of background t
17
Sidebands
B lifetime from PDG 2002
0
B = 1.542 ps
Mixing frequency from PDG 2002
0
md = 0.489 ps-1
Total parameters
34
Global correlation coefficient for sin2: 13%
 All t parameters extracted from data
 Correct estimate of the error and correlations
48
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
“sin2”
Bflav
0.021±0.022
B+
0.017±0.025
49
BABAR Result for sin2 (July 2002)
CP = -1
CP = +1
sin2 = 0.755  0.074
50
Pure Gold : (Clean) Lepton Flavor Tags
BABAR
81.3 fb1
220 lepton-tagged
f = -1 events
98% purity
3.3% mistag rate
20% better t
resolution
CP asymmetry
is obvious !
sin2β  0.79  0.11
51
Systematic Errors on sin2 from BABAR
[sin2]
Description of background events
0.017
CP content of background components
Background shape uncertainties, peaking component
Composition and CP content of J/KL background
0.015
t resolution and detector effects
0.017
Silicon detector residual misalignment
t 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
52
Updated (ICHEP04) sin2 results from Charmonium Modes
205fb 1 on peak or 227M BB pairs
7730 CP events (tagged signal)
BABAR
Limit on
direct CPV
BABAR
53
Belle Results on sin2 from Charmonium Modes
BKS Sample
Belle
2005
386M BB pairs
New Belle value lower than in ’03
but still consistent with BaBar’04
54
CP Violation in B Decays Firmly Established
55
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 56
End of Lecture 3
Tomorrow:
Measurements of angles  and 
++ =?
“Sin2” in bs Penguin decay
Status of Unitarity Triangle
Future Directions : Tevatron, LHC-b….
Direct CPV in B- K- 0
Not in BK- +
Belle
Belle
ACP(K0 ) = 0.04  0.05  0.02
BaBar
ACP(K0 ) = 0.06  0.06  0.01
58
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
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
60
– EW penguins “suppressed” due to EW coupling
B Decay Amplitude Weak Phase Structure
61
Decay Amplitude Weak Phase Structure in CPV
62
Decay Amplitude Weak Phase Structure in CPV
63
Three Major “Classes” of B Decays For CPV
64
CPV in B0 Mixing
2
B0 B0
B0
f

off-shell states f
on-shell
states f
| BL,H   p | B 0   q | B 0  
1   Bd
q

p
1   Bd
2
B0 B0
f
CPV in the B 0 B 0 mixing matrix
results from:
Mass eigenstates | BL , H   CP eigenstates | B 
1
1 | Bd |
2
(| B   Bd | B )
 1  Prob(B 0  B 0 )  Prob(B
0
 B 0)
65
66
Mixing Measurement at Belle (Hadronic Modes)
Mistag rate
BELLE
29.1 fb1
Vivek Sharma , UCSD
67
The “Platinum” Final State
dominant decay
amplitude
68
Sin2 Likelihood Fit
Combined unbinned maximum likelihood fit to t spectra
of flavor and CP sample
Fit Parameters
tagged CP samples
sin2
Mistag fractions for B0 and B0 tags
Signal resolution function
Empirical description of background t
1
8
8
17
B lifetime fixed (PDG value)
Mixing Frequency fixed (PDG value)
B = 1.548 ps
tagged flavor sample
md = 0.472 ps-1
 All t parameters extracted
35 total free parameters
from data
 Correct estimate of the error and
correlations
69
Mixing Measurement with Fully Reconstructed B Sample
Amixing ( t )  1  2ω  cos ΔmBd Δt
29.7 fb1
1
Δmd  (0.516  0.016(stat)  0.010(syst) ) ps : BaBar
t [ps]
Δmd  (0.496  0.007) ps 1 : World Average
Precision measurement consistent with world average
 Well calibrated detector for Flavor tagging
Vivek Sharma , UCSD
70
t Resolution Function
R  dt   1  ftail  foutl   Gcore  dt , Score , dcore,i 
 ftail  Gtail  dt , Stail , dtail 
Outlier
Core
Tail
 foutl  Goutl  dt , outl  0 ps, doutl  8 ps 
core  Score  evt
t
tail  Stail  evt
t
Use the event-by-event
uncertainty on t
R(dt)
B0 flavour
sample
CP sample
t Residual (ps)
Different bias scale factor
For each tagging category
t (ps)
Vivek Sharma , UCSD
71
B0 B0 Mixing Asymmetry with Hadronic Sample
Unfolded raw asymmetry
Amixing ( t ) 
1  2ω  cos ΔmBd Δt
Folded raw asymmetry
t [ps]
~ 1  2w
Flavor mistag rate
well calibrated from
mixing measurement
~ π /md
Vivek Sharma , UCSD
BABAR
29.7 fb1
|t| [ps]72
Belle Results on sin2 from Charmonium Modes
Belle
2003
140 fb 1  152M BB pairs
4347 CP events (tagged signal)
sin 2   0.728  0.056  0.023
  A / A  1.007  0.041  0.033
73
md Measurement in Comparison With World
WA: 0.496 ± 0.007 ps-1
Precision md measurement
 3% statistical error
 2% systematic error
dominated by MC
correction
BaBar Measurements
Well Calibrated Detector for
B flavor tagging
Vivek Sharma , UCSD
74