The CKM Angles a and b
a/f2
Introduction
Theory overview
BABAR & SLAC
Measuring b/f1
Measuring a/f2
Summary
b/f1
g/f3
Richard Kass
Cornell 8/25/2006
1
The Cabibbo-Kobayashi-Maskawa Matrix
• The weak interaction can change
the favor of quarks and lepton
• Quarks couple across generation
boundaries
Vcb
Vub
d
• Mass eigenstates are not the
weak eigenstates
• The CKM Matrix rotates the
quarks from one basis to the
other
Richard Kass
d’
s’
b’
Cornell 8/25/2006
u
s
b
Vud Vus
Vubl d
l
3
= c Vcdl Vcs Vcbl
2
t
Vtdl Vltd Vtb
3
2
l=sin(qc)=0.22
s
b
2
Visualizing CKM information from Bd decays
The Unitarity Triangle
The CKM matrix Vij is unitary with 4
independent fundamental parameters
Unitarity constraint from 1st and 3rd columns:
i V*i3Vi1=0
d
s
b
u
Vud
Vus
Vub
c
Vcd
Vcs
Vcb
t
Vtd
Vts
Vtb
CKM phases
(in Wolfenstein convention)
To test the Standard Model:
Measure angles, sides in as many ways possible
Area of triangle proportional to amount of CP violation
Richard Kass
Cornell 8/25/2006
 1 1 e-iγ 


 1 1 1 
 e-iβ 1 1 


3
Three Types of CP Violation
I) Indirect CP violation/CP violation in mixing
KKlnexpected to be small (SM: 10-3) for B0’s
II) Direct CP violation: Prob(Bf) Prob(Bf)
Only CP violation possible for
/ in K
charged B’s
Br(B0-+) Br(B0+-)
III) Interference of mixing & decay: Prob(B(t)fCP) Prob(B(t)fCP)
B0s
B0+-
(CKM angle b)
(CKM angle a)
B
B
0
0
f CP
Due to quantum numbers of
Y(4S) and B meson we must
measure time dependant
quantities to see this CP violation
In this talk we will be discussing type III) CP violation
Richard Kass
Cornell 8/25/2006
4
CP Violation at the Y(4S)
CPV from the interference between two decay paths: with and without mixing
AfC P
mixing
|BL>=p|B0>+q|B0>
|BH>=p|B0>- q|B0>
B0
q/p
B
t
fCP
AfCP
0
Measure time dependent decay rates
&
m from B0B0 mixing
t 0
ACP (t ) 
 ( B 0 (t )  f ) - ( B 0 (t )  f )
 ( B 0 (t )  f ) + ( B 0 (t )  f )
 S f sin (mt ) - C f cos (m t )
Cf 
Sf 
Richard Kass
1- | l f |
2
1+ | l f |2
- 2 Im l f
1+ | l f |2
q Af
lf  
p Af
Direct CP Violation: C
|Af/Af|≠1→ direct CP violation
|q/p|≠1→ CP violation in mixing
Sf and Cf depend
on CKM angles
Cornell 8/25/2006
5
Getting the Data Sample
Use e+e- annihilations at Y(4S) to get a clean sample of B mesons
At Y(4S) produce B-/B+ (bu/bu) and B0B0 (bd/bd) mesons
BB Threshold
mB0 ~ mB- ~ 5.28 GeV
 
 bb
 0.28
 hadr 
The Y(4S) - a copious, clean source of B meson pairs
1 of every 4 hadronic events is a BB pair
No other particles produced in Y(4S) decay
Equal amounts of matter and anti-matter
Richard Kass
Cornell 8/25/2006
6
Data Collection at PEPII
To get the data set necessary to measure CP-violation with B’s we need a B-factory
SLAC and KEK
Both factories have attained unprecedented high luminosities: >1034/cm/s2
BABAR has collected ~390 fb-1
(BABAR + Belle > 1000 fb-1)
Note: 1fb-1 ~ 1.1 million BB pairs
Richard Kass
Cornell 8/25/2006
7
PEPII-Asymmetric e+e- Collider
Stanford Linear Accelerator Center,
Stanford, California
SLAC is an asymmetric e+e− collider: 9 GeV (e-)/3.1 GeV (e+)
B travels a measurable distance before decay:bg=0.56 → bgct~260mm
Richard Kass
Cornell 8/25/2006
8
The BABAR Detector
Electromagnetic
Calorimeter
(EMC)
1.5 T Solenoid
Detector of
Internally
Recflected
Cherenkov
Light (DIRC)
Drift Chamber
(DCH)
Instrumented
Flux Return
(IFR)
Silicon Vertex
Tracker (SVT)
BABAR features:
Charged particle tracking (silicon+drift chambers+1.5T Bfield)
Electromagnetic calorimetry (CsI)  g and electron ID
/K/p separation up to the kinematic limit (dE/dx+DIRC)
Muon/KL identification
Richard Kass
Cornell 8/25/2006
9
Key Analysis Techniques
Threshold kinematics: we know the initial energy of the Y(4S) system
Therefore we know the energy and magnitude of momentum of each B
*2
mES  Ebeam
- pB*2
Signal
*
E  EB* - Ebeam
Event topology
Signal
(spherical)
Background
Background
(jet-structure)
Most analyses use an unbinned maximum likelihood fit to extract parameters of interest
Richard Kass
Cornell 8/25/2006
10
How to Measure Time Dependent Decay Rates
t =0
We need to know the flavour of the B at a reference t=0.
z = t gbc
0
At t=0 we
B0
know this
meson is B0
B
rec
K s
(4S)
bg =0.56
B0
The two mesons oscillate
coherently : at any given
time, if one is a B0 the
other is necessarily a B0
Richard Kass
tag
W
l - (e-, m-)
In this example, the tagside meson decays first.
It decays semi-leptonically
and the charge of the
lepton gives the flavour of
the tag-side meson :
l -= B0
l += B 0.
Kaon tags also used.
Cornell 8/25/2006
B0
-
l-
nl
b
d
t picoseconds
later, the B 0 (or
perhaps it is
now a B 0)
decays.
11
The Many Ways to Measure b
Can use 3 different categories of B0 decays to measure b:
b) b  cc d charm
(and charmonium )
a) b  cc s
(charmoniu m)
J /K S0
golden mode
 (2S ) K S0 ,  c1 K S0 , c K S0
J /K ( K
Richard Kass
-
*0
+
D D ,D D
*+
fK 0 , K + K - K S0 ,
-
J / , D D
0
J /K L0
*0
*+
*-
K S0 K S0 K S0 , K 0 , K S0 0 ,
K S0 , f 0 (980) K S0
K  )
0
S
c) Penguin - dominated
b  dd s, b  ss s
0
Cornell 8/25/2006
12
Precise Measurement of sin2b from B0charmonium K0
Theoretically very clean:
ACP(t)=Sfsin(mt)-Cfcos(mt)
The dominant penguin amplitude (suppressed by l2Cab) has same phase as tree
SM prediction: Cf=0 ACP(t)=Sfsin(mt)
recent model-independent analyses [e.g. PRL 95 221804 (2005)] S=0.000±0.012
VcsVcb*  VtbVtd*  VcsVcd* 
Vtd*
S f  Im l   *   *   *   Im
 sin 2b
Vtd
VcsVcb  VtbVtd  VcsVcd 
decay
B0 mixing K0 mixing
Experimentally very clean:
Many accessible decay modes
with (relatively) large BFs
CP odd
CP even
B→ψK0~8.5x10-4
B→ψ(2S)K0~6.2x10-4
B→χc1K0~4x10-4
B→ηcK0~1.2x10-3
Richard Kass
Cornell 8/25/2006
13
Precise Measurement of sin2b from B0charmonium K0
Results from ICHEP 2006
ACP(t) = -ηfsin2bsin(mdt)
Results from 2005
(cc) KS (CP odd) modes
J/ KL (CP even) mode
PRL94, 161803 (2005)
227x106 BB
sin2b=0.722±0.040±0.023
Richard Kass
hep-ex/0607107
348x106 BB
sin2b=0.710±0.034±0.019
Cornell 8/25/2006
14
Brief History of sin2b from B0charmonium K0
Pre-ICHEP 2006
ICHEP 2006
1 CKM fit
2
·
ICHEP 2006
Richard Kass
Great success for Standard Model
Great success for all of us:
theorists,
experimentalists,
accelerator physicists
Cornell 8/25/2006
15
Resolving the sin(2b) Ambiguity
sin(2b) is the same for b/2-b+b3/2-b
Several methods available to resolve the ambuguity
Can resolve ambiguity with a time-dependent analysis of D0→Ksπ+πUse bcud decays: B0D(*)0h0 with D0DCPKsπ+π[A.Bondar, T.Gershon, P.Krokovny, PL B624 1 (2005)]
h0
h0
h0=,, ’,
Theoretically clean (no penguins), Neglect DCS B0DCPh0 decay
Interference of Dalitz amplitudes sensitive to cos2b
M B 0  f + cos( mt / 2) - ie + i 2 b h 0 (-1)l f - sin( mt / 2)
M B 0  f - cos( mt / 2) - ie
-i 2 b
 h (-1) f + sin( mt / 2)
l
| f  |  | f (mK2   , mK2   ) |2
S
S
0
The Dalitz plot model is taken from a sample of D*D0π+ decays, D0Ksπ+πUse CLEO isobar formalism for the D0 decay amplitude
(PRD 63,092001 (2001), PRL 89, 251802 (2002), erratum: 90,059901 (2003))
Richard Kass
Cornell 8/25/2006
16
Resolving the sin(2b) Ambiguity with B0D(*)0h0
B0-tagged
B0-tagged
Preliminary result: hep-ex/0607105
Analysis uses 311BB pairs
Nominal Fit: float cos2b, sin2b, l:
(errors are stats, syst, Dalitz)
cos 2b  0.54  0.54  0.08  0.18
sin 2b  0.45  0.35  0.05  0.07
093
| l | 0.975+-00..085
 0.12  0.002
Perform MC experiments to find favored b:
Generate 2 “toy” samples with:
sin2b=0.685, |l|=1, cos2b=+0.729 or -0.729
Fit each sample with cos2b as free parameter
Study shows that data favors b=220 over 680 at 87% CL
Richard Kass
Cornell 8/25/2006
17
Resolving the sin(2b) Ambiguity
Similar result from Belle using B0D0h0:
cos2b>0 at 98%CL (hep-ex/0605023)
Other techniques show cos2b>0 too:
BABAR: Time dependent analysis of B0D*+D*-Ks
cos2b>0 at 94% CL (hep-ex/0608016)
model dependent analysis: PRD 61, 054009 (2000)
BABAR: Extract cos2b from interference of
CP-even and CP-odd in states (L=0,1,2) in
time-dependent transversity analysis of
B0J/K*0(K*0Ks0)
cos2b<0 excluded at 86% C.L.
PRD 71, 032005 (2005)
Richard Kass
Cornell 8/25/2006
18
bccd Decays and sin2b
These decays suffer from potential penguin-pollution:
Example: B0 J/0
bd penguin amplitude
has different weak & strong
phases with respect to tree.
S  sin 2b , C  0
BABAR: B0 J/0 updated measurements [hep-ex/0603012, submitted PRD-RC]:
Br(B0J/0)=(1.94±0.22±0.17)x10-5
SJ/0=-0.68±0.30±0.04
CJ/0=-0.21±0.26±0.06
Consistent with previous Belle results:
PRL93, 261801 (2004)
SJ/0=-0.72±0.42±0.09
CJ/0=-0.01±0.29±0.03
Richard Kass
Cornell 8/25/2006
19
b  cc d decays : summary
All results consistent with SM expectation of tree dominance
SDD≡SDD-sin2b~.2-.5[Z-Z. Xing, PR D61 014010 (2000)]
Still below current experimental sensitivity
Richard Kass
Cornell 8/25/2006
20
Sin2beff in b → s Penguins
Decays dominated by gluonic penguin diagrams
Golden example: B0→fKS
No tree level contributions: theoretically clean
SM predicts: ACP(t) = sin2bsin(mt)
NP
SM
d
d
Impact of New Physics could be significant
New particles could participate in the loop → new CPV phases
Measure ACP in as many b→sqq
penguins as possible!
Richard Kass
Cornell 8/25/2006
φK0
η′ KS, η′ KL
KS KS KS
KS π0
K+ K− KS, K+ K− KL
ω KS
f0(980) KS
21
Hunting for new physics: CPV + b → s Penguins
Complications:
B  J/K0
100.3
B  ′K0
63.2
16.6
B  K+K-K0
20.6
17.4
B  fK0
8.3
3.4
B  KS
2.4
2.1
B  f0 KS
2.7
1.8
B  KSKSKS
3.1
1.4
K+
B  0KS
5.8
3.9
K-
B  00KS
11
7.5
detached vertices
Non-penguin processes can pollute:
W
b
B
t
g
0
 VubVus ~ l 4Ru e - ig
 VtbVts ~ l 2
d
s
u
u
s
s
d
b
KK+
K0
B
0
W
-
d
u
s
s
u
s
d
PiBFi
x106
850.0
Low branching fractions
Experimentally challenging:
-
BF(B→f)
x106
Decay
mode
K0
sin2beff-sin2b
Use theory to estimate deviation from sin2b
SM corrections to naïve model:
QCD factorization:
2-bod: [Beneke; PL B620, 143 (2005)]
3-body: [Cheng,Chua,Soni; PRD72, 094003 (2005)]
SU(3) based model independent bounds
Use measured BFs & parameters in models
Richard Kass
Cornell 8/25/2006
sin2b
22
Latest BABAR CPV & b → s Penguins Results
Just in from ICHEP06 new results on:
B0→K+K-K0, B0→η’K0, B0→π0Ks, B0→KsKsKs, B0→ρ0Ks, B0→ω0Ks
To save time will just discuss B0→K+K-K0 & B0→η’K0
Analysis of B0→K+K-K0
hep-ex/0607112
Use Ks→+-,  and KL interactions in EMC or IFR (instrumented flux return)
Use a time dependent Dalitz Plot analysis to account for the varying CP content and
interference over the allowed phase space.
Use an isobar model which includes: f(1020)K0, f0(980)K0,
sPlot
X0(1550)K0, Non-resonant, c0K0, D+K−, DS+K−
fp=relative p-wave fraction
B0→fK+
[Pivk, Le Diberder,
NIMA 555, 356 (2005)]
Angular moment analysis determines
the fraction of P-wave:
~89 % in B0→fK+
Ap=absolute p-wave strength
~29% over entire Daltiz plot region
for B0→K+K-K0
Richard Kass
Cornell 8/25/2006
23
Analysis of B0→K+K-K0
347  106 BB pairs  1516 ± 65 signal events
Fit to low mass K+K− region (<1.1 GeV) to
extract fK0 and f0(980)K0 CPV parameters
B0-tagged
B0-tagged
K+K-Ks(+-)
Main Systematic Contribution= Dalitz model
Averaged over the entire Dalitz plot
ACP=-0.034±0.079±0.025
beff= 0.361±0.079±0.037 (bcharmonium= 0.379±0.023)
beff
Richard Kass
Resolve trigonometric
ambiguity in beff at 4.6
Cornell 8/25/2006
24
Analysis of B0→K0
347  106 BB pairs  ~1100signal events
hep-ex/0607100
Reconstructed 6 sub-decay modes:
5 with K0→K0S (CP = −1)
(gg+−)KS with Ks→ +- or 
(rg)KS with Ks→ +- or 
(3+−)Ks with Ks→ +-
1 with K0→K0L (CP = +1)
solid curve is ML fit function
dashed curve is background
projections have L(sig)/[L(sig)+L(back)] cut
Richard Kass
Cornell 8/25/2006
25
Analysis of B0→K0
B0→Ks
B0→KL
main systematic error is from signal PDF
Combined fit yields:
4.9 from zero
Richard Kass
Cornell 8/25/2006
26
BABAR Summary of CPV + b → s Penguins
sin 2 b [cc ]
0.710  0.039
( New BaBar )
Individual modes are consistent with the
charmonium value
C[cc ]
0.070  0.033
( New BaBar )
no evidence for direct CPV
sin2beff-sin2b
BUT the naïve bs average is still lower by
~2 compared with charmonium sin2b value
sin2b
Richard Kass
Cornell 8/25/2006
27
All “sin2b” Results Compared
Naïve average of all bgs modes:
sin2beff = 0.52 ± 0.05
penguin & tree differ by 2.6 
Hazumi ICHEP06
Richard Kass
bgs modes smaller than
bgccs in all 9 modes
Cornell 8/25/2006
28
The Unitarity Triangle
(r,)
Vub* Vud
Vcd Vcb*
a
Vtd Vtb*
Vcd Vcb*
g
(0,0)
Richard Kass
o
(0,1)
[21.2 ± 1.3]
Cornell 8/25/2006
29
The CKM angle a
In an ideal world we could access a from the interference of
a b→u decay (g) with B0B0 mixing (b):
Tree decay
B0B0 mixing
b
B
0
d
Vtb*
Vtd*
t
t
Vud*
g
d
B
b
Vtb
Vtd
q / p  Vtb*Vtd / VtbVtd*
0
B
0 b
d
Vub
d
u
u
d
-
+
A  Vud* Vub
q A
l
 e -i 2 b e -i 2g  ei 2a
p A
But we do not live in the ideal world.
There are penguins...
Richard Kass
Cornell 8/25/2006
a- b- g
B0→K+- large BF
Br~2x10-5
~Penguin/Tree~30%
30
sin(2a): Overcoming Penguin Pollution
Access to a from the interference of a b→u decay (g) with B0B0 mixing (b)
complicated by Penguin diagram
Tree decay
B0B0 mixing
b
B
0
d
Vtb*
Vtd*
t
t
Vud*
g
d
B
0
B
b
Vtb
Vtd
q / p  Vtb*Vtd / VtbVtd*
Penguin decay
Vub
0 b
d
d
u
u
d
-

+

B
b
0 u,c,t
d
lCP
lCP  e
i 2a
Inc. penguin contribution
T + P e + ig ei
T + P e -ig ei
C  sin 
T = "tree" amplitude P = "penguin" amplitude =strong phase
Richard Kass
+
S  1 - C 2 sin( 2a eff )
S  sin( 2a )
C 0
Time-dep. asymmetry :
-
A  Vtd*Vtb
A  Vud* Vub
q A

 e -i 2 b e -i 2g  ei 2a
p A
g
d
u
u
d
A(t )  S sin( md t ) - C cos(md t )
Cornell 8/25/2006
How can we
obtain α
from αeff ?
31
How to estimate |a-aeff|: Isospin analysis
Use SU(2) to relate decay rates of different  final states
+-+
Important point is that  can have I=0 or 2 but gluonic penguins only
contribute to I=0 (by I=1/2 rule) &EW penguins are negligible
Need to measure several B.F.s:
a2|a -a|
eff
B 0   + - B 0   + B 0   0 0 B 0   0 0
B -   - 0 B +   + 0
1
2
+-
AB->
BF(B++)=BF(B--) since
+ is pure I=2, only tree amplitude
1
2
~
+AB->
Richard Kass
~

AB->
f
However, for this technique to work
 amplitudes must be very small
or very large!
~

AB->
-
- 
++
AB-> AB->
Gronau-London: PRL65, 3381 (1990)
Cornell 8/25/2006
32
B0→+Use DIRC to separate ’s from K’s
Rely on kinematics of decay for additional separation
Simultaneous EML to B0→+-B0→+-B0→+-
hep-ex/0607106
347×106 BB pairs  675±42 signal events
background
signal
B0-tag
sPlot
B0-tag
sPlot
Asym  ( N B 0 - N B 0 ) /( N B 0 + N B 0 )
Richard Kass
Cornell 8/25/2006
33
B0→+S = −0.53±0.14±0.02
C = −0.16±0.11±0.03
(S,C)= (0.0, 0.0) excluded @ 0.99970 CL (3.6 )
BABAR observes evidence @ 3.6  for CPV in B0→+BUT no (convincing) evidence for DIRECT CPV (C0)
Richard Kass
Cornell 8/25/2006
34
History of B0→+− decay
Hazumi-ICHEP2006
(C = -A)
2.3 diff. btw.Belle & BaBar
Results support the expectation from SU(3) symmetry that ACP(+-)~-3ACP(K+-)
N.G. Deshpande and X.-G. He, PRL 75, 1703 (1995), M. Gronau and J.L. Rosner, PLB 595, 339 (2004)
ACP(K+-) = -0.115±0.018 (HFAG summmer 2005) ACP(+-)=+0.3
ICHEP2006 World Average: ACP(+-)~+0.39±0.07
Richard Kass
Cornell 8/25/2006
35
B-→-& B0→
hep-ex/0607106
B-→-: Simultaneous EML to B-→-B-→- &use DIRC for /K ID
Improve  reconstruction by 10% using merged ’s & g→e+e- conversions (+ →gg )
Measure time integrated CP asymmetries (no vertexing!)
B-→-
347×106 BB pairs
B-→
B-→r- bkg
Signal events=572±53
BR(B-→-)=(5.12±0.47±0.20)x10-6
A-=-0.19±0.088±0.014
Richard Kass
Signal events=140±25
BR(B0→)=(1.48±0.26±0.12)x10-6
C=-0.33±0.36±0.08 C  - A
 0 0
A 0 0 
Cornell 8/25/2006
 0 0
| AB 0  0 0 |2 - | AB 0  0 0 |2
| AB 0  0 0 |2 + | AB 0  0 0 |2
36
Using isospin in  system to measure a
8-fold ambiguity
a
a
|a|<41°@90% C.L.
a=0 excluded at 1-CL=4.4X10-5due to
S=C exclusion @3.6.
These plots use a frequentist interpretation.
Only the B→ isospin triangle relations are
used in arriving at these constraints on a & a.
One of many possible Gronau-London
triangles using BABAR  results.
Precision measurement of a not possible with current stats using 
Richard Kass
Cornell 8/25/2006
37
Using isospin in  system: BABAR + Belle
inputs
B(+0) = (5.75 0.42)
B(+-) = (5.20 0.25)  10-6
B(00) = (1.30 0.21)
A(00) = +0.35 0.33
S(+-) = -0.59  0.09
A(+-) = +0.39  0.07
Still can not get a stringent
bound on a with only 
Use info from rr and r
Richard Kass
Cornell 8/25/2006
38
B→rrto the Rescue (sort of..)
Pseudoscalar→ Vector Vector
3 possible ang. mom. states:
S wave (L=0, CP even)
P wave (L=1, CP odd)
D wave (L=2, CP even)
d 2N
 f L cos 2 q1 cos 2 q 2 + 14 (1 - f L ) sin 2 q1 sin 2 q 2
d cosq1d cosq 2
Nature is KIND!
PRL 93 (2004) 231801
B0r+r-~100% longitudinally polarized!
essentially all CP even:
f L ( B 0  r + r - )W A  0.967 +-00..023
028
r helicity angle
signal
Large Branching Fraction!
bkg
(new for ICHEP hep-ex/0607098)
Br(B0r+r-)=(23.5±2.2±4.1)x10-6
Br(B0r+r-)~5xBr(B0+-)
Richard Kass
Cornell 8/25/2006
39
B0 → r + r hep-ex/0607098
highest purity tagged events
sum of
all backgrounds
qq background
347 x 106 BB615±57events
f L ( B 0  r + r - )  0.977  0.024+-00..015
013
Br ( B 0  r + r - )  (23.5  2.2  4.1) 10-6
Richard Kass
05
S rr  -0.19  0.21+- 00..07
C rr  -0.07  0.15  0.06
Cornell 8/25/2006
40
B±→r±r0
Updated results: hep-ex/0607092
232 x 106 BB events39±49events
Br  (16.8  2.2  2.3) 10 -6
023
f L  0.905  0.042 +-00..027
ACP  -0.12  0.13  0.10
Previous results for this mode were “too large”
and triangle did not close.


Belle : 31.7  7.1+-36..87 10 -6 PRL 91,221801 (2003)


BABAR : 22.5+-55..47  5.8 10 -6 PRL 91,171802 (2003)
PDG04 : 26  6 10 -6
New measurement allows the triangle to close
Richard Kass
Cornell 8/25/2006
41
But How Large is B0→rr ?
Phys.Rev.Lett. 94 (2005) 131801
Previous BABAR result:
227 106 BB  33+-2220  12
Br < 1.110-6 @ 90% CL
NEW BABAR results:
347 10 BB  98
6
+32
-31
 22
37
Br  (1.16 +-00..36
 2.7) 10 -6 “3”
r0f0
r0r0
11
f L  0.86 +-00..13
 0.05
More data + improvements in event selection and analysis technique
Isospin triangle for rr is flattened compared to but not squashed L
Richard Kass
Cornell 8/25/2006
42
Using isospin in rr system to measure a
a
|a|<18° @ 68% CL
|a|<21° @ 90% CL
a
74°<a<117° @ 68.3% CL
We use a frequentist interpretation:
Only use rr BFs, polarization and isospin triangles.
The new rr result actually weakens
the a bound (|a| was <11° @ 68% CL)
Combining with Belle does not help much either:
Richard Kass
Cornell 8/25/2006
43
B0 → r Analysis
B0 → r→+ is not a CP eigenstate
– 6 decays to disentangle:
B 0 B 0  r   , r 0 0
– Tried by BaBar and Belle for just r± phase space
– Did not set limits on a
– Can use a Dalitz plot analysis to get a from decays
 
Snyder & Quinn: Phys. Rev. D48, 2139 (1993)
r+-
MC
Convert to a square Dalitz plot
Mostly resonant decays
Move signal away from edges
Simplifies analysis
q 
m 
r-+
Richard Kass
q0

1

q0=r helicty angle
cos -1 (2
m0 - 2m +
mB0 - m 0 - 2m +
- 1)
m0=invariant mass of charged tracks
Cornell 8/25/2006
44
B0 → (r)0 Dalitz plot analysis
Time dependent Dalitz analysis yields CP asymmetries & strong phases of decays
measure 26 coefficients of bilinear form factors
includes interference effects (2004 analysis didn’t)
hep-ex/0608002
347 106 BB  1847  69 events
C  0.154  0.090  0.037
S  0.01  0.12  0.028
Ar  -0.142  0.041  0.015
m’ and q’ are square Daltiz plot variables
continuum
continuum+B bkg
continuum+B bkd+mis-recon signal
Analysis provides a weak
determination of a:
75°<a<152° @ 68.3% CL
However, useful for
resolving ambiguities…..
Richard Kass
Cornell 8/25/2006
45
BABAR Combined Constraints on a
rrgives 3 windows
r chooses the window (~/2)
 fine tunes position in window
Richard Kass
Cornell 8/25/2006
46
BABAR + Belle constraints on a
aB-Factories = [ 93
Richard Kass
+11
]
-9
º
Global fit without a:
+5
aGlobal Fit = [ 98 -19
]º
Cornell 8/25/2006
47
The Unitarity Triangle
[93(r,)
± 11]o
Vub* Vud
Vcd Vcb*
Vtd Vtb*
Vcd Vcb*
g
b
(0,0)
Richard Kass
[21.2 ±(0,1)
1.3]o
Cornell 8/25/2006
48
Summary and Outlook: b
BABAR & Belle measure sin2b in ccK0 modes to 5% precision
sin2bcharmonium=0.674±0.026 (HFAG)
Comparison with sin2beff in bs penguins could reveal new
physics
sin2beff = 0.52 ± 0.05
Need to carefully evaluate SM contributions
Expected precision Vs Lum.
sin2beff measurements are statistically limited
but we can add new modes & beat 1/√L scaling
 rKs, 00Ks
sin2b in
penguins
Luminosity (ab-1)
Richard Kass
Cornell 8/25/2006
49
Summary and Outlook: a
Extraction of a depends crucially on penguin contributions
Must combine many measurements for precise determination
B→rr/r+r/r+r- B→/+/+- B→(r
Theory  experimental feedback is helpful
Extraction of a depends statistical technique:
baysian
frequentist
Richard Kass
Cornell 8/25/2006
50
Putting it All Together
As of today the complex phase in the CKM matrix correctly
describes CP Violation in the B meson system!
a+b+g= (93±11)º+ (21±1)º+ (78±30)º = (192±32)º
CKMfitter Inputs:
Vub
Vcb
md
ms
¿
B  tn
K
sin2b
a
g
É
More to come from BABAR/Belle, CDF/D0, and LHCb
Will they find CKM violation????
Richard Kass
Cornell 8/25/2006
51
Extra Slides
Richard Kass
Cornell 8/25/2006
52
Asymmetric e+e- Colliders
KEKII
PEPII
KEK/SLAC are asymmetric e+e− colliders
KEK: 8 GeV (e-)/3.5 GeV (e+)
SLAC: 9 GeV (e-)/3.1 GeV (e+)
B travels a measurable distance before decay:
SLAC: bg=0.56 → bgct~260mm
KEK: bg=0.42 → bgct~193mm
Richard Kass
Cornell 8/25/2006
53
B Factories
To get the large data set necessary to measure CP-violation with B’s use B-factories
SLAC and KEK
Both factories have attained unprecedented high luminosities: >1034/cm/s2
BaBar has 352 fb-1 and Belle has 610fb-1 of data
Note: 1fb-1 ~ 1.1 million BB pairs
Richard Kass
Cornell 8/25/2006
54
Detectors at Asymmetric e+e- Colliders
Both detectors feature:
Charged particle tracking (silicon+drift chambers + 1.5T B-field)
Electromagnetic calorimetry (CsI)  g and electron ID
/K/p separation up to the kinematic limit
BABAR: dE/dx+DIRC
Belle: dE/dx+aerogel+ToF
Muon/KL identification
Richard Kass
Cornell 8/25/2006
55
b  cc d decays : B  D
0
(*)+
D
(*)-
D*+D*-: [PRL 95, 151804 (2005)]
VV decay: both CP-odd and CP-even components.
CP-odd fraction extracted with transversity analysis:
fodd=0.125±0.044±0.070
S+=-0.75±0.25±0.03
C+=+0.06±0.17±0.03
D(*)+D- [PRL 95, 131802 (2005)]:
SDD =-0.29±0.63±0.06
CDD =+0.11±0.35±0.06
SD*+D-=-0.54±0.35±0.07
CD*+D-=+0.09±0.25±0.06
SD*-D+=-0.29±0.33±0.07
CD*-D+=+0.17±0.24±0.04
Richard Kass
D*+D-
Cornell 8/25/2006
D*-D+
D+D-
56
Adding Theoretical Uncertainties
•
size of possible discrepancies
Δsin2β have been evaluated for
some modes:
– estimates of deviations based on
QCD-motivated specific models;
some have difficulties to reconcile
with measured B.R.
•
•
•
•
•
Beneke at al, NPB675
Ciuchini at al, hep-ph/0407073
Cheng et al, hep-ph/0502235
Buras et al, NPB697
Charles et al, hep-ph/0406184
2xΔsin2β
– model independent upper limits
based on SU(3) flavor symmetry
and measured b d,sqq B.R.
• [Grossman et al, PRD58;
Grossman et al, PRD68; Gronau,
Rosner, PLB564; Gronau et al,
PLB579; Gronau et al, PLB596;
Chiang et al, PRD70]
‘naive’ upper limit based on final state quark content,
CKM (λ2) and loop/tree (= 0.2-0.3) suppression factors
[Kirkby,Nir, PLB592; Hoecker, hep-ex/0410069]
Richard Kass
Cornell 8/25/2006
57
There is a problem


B0  +K
K
K
B0  K+-
q
q

B0+-
157  19
(4.7  0.6  0.2) x 10-6
B0K+-
589  30
(17.90.9 0.7) x
Richard Kass
10-6
Cornell 8/25/2006
Penguin/Tree ~ 30%
58
a from rr
Extraction of a depends crucially on penguin
contributions
B→rr/r+r
Theory  experimental feedback is helpful
Expected precision Vs Lum.
reference +1
reference (current r0r0 Br)
a/a %
reference -1
a from rronly
Richard Kass
Cornell 8/25/2006
59