Transcript Diapositive 1 - Harvard LPPC

Study of CP Violation in B0  +–0/KS Decays
Jinwei Wu
Harvard University
Aug 21st, 2006




CP violation
Extraction of α from B  ρ decay
Extraction of β from B  KS decay
Conclusion
1
Direct CP Asymmetry
ACP 
Af
Af
2
2
 Af
2
 Af
2
A  A1  A2

A1  A1
 0  Direct CPV
A2
A2
A  A1  A2
no CPV
• Sources of direct CP asymmetries:

A  A1  A2
Interference between two decay
amplitudes (Ai) with different strong
(i) and weak phases (i)
2sin 1  2  sin 1   2 
ACP 
,
R  1/ R  cos 1  2  cos 1   2 
A2

A  A1  A2
 A2
A1  A1
CPV
A1
R
A2
2
Time-dependent CP Asymmetry
B0
oscillation
A2  ie
B0
0
  B phys
(t )  f CP 
 m  t 
A1  eiD cos 

 2 
no oscillation
2iM
fCP
AfCP  t  

 m  t 
A1  eiD cos 

 2 
no oscillation
 m  t   iD
A2  ie2iM sin 
e
2


0
  B phys
(t )  f CP 
B0
 m  t  iD
sin 
e
 2 
oscillation

 CPV
fCP H B  t 
2
 f CP H B  t 
2
fCP H B  t 
2
 fCP H B  t 
2
0
0
2 Im 
1 
2
0
sin  m  t  
0
1 
2
1 
2
cos  m  t 
fCP
B0
i *
0
M12*  12
f
H
B
CP
2

0
i
f
H
B
M12  12 CP
2
3
Mixing induced CPV in Charmless B Decay
 VubVud
 VtbVtd
 3
 3
• Decay-amplitude weak-phase structure for b → uud :




A  VudVub* T u  P u  P c  VtdVtb* P t  P c  VudVub* T  VtdVtb* P  Ru e  i  T  Rt e  i  P
CP
q A Ru e+i T  Rt P
2ieff



e
p A Ru e-i T  Rt P
• Time dependent asymmetry probes eff:
a(t ) 
0
0
  B phys
 t   fCP     Bphys
 t   fCP 
0
0
  Bphys
 t   fCP     Bphys
 t   fCP 
 1  C 2 sin  2 eff  sin  mt   C cos  mt 
4
Quasi-two-body Analysis
 Quasi-two-body approximation, ignore interference effect
 6 observables through a time-dependent fit:
 t / 
R. Aleksan et al, 1990
e
f (t , Q , Qtag )  (1  Q ACP )
4
1  Qtag  S  Q S  sin  md t    C  Q C  cos  md t  




free
ACP Direct CPV
C
Direct CPV
C
Dilution
S
Mixing-induced CPV
S
Strong phase difference
  arg  A A

*
T 
 , rT  T 
C 0
ACP  0
S  
S  
2rT 
1 r
2
T 
2rT 
1 r
2
T 
sin 2 cos 
cos 2 sin 
C 
1  rT2
1  rT2
Measure CP violation, but not necessarily phase 
5
Snyder-Quinn Method
Quinn, Snyder
PRD 48, 2139, (1993)
Idea: Extract  and the strong phases
using the interference between B0  +0 amplitudes
A3 = f+A+ + fA+ + f0A00
A3 = f+A+ + fA+ + f0A00
 The f+, ,0 are relativistic
Breit-Wigner form factors

f (t , Qtag )  A3  A3
2
2

e
m(0)2 (GeV2)
+0 amplitude parameterization:
00
+–
+
 t / 
4
m(+0)2 (GeV2)
2
2
*




Im  A3 A3 
A3  A3
1  2Q
sin  md t   Qtag
cos  md t  
tag
2
2
2
2

6

A3  A3
A3  A3


The Square Dalitz Plot
Toy MC
 
1

cos 1  cos   
 m  mmin
m  cos  max
min
 m  m


1
1



det|J|
7
Fit Projection Plots
Strong signal with
347M BBbar
ρ(770)
dominate
8
Extract physics parameters
 Time-dependent Dalitz plot approach should supersede the
previous quasi-two-body analysis, with interference among
resonances taken into account.
Dalitz Plot Analysis
–0.114 ± 0.062 ± 0.027
–0.142 ± 0.041 ± 0.015
Aρ
Direct CPV
C
Direct CPV
0.35 ± 0.14 ± 0.05
0.154 ± 0.090 ± 0.037
C
Dilution
0.20 ± 0.14 ± 0.05
0.377 ± 0.091 ± 0.021
S
Mixing-induced CPV
–0.13 ± 0.18 ± 0.04
0.01 ± 0.12 ± 0.03
S
Strong phase difference
0.33 ± 0.18 ± 0.03
0.06 ± 0.13 ± 0.03
hep-ex/0608002
Q2B, LP2003
* Using a Q2B approach and 144fb-1 data, BELLE measured:
ACP  0.16  0.10, C  0.25  0.17, C  0.38  0.18, S  0.28  0.24, S  0.33  0.18
9
Probing Direct CP Violation
Define physically more intuitive quantities:

A 
A
A
 2
 2
 2
A
 2
 A

A  C  A C
1  C  A C
 0.03  0.07  0.03
ρ

ρ+

A 
=?
+
B0
A
A
 2
 2
 A
 2
 A
 2

B0
A  C  A C
1  C  A C
3.0
 0.380.15
0.16  0.07
ρ+
+
ρ
=?
B0

B0
Large Direct CPV not expected…
10
Road to 
Dalitz plot specific measurements:
 What is the strong phase between
B0ρ+ and B0ρ+?
 What is ?
11
Measuring sin2β with Charmless B decay
b  ccs decays are tree and penguin diagrams, with equal dominant weak phases
b  sss 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:
c
b

cb
V
W

Vcs
d
c J /y
K0
d
s
b
d
u, c , t
3
g, Z,

tb ts
VV
BR~ 10-3
s
s
sin2 =0.69±0.03
B0K0
Penguin:
New Physics?
B0J/yK0

s
K
0
BR~ 10-5
?
sin2 [charmonium]  sin2 [s-penguin]
d
12
Sources of Standard Model Pollution
There are many modes that dominantly decay via
bs(qq)…but not all modes were created equal
There are various estimates for the deviation from sin2β
due to SM pollution…most of them expect a larger value!
B0
b
c,t
s
d
d
d
d
b
B0
d
u
u
s
d
K0
This is ok; still gives
sin2 in SM.
w,0,0,h’(?),f0(?)…
w,0,0,h’(?),f0(?)…
K0
CKM and color suppressed..
but will lead to slight deviation.
13
sin2β from B0  KS Final State
BR ( 10–6) HFAG
B0 →ππK0 (inclusive)
44.8 ± 2.6
B0 →f0K0
5.9 ± 0.8
B0 →ρ0K0
5.6 ± 1.1
B0 →π–K*+
9.8 ± 1.1
B0 →π–K*(1430)+
46.6 ± 6.6
o quite a few CP events in
this decay including 0KS
and f0KS
o also a higher (f?)
resonance ~1500 MeV
o there is a possible tree
diagram which
contaminates the sin2
measurement
o time-dependent CP has
been measured for f0Ks
and 0Ks
Last summer, Belle presented a (time and tag independent) Dalitz Plot
analysis of this mode…this approach will be important in the future!
14
B0  KS Final State
K*(890)
K*(1430)
o A Dalitz plot with rich
structures, apart from CP
eigenstates, there are
also flavor eigenstates.
o K*(890)π, K*0(1430)π are
important for testing QCD
factorization and other
schemes.
o Can look for direct CP
violation and test SU(3)
symmetry in the B → PV
decays
o Interference with flavor
eigenstates can help lift
the degeneracy in the
sin2β measurement
15
B0  f0 KS
BR(B0  f0 (980)KS0 ) ~ 6.0 106
0
Btag
0
Btag
ML fit :
Asymmetry
Sf K 0  0.95
0 S
 0.32
 0.23
 0.10
Cf K 0  0.24  0.31  0.15
0 S
Systematic errors dominated by
Fit bias & interference with other modes
16
B0  ρ0 KS
Complications
o high level of bkg
o ρ is broad
o Interference with
ππ s-wave at
both high mass
and low mass
BaBar:
S=0.17±0.52±0.26
C=0.64±0.41±0.25
17
Analysis of B0  KS Dalitz Plot
Similar analysis technique,
need to handle additional
flavor eigenstates
f0
0
f???
Strong signal with 347M BBbar
18
Conclusion
 Extraction of α from B  ρπ
o The isospin analysis appears hopeless for the near future
o There is hope for the Dalitz plot analysis although it’s technically
difficult.
o Extract α with no ambiguities. Especially useful when combined
with other experiments or other measurements of α.
o Latest result in hep-ex/0608002
 Pioneered time-dependent Dalitz plot analysis for B decays.
Framework setup to study other three-body B decays.
o Already tested on B0→K+–0
o Close to finish CP measurement of B0→K0+–, where CP
violation in s-penguin decay and direct CP violation will be tested
o Foresee preliminary results in September.
19