Measurements of φ3/γ
Anton POLUEKTOV
Budker Institute of Nuclear Physics,
Novosibirsk, Russia
FPCP, Taiwan. May 5, 2008
A. Poluektov. Measurements of φ3/γ
1
CKM matrix and φ3/γ
quark
Cabibbo-Kobayashi-Maskawa quark mixing matrix (CKM):
iφ 3
~e

A (   i ) 
Vud Vus Vub   1  / 2



2
2
V   Vcd Vcs Vcb   

1  / 2
A


 V V V   A3 (1   i )  A2
1
 td ts tb  

2
3
i
g Vij
quark
i
m
W
j
W
g Vij*
j
CKM unitarity leads to triangle in complex
plane:
∗
i=1,k=3: V ub
V ud V ∗cb V cdV ∗tb V td=0
≃
FPCP, Taiwan. May 5, 2008
V ∗ub V ud
∗
ub
V V ud
1
A. Poluektov. Measurements of φ3/γ
V ∗tb V td
∗
ub
V V ud
=0
2
Constraints on CKM parameters
Direct angle measurements
(CKMfitter world averages, 2007):
• φ1/β = 21.5 ± 1.0º (B→J/ψK0)
• φ2/α = 88 ± 6º
(B→ρρ)
• φ3/γ = 77 ± 30º
(B→DK)
[BaBar (SLAC) , Belle (KEK)]
Good agreement so far.
Trees
FPCP, Taiwan. May 5, 2008
Loops
A. Poluektov. Measurements of φ3/γ
3
KEKB and Belle detector
KEKB Collider
3.5 GeV e+ & 8 GeV e– beams
3 km circumference, 11 mrad crossing angle
L = 1.7 x 1034 cm–2s–1 (world record)
∫ L dt ~ 820 fb–1 @ Υ(4S)+off(~10%)
FPCP, Taiwan. May 5, 2008
A. Poluektov. Measurements of φ3/γ
4
PEP-II and BaBar detector
Silicon Vertex
Tracker (SVT)
1.5T magnet
e
+
Drift Chamber
(DCH)
e
­
Instrumented
Flux Return
(IFR)
Electromagnetic
Calorimeter (EMC)
Detector of
Internally
Reflected
Cherenkov Light
(DIRC)
3.1 GeV e+ & 9 GeV e– beams
L = 1.2 x 1034 cm–2s–1
∫ L dt = 530 fb–1 @ Υ(4S)+off (~10%)
FPCP, Taiwan. May 5, 2008
A. Poluektov. Measurements of φ3/γ
5
B+→D0K+ decay
CP violation enters the Standard Model as a complex phase ⇒ only observable in the
interference. To measure φ3/γ, use interference on Vub and Vcb amplitudes:
B– D0K–:
B– D0K– :
A1 ~ VcbVus* ~ A3
A 2 ~VubVcs* ~Aλ 3(ρ  i ) ~ e  i3
Amplitudes interfere if D0 and D0 decay into the same final state
Relative phase:    3   (B–→DK–),   3   (B+→DK+)
 0 ⟩ =∣D0 ⟩ r B ei ∣D0 ⟩
∣D
includes weak (φ3/γ) and strong (δ) phase.
Magnitude of CP violation is determined by the ratio of the two amplitudes:
0
rB  A ( B   D K  ) / A ( B   D 0 K  ) 
Vub* Vcs
Vcb* Vus
 [color supp ] ~ 0.1
Precision of γ/φ3 depends on rB: σ(φ3/γ) ~ 1/rB. Measuring rB is also essential.
FPCP, Taiwan. May 5, 2008
A. Poluektov. Measurements of φ3/γ
6
Methods of φ3/γ measurement
●
Based on B→DK. Different D0 modes can be used:
–
GLW (CP eigenstates: D0→ππ, KK, Kφ, Kω)
Belle: 275M BB pairs (B→DCPK, B→D*CPK: PRD 73 051106 (2006))
BaBar: 382M BB pairs (B→DCPK: arXiv:0802.4052,
B→D*K: Hot topic, B→DCPK*: PRD 72 071103 (2005))
–
ADS (CF and DCS states: D0→Kπ, Kππ)
Belle: 657M BB pairs (B→DK: arXiv:0804:2063)
BaBar: 232M BB pairs (B→DK, B→D*K, B→DK* with D→Kπ: PRD 72 032004 (2005))
–
Dalitz (multibody states: D0→Kππ, KKK, πππ)
Belle: 657M BB pairs (B→DK, B→D*K with D*→Dπ0, D0→KSπ+π-: arXiv:0803.3375)
BaBar: 382M BB pairs (B→DK, B→D*K with D*→Dπ0,Dγ,
D0→KSπ+π-,KSK+K-: arXiv:0804.2089)
371M BB pairs (B0→D0K*0: Moriond EW 2008)
●
Based on B0 decays (measurement of 2φ1+φ3 )
Belle: 386M BB pairs (B→D*π partial, B→D(*)π full rec.: PRD 73 092003 (2006))
BaBar: 232M BB pairs (B→D*π partial: PRD 71 112003 (2005),
B→D(*)π, Dρ full rec.: PRD 73 111101 (2006))
347M BB pairs (B→DKπ time-dependent Dalitz: arXiv:0712.3469)
FPCP, Taiwan. May 5, 2008
A. Poluektov. Measurements of φ3/γ
7
GLW method
M. Gronau, D. London, D. Wyler PLB 253, 483 (1991); PLB 265, 172 (1991)
СР eigenstate of D-meson is used (DCP).
CP-even: D1 →K+K–, π+ π –,
Double ratio
R C P± =
CP-odd: D2 → KS π0, KS ω, KS φ, KSη…
Br  B  D C P± K / Br  B  D C P± 
0
0
Br  B  D K / Br  B  D 
2
=1r B2r B cos ' cos 
Br  B  D C P± K −Br  B  D C P±  2r B sin  ' sin 
=
СР-asymmetry: A C P± =
Br  B  D C P± K Br  B  D C P± 
R C P±
for D1
 
 A1,2 have opposite signs
 



for D2

Alternative variables:
x± =r B cos±=
R 1 A 1− R2 1 A 2
= 1
4
R R2−2
2
r B= 1
2
FPCP, Taiwan. May 5, 2008
A. Poluektov. Measurements of φ3/γ
8
BaBar: GLW method (B→DK)
BaBar collaboration, 382M BB pairs [arXiv: 0802:4052]
CP-even modes: DCP+→K+K–, π+ π –
CP-odd modes : DCP−→KS π0, KS ω
●
Cut on mES, event shape variables
●
ΔE and PID variable included into likelihood
ACP+
+0.27 ± 0.09 ± 0.04
ACP-
−0.09 ± 0.09 ± 0.02
RCP+
1.06 ± 0.10 ± 0.05
RCP-
1.03 ± 0.10 ± 0.05
The same result expressed in Cartesian variables:
x+ −0.09 ± 0.05± 0.02
x− +0.10 ± 0.05 ± 0.03
r2
0.05 ± 0.07 ± 0.03
x± precision comparable to Dalitz analysis
FPCP, Taiwan. May 5, 2008
A. Poluektov. Measurements of φ3/γ
9
*
BaBar: GLW method (B→D K)
BaBar collaboration, 382M BB pairs, B→D*K with D*→Dπ and D*→Dγ
CP-even modes: DCP+→K+K–, π+ π –
New!
Preliminary
CP-odd modes : DCP−→KS π0, KS ω, KS ϕ
●
Cut on mES, event shape variables
●
ΔE and PID variable included into likelihood
D*→Dπ and D*→Dγ have strong phase difference
exactly 180° ⇒ Can combine both
ACP+
−0.11 ± 0.09 ± 0.01
ACP-
+0.06 ± 0.10 ± 0.02
RCP+
1.31 ± 0.13 ± 0.03
RCP-
1.10 ± 0.12 ± 0.04
See als
o
BaBar
ho
topic ta t
lk
The same result expressed in Cartesian variables:
x+* +0.09 ± 0.07 ± 0.01
x−* −0.02 ± 0.06 ± 0.01
r*2 0.22 ± 0.10 ± 0.03
(KS ϕ excluded to allow comparison with Dalitz)
FPCP, Taiwan. May 5, 2008
A. Poluektov. Measurements of φ3/γ
10
ADS method
D. Atwood, I. Dunietz and A. Soni, PRL 78, 3357 (1997)
Enhance magnitude of CP violation by using Doubly Cabibbo-suppressed D decays
e.g. B−→[K+π−]D K−:
Observable:
R ADS =
Br B  D supp K  2 2
=r B r D 2r B r D cos 3 cos
Br B  D fav K 
where
 ≡ B  D
∣
∣
A D 0  K   − 
r D=
=0.0578±0.0008
0
 −

A D  K  
FPCP, Taiwan. May 5, 2008
A. Poluektov. Measurements of φ3/γ
11
Belle: ADS method
Belle collaboration, 657M BB pairs [arXiv: 0804:2063, submitted to PRD(RC)]
B−→[K+π−]D K− (suppressed) and B−→[K–π+]D K− (favored) modes are selected.
●
●
Cut on Mbc, MD, PID likelihood,
event shape
B→DsuppK
B→DfavK
Fit ΔE to extract signal yield
2.0
−3
R ADS =8.06.3
−5.7 −2.8 ×10
CP asymmetry:
A ADS=−0.130.98
−0.88 ±0.26
rB<0.19 at 90% CL
(with the conservative
assumption cos φ3 cos δ = –1)
11 9 °
Using CLEO measurement =22−12 −11  [arXiv: 0802:2268]
and φ3,δB measurements from Dalitz analysis, See
talk by
D
avid As
tighter rB constraint can be obtained.
ne
on Frid
ay
FPCP, Taiwan. May 5, 2008
r
A. Poluektov. Measurements of φ3/γ
12
Dalitz analysis method
A. Giri, Yu. Grossman, A. Soffer, J. Zupan, PRD 68, 054018 (2003)
A. Bondar, Proc. of Belle Dalitz analysis meeting, 24-26 Sep 2002.
 0 ⟩ =∣D0 ⟩ r B ei ∣D0 ⟩
∣D
Using 3-body final state, identical for D0 and D0: Ksπ+π-.
Dalitz distribution density:
∣A
D
2

K S
m
2
−
K S
,m
d  m2K
S


, m2K
2
S

−
∝∣ AD∣ dm2K
S


dm2K
S
−
2
∣

(assuming СР-conservation in D0 decays)
2
2
If A D  mK  ,mK   is known, parameters 3 /  ,r B , are obtained from the fit to Dalitz
distributions of D→Ksπ+π– from B±→DK± decays

S
−
S
Need to know a complex form of the D0 decay amplitude, but only |A|2 is obtained from D*→Dπ
⇒ Need to use model description, model uncertainty as a result
FPCP, Taiwan. May 5, 2008
A. Poluektov. Measurements of φ3/γ
13
Belle Dalitz: D0→KSπ+π− amplitude
[preliminary]
Belle collaboration, 657M BB pairs [arXiv: 0803:3375]
2
M Ksπ – (GeV 2 )
Isobar model is used as a baseline. K-matrix for systematics test.
M K2   (GeV 2 )
M K2   (GeV 2 )
M K2   (GeV 2 )
M 2  (GeV 2)
s
s
σ1(M=522±6 MeV, Γ=453±10 MeV)
σ2(M=1033±7 MeV, Γ=88±7 MeV)
FPCP, Taiwan. May 5, 2008
s
Intermediate
state
K S σ1
KS ρ(770)
KS ω
KS f0(980)
K S σ2
KS f2(1270)
KS f0(1370)
KS ρ(1450)
K* (892)+π–
K*(892)–π+
K*(1410)+π–
K*(1410)–π+
K*0(1430)+π–
K*0(1430)–π+
K*2(1430)+π–
K*2(1430)–π+
K*(1680)+π–
K*(1680)–π+
Nonresonant
Amplitude
Phase, °
1.56±0.06S
1 (fixed)S
0.0343±0.0008S
0.385±0.006S
0.20±0.02S
1.44±0.04S
1.56±0.12S
0.49±0.08S
1.638±0.010
0.149±0.004
0.65±0.05
0.42±0.04
2.21±0.04S
0.36±0.03S
0.89±0.03S
0.23±0.02S
0.88±0.27
2.1±0.2
2.7±0.3
214±3S
0 (fixed)S
112.0±1.3S
207.3±2.3S
212±12S
342.9±1.7S
110±4S
64±11S
133.2±0.4
325.4±1.3
120±4
253±5
358.9±1.1S
87±4S
314.8±1.1S
275±6S
82±17
130±6
160±5
A. Poluektov. Measurements of φ3/γ
14
( )
Belle B→D * K Dalitz: signal selection
[preliminary]
Belle collaboration, 657M BB pairs [arXiv: 0803:3375]

B 
D*K 
DK
B

ΔE (GeV)
Mbc (GeV/c2)
ΔE (GeV)
• |ΔE|<30 MeV
• |Mksππ–MD| < 11 MeV/c2
• Mbc>5.27 GeV/c2
• 144.9 < ΔM < 145.9 MeV/c2 (B→D*K only)
Mbc (GeV/c2)
• Continuum rejection variables cosθthr, “virtual calorimeter” Fisher discriminant:
|cosθthr| < 0.8, F > −0.7 in (Mbc, ΔE) fit to determine background composition.
Whole range is used in Dalitz fit, included into likelihood.
756 events, 29% background (B→DK).
149 events, 20% background (B→D*K, D*→Dπ0).
FPCP, Taiwan. May 5, 2008
In “clean” signal region
(|cosθthr| < 0.8, F > −0.7)
A. Poluektov. Measurements of φ3/γ
15
Belle Dalitz: fit results
[preliminary]
Fit parameters are x±= rB cos(±φ3+δ) and y±= rB sin(±φ3+δ)
Unbinned maximum likelihood fit with event-by-event background treatment
(ΔE, Mbc, |cosθthr|, F included into likelihood)
B 
D*K 
K
D
B

Errors are statistical and
experimental systematic.
Model error not included.
FPCP, Taiwan. May 5, 2008
x–= +0.105 ± 0.047 ± 0.011
y–= +0.177 ± 0.060 ± 0.018
x+= –0.107 ± 0.043 ± 0.011
y+= –0.067 ± 0.059 ± 0.018
x–= +0.024 ± 0.140 ± 0.018
y–= –0.243 ± 0.137 ± 0.022
x+= +0.133 ± 0.083 ± 0.018
y+= +0.130 ± 0.120 ± 0.022
A. Poluektov. Measurements of φ3/γ
16
Belle Dalitz: fit results
B →DK only:
±
±
[preliminary]
φ3=81 +13
° ± 5°(syst) ± 9°(model)
−15


B
K
D
B±→D*K± only:
φ3=64
° ± 4°(syst) ± 9°(model)
+21
−23
B±→DK±, B±→D*K± combined:
+12
φ3=76 −13
° ± 4°(syst) ± 9°(model)
rDK=0.16 ± 0.04 ± 0.01(syst) ± 0.05(model)
B 
D*K 
rD*K=0.21 ± 0.08 ± 0.01(syst) ± 0.05(model)
δDK=136 +14
° ± 4°(syst) ± 23°(model)
−16
+20
δD*K=343 −22
° ± 4°(syst) ± 23°(model)
Model error estimate is the same as in
previous analysis.
Stat. confidence level of CPV is (1-5.5·10-4) or 3.5σ !
FPCP, Taiwan. May 5, 2008
A. Poluektov. Measurements of φ3/γ
17
BaBar Dalitz: D0→KSπ+π− and KSK+K− modes
BaBar collaboration, 383M BB pairs [arXiv: 0804:2089]
K * 892 ± , K *0 1430± , K *2 1430 ± ,
K * 1680 − , 770, 782 , f 2 1270 ,
K-matrix for ππ S-wave and running phase
a0  9800 , 1020 , f 0 1370 , f 2 1270 ,
a0 14500 , a0 980± , a0 1450+
non-resonant for Kπ S-wave
FPCP, Taiwan. May 5, 2008
A. Poluektov. Measurements of φ3/γ
18
BaBar Dalitz: signal selection
7 modes used: B→DK, B→D*K with D*→Dπ0 and Dγ, B→DK*
D0→KSπ+π- and KSK+K- (except for B→DK*)
D0→KSK+K-
D0→KSπ+π-
B±  D K ±
B ± [ D 0 ] D K ±
∗
B ± [ D ]D K ±
∗
B ±  D [ K S  ± ]K
∗
133±15 ev
129±16 ev
600±31 ev
112±13 ev
FPCP, Taiwan. May 5, 2008
32±7 ev
118±18 ev
21±7 ev
A. Poluektov. Measurements of φ3/γ
19
BaBar Dalitz: fit results
Fit results expressed in Cartesian coordinates x±= rB cos(±γ+δ), y±= rB sin(±γ+δ)
B DK
±
B D K
±
±
B→ D 0K
∗
±
B→ D*0K
B±  D K ∗
B→ D 0K*
x−
y−
+0.090 ± 0.043 ± 0.015 ± 0.011 −0.111 ± 0.069 ± 0.014 ± 0.004 +0.115 ± 0.138 ± 0.039 ± 0.014
x+
−0.067 ± 0.043 ± 0.014 ± 0.011 +0.137 ± 0.068 ± 0.014 ± 0.005 −0.113 ± 0.107 ± 0.028 ± 0.018
y+
−0.015 ± 0.055 ± 0.006 ± 0.008 +0.080 ± 0.102 ± 0.010 ± 0.012 +0.125 ± 0.139 ± 0.051 ± 0.010
+0.053 ± 0.056 ± 0.007 ± 0.015 −0.051 ± 0.080 ± 0.009 ± 0.010 +0.226 ± 0.142 ± 0.058 ± 0.011
Statistical
Systematic
FPCP, Taiwan. May 5, 2008
D0 model
A. Poluektov. Measurements of φ3/γ
20
BaBar Dalitz: combined result
°
=7623
−24 ±5±5
30
−28
=63
°
±8±7
(D →KSπ π modes only)
0
+ -
CPV significnce is 3.0σ
FPCP, Taiwan. May 5, 2008
r B= 0.086± 0.035±0.010± 0.011
r B= 0.135±0.051±0.011± 0.005
∗
0.088
±
− 0.105
 r s= 0.163

0.037± 0.021
28
°
 B =109−31±4±7
∗
28
°
 B =−63−30±5±4
43
°
 s=104−41±17±5
Accounts for possible
non-resonant B→DKπ
A. Poluektov. Measurements of φ3/γ
21
Dalitz analisys: model-independent way
Model-independent way: obtain D0 decay strong phase from ψ(3770)→DD data
PB (m2 , m2 ) | f D  ( x  iy ) f D |2  PD  rB2 PD  2 PD PD [ xC  y S ]
PD (m2 , m2 ) | f D (m2 , m2 ) |2
PD (m , m ) | f D (m , m ) |
2

2

2

2

2
x  rB cos(  3 )
y  rB sin(  3 )
C (m2 , m2 )  cos( D (m2 , m2 )   D (m2 , m2 ))
S (m2 , m2 )  sin( D (m2 , m2 )   D (m2 , m2 ))
Free parameters
Unknown, can be obtained
from charm data at ψ(3770):
See
Bru talk
tom ce Ya by
orr bsle
ow
y
PCP  (m2 , m2 ) | f D  f D |2  PD  PD  2 PD PD C
DCP→KSπ+π–:
ψ(3770)→(KSπ π )D (KSπ π )D :
+ –
+ –
PCorr ( m2 , m2 , m2 , m2 ) | f D f D  f D f D |2 
 PD PD  PD PD  2 PD PD PD PD (CC   SS )
Contribution to φ3/γ error: ~5° with CLEO data
(but this is stat. error, more reliable than current model uncertainty)
~1° with BES data (20 fb-1)
FPCP, Taiwan. May 5, 2008
A. Poluektov. Measurements of φ3/γ
22
Techniques using neutral B decays (BaBar)
Decay
Both amplitudes are color-suppressed, rB ~0.4
B0D0K*0:
°
0
∗0
/3 =162±56 , r D K 0.5590%
Decay B0  D∓ K 0 :±
BaBar collaboration, 347M BB pairs [arXiv: 0712:3469]
Use B flavor tag, perform time-dependent Dalitz plot analysis. Sensitive to 2β+γ
0
Interference between B  D
∗∗0
0
0
−
∗
K S (b→u and b→c) and B  D K (b→c)
°
2 /213=83±53±20
FPCP, Taiwan. May 5, 2008
A. Poluektov. Measurements of φ3/γ
23
World average (UTfit)
UTfit averages
including all results
available today
γ/φ3=81±13°
rDK=0.098±0.017
FPCP, Taiwan. May 5, 2008
[ provided
by V. Sordini ]
rD*K=0.092±0.038
A. Poluektov. Measurements of φ3/γ
rDK*=0.13±0.09
24
Conclusion
●
Many new measurements related to φ3/γ appeared in 2008:
–
BaBar GLW, Belle ADS updates,
–
Belle Dalitz update with D0→KSπ+π-
–
BaBar Dalitz update with D0→KSπ+π- and new D0→KSK+K-.
●
Combining all B-factory results, there is strong evidence of CP violation in B→DK.
●
rB is shown to be significantly non-zero.
Can predict future sensitivity with confidence.
●
φ3/γ statistical precision is now comparable to D0 model uncertainty.
Model-independent Dalitz analysis using charm data (CLEO) will allow to
obtain a more reliable result.
FPCP, Taiwan. May 5, 2008
A. Poluektov. Measurements of φ3/γ
25
B-meson selection
In Υ(4S) decays, pairs of B-mesons are produced (near BB threshold)
 E B  E cm / 2,
small CM momentum (300 MeV/c)
Selection variables:
• CM energy difference:
E   E i  ( E cm / 2)
B-meson “beam-constrained mass” Mbc (Belle) or
“energy substituted mass” MES (BaBar):
M bc  ( E cm / 2) 2  ( pi ) 2
• Event shape (e+e-bb and e+e-uu,dd,ss,cc separation):
e+e-uu,dd,ss,cc
FPCP, Taiwan. May 5, 2008
e+e-bb
A. Poluektov. Measurements of φ3/γ
26