unitarity triangle 2 angles at babarbeach2008.sc.edu/.../sessions/martinez-vidal.talk.pdfbeach 2008,...
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BEACH 2008, 22-28 June, 2008 F. Martínez-Vidal , Unitarity Triangle angles at BaBar 1
Unitarity Triangle angles at BaBar
F. Martínez-Vidal
IFIC – Universitat de València-CSIC
g, f3
a, f2
b, f1
2
The matrix and the “db” Unitarity
Triangle angles
• In the Standard Model (SM), the CKM matrix elements Vij describe the (complex)
electroweak couplings of the W± to quarks
• The 6 unitarity conditions can be represented with triangles in a complex plane
– One only has roughly equal-length sides “db” Unitarity Triangle
β
-i
-i
γ1 1
1 1 1
1 1
e
e
* * * 0ub ud cb cd tb tdV V V V V V
CKM phases(in Wolfenstein convention)
(0,0)
( , )
(1,0)
2 3
2 2
3 2
1 / 2 ( )
1 / 2
(1 ) 1
ub
t
ud us
cd cs cb
tbd ts
V V A i
V V V A
A
V
V i AV V
Wolfenstein parameterization:
4( )O
~ 0.23, ~ 0.8, ~ 0.2, ~ 0.4A
Non-zero phase implies CP violation
*
2
*( )ud ub
cd cb
V Vi i O
V V
3
Measuring the phases from CPV• CKM phases measurable when there are two paths to reach the same final state, and
strong phases do not vanish
• Text book example: interference between B0J/YKS (bccs) and B0
J/YKS
(bccs) decays allows determination of b
mixing decay mixing decay
2
2
1 | |0
1 | |
f
f
2
2Imsin 2
1 | | CP
f
f
f
C
P a
sym
met
ry
2/ ip q e
f
f
f
q
p
Aλ
A
Next largest amplitude (l2) has same weak phase
Other CKM corrections are Cabibbo suppressed O(l4)
and depend on the CKM anglesf fS C
0 0
0 0
CP,
( ) ( )( ) cos( ) sin( )
( ) ( )f f
B fB f
f
B fB f
t tA t m t m t
t tC S
weak
we
strong
str
2 2 2
1 2 1 2
2 2 2
ong2 ak1 2 1
| ( ) | | | | | 2 | || |
|
(cos
c( ) | | | | |
)
( )|| o| s2 |
A B f A A A A
A B f A A A A
Uncertainty ~1%
BEACH 2008, 22-28 June, 2008 F. Martínez-Vidal , Unitarity Triangle angles at BaBar 4
Time dependent measurements in a nutshell
e-e
tagB 4S
Start the Clock
z ~250 mm
c
zt
1
Δt is a signed quantity
recB
Exclusive B Meson and vertex reconstruction
/J
0
SK
Tag vertex reconstruction
B-FlavorTagging
K
Tagging performance:
Q=e(1-2w)2~30%
~ 1 ps 170 mt
(9.0 GeV)(3.1 GeV)
(4 ) 0.55S
High-statistics self-tagging
“B-flavor” sample to
calibrate tagging
measure Dz resolution
Coherent B meson production (L=1)
BEACH 2008, 22-28 June, 2008 F. Martínez-Vidal , Unitarity Triangle angles at BaBar 5
Common experimental techniques
• Veto significant/potentially dangerous B decay backgrounds
• Resonance masses, decay angles, helicity in
PPV, VPP decays
• Suppress continuum e+eqq (q=u,d,s,c) background
using event topology (multivariate methods)
• Characterize B candidates using
– Beam-energy substituted mass
– Energy difference
• Maximum likelihood fits to mES,
E, Fisher, PID, Dt, tagging, etc
• Use sidebands and control samples
to check backgrounds
Search for a needle in a haystack
MeVbeammES7.2~~
MeVBEE 5010~ *
BEACH 2008, 22-28 June, 2008 F. Martínez-Vidal , Unitarity Triangle angles at BaBar 6
Final collisions 12:43pm,
Monday 7 Apr 2008
Runs 1-4
Runs 1-5
BEACH 2008, 22-28 June, 2008 F. Martínez-Vidal , Unitarity Triangle angles at BaBar 7
sin2b in b→ccs decays: “golden modes”PRL 99, 171803 (2007) 383M BB
sin2b in individual charmonium modes
CP-odd
CP-even
sin 2 0.714 0.032 0.018
| | 0.952 0.022 0.017
BEACH 2008, 22-28 June, 2008 F. Martínez-Vidal , Unitarity Triangle angles at BaBar 8
b→ccd decays: B0→J/yp0 and B0→D(*)+D(*)-
arXiv:0804.0896 [hep-ex]
accepted by PRL 466MBB
Penguins with additional phases could contribute
If not, SM predicts S=sin2b, C=0
NEW!
184±15
5
1.23 0.21 0.04
0.20
(1.69 0.14 0
0.19
.07)
0.0
0
3
1
S
C
BF
0.66 0.19 0.04
0.02 0.11 0.02
S
C
617±33
D(*)+D(*)- are consistent with bccs.
E.g. for D*+D*-:
PRD 76, 111102 (2007) 383M BB
BEACH 2008, 22-28 June, 2008 F. Martínez-Vidal , Unitarity Triangle angles at BaBar 9
• If single phase dominates, SM
predicts S=sin2b, C=0
• Dominant CKM factors as
in J/yKS
Penguin-dominated b→qqs (q=s,d) decays
• Sensitivity in the loop to New Physics effects
• No recent updates
• Systematic (non statistically significative) shift
with respect to charmonium persists
• SM (hadronic) corrections to single-phase-
dominance would in general predict opposite
shift
pen pen sin 2S S
B0
b
d
u, c, t
g
W+
f, h,
(KK)
s
s
s
dK0
BEACH 2008, 22-28 June, 2008 F. Martínez-Vidal , Unitarity Triangle angles at BaBar 10
Measuring a• Access to a from the interference of bu decay (g) with B0-B0 mixing (2b)
complicated by penguin contribution
– Need additional information to extract a
d
d
0B
*
tbV
tdV
b
b
0Bt
t
*
tdV
tbV** // tdtbtdtb VVVVpq
B0B0 mixing
d
u
dd
0B
/ubV
*
udV
b /u
Tree decay
ubudVVA *
d
u
dd
0B
/g
b
/u
tcu ,,
Penguin decay
tbtdVVA *
2 2 2
sin 2
0
CP CP CP
CP CP
CP
i i i
f f f
f f
f
q Ae e e
p A
S
C
22
2
| |
1 sin 2
sin
eff
f CP CP CPCP
CP CP CP
CP
i iii
f f fi i
f f f eff
f
T P e ee e
T P e e
S C
C
How can we
obtain
from αeff ?
( )
T(P) = tree (penguin) amplitude
d = dP-dT , strong phase difference
BEACH 2008, 22-28 June, 2008 F. Martínez-Vidal , Unitarity Triangle angles at BaBar 11
Measuring a: dealing with penguins
• SU(2) isospin symmetry relates u and d quarks: mu ~ md
• Bhh can have I=0 or 2 but gluonic penguins only contribute to I=0 (by DI=1/2 rule)
– B+h+h0 (mediated DI=3/2) is pure I=2,
with negligible EW penguins (1-2o)
only tree amplitude
• Different Bhh final states can be related to
each other through isospin amplitudes
• These amplitude relations can be used to
constrain the penguin shift in time dependent measurement bounds |aeff-a|=k/2
• Need 6 samples: 4 tagged neutral decays + 2 charged decays
• Still a 8-fold ambiguity (mod 180o) (4-fold from k, 2-fold from 2a)
0 000 001 1 A
2 2A A A A A
00A A
22eff
21 sin(2 )hh hhS C
Gronau, London, PRL 65, 3381 (1990)Gronau/London analysis
BEACH 2008, 22-28 June, 2008 F. Martínez-Vidal , Unitarity Triangle angles at BaBar 12
a from B0p
+p
-
• Simultaneous EML to B0p
+p
-, K+p
-, K+K-
0.60 0.11 0.03 (5.1 )
0.21 0.09 0.02 (2.2 )
S
C
Still, 2.1s
difference
on Cp+p-
with Belle
1139±49
PRL 99, 021603 (2007) 383M BB
)96( 116
Isospin analysis to extract a (6 unknowns)
• Use 00 0 00, , , , ,S C C BF BF BF
CPV well established in B0p
+p
-
Includes SU(3) constraints
on penguin amplitude from BS→K+K-
[Fre
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PRD 76, 091102 (2007) 383M BB
BEACH 2008, 22-28 June, 2008 F. Martínez-Vidal , Unitarity Triangle angles at BaBar 13
• First measurement of TD CP
asymmetries in r0r
0
6
,00
,00
0.70 0.14 0.05
(0.84 0.29 0.17) 1
0.5 0.9 0.2
0.4 0.9 .2
0
0
L
L
Lf
S
C
BF
BABAR Preliminary: arXiv:0708.1630
(2007) 427M BB
Favored Da=11.3o
NEW!
B0r
0r
0 and isospin analysis
[Fre
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]
00 00 00 0, , , , , ,S C C BF B BS F F
Nsig=85±28±17
3.6s
Isospin analysis to extract a
• Use
BEACH 2008, 22-28 June, 2008 F. Martínez-Vidal , Unitarity Triangle angles at BaBar 14
• First measurement of TD CP
asymmetries in r0r
0
6
,00
,00
0.70 0.14 0.05
(0.84 0.29 0.17) 1
0.5 0.9 0.2
0.4 0.9 .2
0
0
L
L
Lf
S
C
BF
BABAR Preliminary: arXiv:0708.1630
(2007) 427M BB
Favored Da=11.3o
NEW!
B0r
0r
0 and isospin analysis
[Fre
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enti
st i
nte
rpre
tati
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]
00 00 00 0, , , , , ,S C C BF B BS F F
Nsig=85±28±17
3.6s
Isospin analysis to extract a
• Use
PRD 76, 052007 (2007) 383M BB
729±60
0.05
, 0.06
,
0.17 0.20
0.01 0.15 0.06
L
L
S
C
BEACH 2008, 22-28 June, 2008 15
a from B0p
+p
-p
0
• Isospin analysis not viable Isospin pentagon (6 tagged decays+4 charged)
• Better approach: TD p+p
-p
0 Dalitz analysis assuming isospin symmetry
– Amplitude A3pdominated by r+
p-,r-
p+,r
0p
0 and radial excitations
– Interference at equal masses-squared (in the corners)
provides the information on relative strong phases
0
3 0
0
3 0
A f A f A f A
A f A f A f A
0( )A A B
0
+
0
0
+
0B
0B
Snyder, Quinn, PRD 48, 2139 (1993)
PRD 76, 012004 (2007) 375M BB
74o < a < 132o @ 68.3%C.L.
[Fre
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i
i
A T e P
A T e P
Resolve some ambiguities
BEACH 2008, 22-28 June, 2008 F. Martínez-Vidal , Unitarity Triangle angles at BaBar 16
g from BD(*)K(*)
• Use interference between bcus and bucs decay processes
• Sensitivity to g driven by the ratio
– s(g)~1/rB , need to measure rB from data
• B0D(*)0K(*)0 self-tagged decays also used (rB~0.37), but both diagrams are color
suppressed
• 3 different
final states
*
*
| |( )0.37 ~ 0.1
( ) | |
cs ubB F F
us cb
V VA b ur c c
A b c V V
Giri, Grossman, Soffer, Zupan,
PRD 68, 054018 (1993)
Bondar, PRD 70, 072003 (2004)
Atwood, Dunietz, Soni,
PRL 78, 3257 (1997),
PRD 63, 036005 (2001)
Gronau, London, PLB 253, 483 (1991)
Gronau, Wyler, PLB 265, 172 (1991)
BEACH 2008, 22-28 June, 2008 F. Martínez-Vidal , Unitarity Triangle angles at BaBar 17
arxiv:0802.4052,
Accepted PRD 383M BB
NEW!
Updated B+D*K+ and B+DK+ GLW
B+DK+ B+
D*K+
ACP+ 0.27 ± 0.09 ± 0.04 -0.11 ± 0.09 ± 0.01
ACP- -0.09 ± 0.09 ± 0.02 +0.06 ± 0.10 ± 0.02
RCP+ 1.06 ± 0.10 ± 0.05 1.31 ± 0.13 ± 0.04
RCP- 1.03 ± 0.10 ± 0.05 1.10 ± 0.12 ± 0.04
2
00
( ) ( )1 2 cos cos
[ ( ) ( )] / 2
CP CPCP B B B
B D K B D KR r r
B D K B D K
( ) ( )2 sin sin /
( ) ( )
CP CPCP B B CP
CP CP
B D K B D KA r R
B D K B D K
CP CP CP CPA R A R
• Based on triangle relations of amplitudes inherent 8-fold ambiguity
Preliminary 383M BB
B±DK±
B-
149
B+
106
BEACH 2008, 22-28 June, 2008 F. Martínez-Vidal , Unitarity Triangle angles at BaBar 18
• The idea in pictures:
• B± Dalitz plot distribution depends on g, rb and d. Write Likelihood as a function of the cartesian coordinates x± and y±
– Likelihood is Gaussian and unbiased
• No ambiguities mod 180o, only usual mirror solution: (dB,g)(dB+p,g+p)
2 2 2 2 2 * *( , ) | | | | 2 Re[ ] Im[ ]D B D D D D Dm m A r A x A A y A A
B+D(*)K+ Dalitz
A(B-)=|A(B→D0K-)|×+rBei(-g+d
B)
m(KS p-)2
m(K
Sp
+)2
m(KS p-)2
m(K
Sp
+)2
2 2 0 2 2 2 2
2 2 0 2 2 2 2
( , ) ( ) ( , ) ( , )
( , ) ( ) ( , ) ( , )
B
B
i i
D B D
i i
D B D
A m m A B D K A m m r e e A m m
A m m A B D K A m m r e e A m m
2 2 0 2( )Sm m K
D0→Ks pp D0→Ks pp
Neglect D mixing and CP violation in D decays
+D0→KsKK, p0pp
cos( )
sin( )
B B
B B
x r
y r
k accounts for natural width of K*
h accounts for different parity of D*0D0
g wrt D0p
0
BEACH 2008, 22-28 June, 2008 F. Martínez-Vidal , Unitarity Triangle angles at BaBar 19
• As interference depends on Dalitz position requires modelization of
• Extract D0/D0 decay amplitudes from DP analysis of independent high-statistics cc
sample with flavor-tagged D0→KS p+p
-, KS K+K- decays from D*+→D0
p+
• For D→Kspp use 9 BW resonances + K-matrix formalism for pp and Kp S-waves
– K-matrix deals with broad, overlapping, multi-channel scalar resonances
487k Evts
purity:97.7%
69k Evts
purity:99.3%
arXiv:0804.2089 subm.
to PRD 383M BB
2 2( , )DA m m
NEW!
B+D(*)K+ Dalitz: analysis of D0/D0 decays
2/dof1.11
D0→
Ks p
pD
0
Ks K
K
2/dof1.09
First time!
BEACH 2008, 22-28 June, 2008 F. Martínez-Vidal , Unitarity Triangle angles at BaBar 20
Distance between (B+B-)
points is 2rB|sin 2g|
extract CL for g, rb and db from x±,y± with frequentist stat. procedure
B→D0K
CPV 2.2s
B→D0*K
CPV 2.5s
B→D0K*
CPV 1.5s
*
* 0.088
0.105
23
24
(DK) 0.086 0.035
(D K) 0.135 0.051
(DK ) 0.163
(76 )
B
B
s
r
r
kr
Includes exp. (5O) and
Dalitz (5O) errors
arXiv:0804.2089 subm.
to PRD 383M BB
B+D(*)K+ Dalitz: results
[Fre
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]
B-
B+
2g
rB-
rB+ 2 | sin | 0 direct CPVBr
BEACH 2008, 22-28 June, 2008 F. Martínez-Vidal , Unitarity Triangle angles at BaBar 21
Despite BaBar
errors on x,y are
comparable with
Belle, error on g
is worse: the
“1/rB effect”
Belle preliminary arXiv:0803.3375 657M BB
22 o
23
12 o
13
(76 5 5)
(76 4 9)
Comparison with Belle
*
( ) 0.086 0.035
( ) 0.135 0.051
B
B
r DK
r D K
stat exp model
BEACH 2008, 22-28 June, 2008 F. Martínez-Vidal , Unitarity Triangle angles at BaBar 22
• b in charmonium is a precision measurement
– d(sin2b)~0.035 (2%) approaching accuracy of SM calculations (~1%)
• All b measurements in many different channels are consistent
– Sensitivity to NP for some channels
Summary and Outlook
BEACH 2008, 22-28 June, 2008 F. Martínez-Vidal , Unitarity Triangle angles at BaBar 23
• b in charmonium is a precision measurement
– d(sin2b)~0.035 (2%) approaching accuracy of SM calculations (~1%)
• All b measurements in many different channels are consistent
– Sensitivity to NP for some channels
• a ultimately limited by penguin pollution
– da~10o now
– The decay modes Bpp,rr,rp consistent
and complementary
– Still more new channels being added
(e.g. Ba1p)
Summary and Outlook
CKM fitter group combination
13.5
5.7(83.5 )
Eur. Phys. J C 41, 1 (2005)
http://ckmfitter.in2p3.fr
BEACH 2008, 22-28 June, 2008 F. Martínez-Vidal , Unitarity Triangle angles at BaBar 24
• b in charmonium is a precision measurement
– d(sin2b)~0.035 (2%) approaching accuracy of SM calculations (~1%)
• All b measurements in many different channels are consistent
– Sensitivity to NP for some channels
• a ultimately limited by penguin pollution
– da~10o now
– The decay modes Bpp,rr,rp consistent
and complementary
– Still more new channels being added
(e.g. Ba1p)
• Being able to measure g at the B Factories
was unexpected
– rB ratios confirmed to be ~0.1 (and >0)
– dg~20o now, dominated by B+DK+ Dalitz
Summary and Outlook
My personal Dalitz+D(*)K GLW
combination
0.028
0.027
* 0.057
0.046
* 0.09
0.10
21
22
(DK) 0.090
(D K) 0.113
(DK ) 0.17
(72 )
B
B
s
r
r
kr
BEACH 2008, 22-28 June, 2008 F. Martínez-Vidal , Unitarity Triangle angles at BaBar 25
• b in charmonium is a precision measurement
– d(sin2b)~0.035 (2%) approaching accuracy of SM calculations (~1%)
• All b measurements in many different channels are consistent
– Sensitivity to NP for some channels
• a ultimately limited by penguin pollution
– da~10o now
– The decay modes Bpp,rr,rp consistent
and complementary
– Still more new channels being added
(e.g. Ba1p)
• Being able to measure g at the B Factories
was unexpected
– rB ratios confirmed to be ~0.1 (and >0)
– dg~20o now, dominated by B+DK+ Dalitz
• Measurement of all angles still statistically limited
• SM surviving all challenges from B Factories, so far
Summary and Outlook