Measurements of the angle : , (BaBar & Belle results) Georges Vasseur WIN`05, Delphi June 8, 2005.
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Transcript of Measurements of the angle : , (BaBar & Belle results) Georges Vasseur WIN`05, Delphi June 8, 2005.
Measurements of the angle : , (BaBar & Belle results)
Georges Vasseur
WIN`05, Delphi
June 8, 2005
June 8, 2005 Georges Vasseur 2
Outline
• Physics motivation
• Measurement of in B→
• Measurement of in B→ Dalitz.
• Summary on .
June 8, 2005 Georges Vasseur 3
CP violation
• CP violation is explained in the Standard Model by a phase in the CKM unitary matrix.
• In the Wolfenstein parameterization:
with0.22 , A 0.83• CP violation if ≠ 0.
1)1(
1
)(1
23
22
32
2
2
AiA
A
iA
VVV
VVV
VVV
V
tbtstd
cbcscd
ubusud
CKM
June 8, 2005 Georges Vasseur 4
The unitarity triangle
= process involving both B0 mixing and b→u transition
0*** tbtdcbcdubud VVVVVV 0*** tbtdcbcdubud VVVVVV
(0,0) (0,1)
Vub Vud* Vtd Vtb*
VcdV*cbVcd Vcb*
= phase of Vtd (B0 mixing)
= phase of Vub (b→u transition)
June 8, 2005 Georges Vasseur 5
CP violation in the interference between mixing and decay
• For a CP final state fCP, time-dependent asymmetry is:
• With
)cos()sin(
)()(
)()()(
00
00
tmCtmS
fBfB
fBfBtA
dfdf
CPCP
CPCPf
CPCP
CP
C 0 : Direct CP violation
CP
CP
CP
f
ff A
A
p
q21
)(2
CP
CP
CP
f
ffS
2
2
1
1
CP
CP
CP
f
ffC
S 0 : Indirect CP violation
FinalStateAmplitudes
00
00
BqBpB
BqBpB
H
L
from mixing
B0
B0
fCP
Mixing (q/p) CPfA
CPfA
June 8, 2005 Georges Vasseur 6
CP violation in B0→ρ+ρ-
• I
• Access to from the interference of a b→u decay () with B0B0 mixing ().
d
d
0B
*tbV
tdV
b
b
0Bt
t
*tdV
tbV** // tdtbtdtb VVVVpq
B0B0 mixing
du
dd0B
ubV
*udV
b u
Tree decay
ubudVVA *
sin
)2sin(1 2
C
CS eff
ii
iii
eePT
eePTe
2
du
dd
0B
g
b
utcu ,,
Penguin decay
tbtdVVA *
Inc. penguin contribution
0
)2sin(
C
S
222 iii eeeA
A
p
q
How can we obtain α from αeff ?
T = tree amplitude P = penguin amplitude = strong phase difference between penguin and tree
Tree only Tree + Penguin
June 8, 2005 Georges Vasseur 7
Isospin analysis• Use SU(2) to relate amplitudes of all modes.
Gronau, London : PRL65, 3381 (1990)Gronau, London : PRL65, 3381 (1990)
)( 0 BAΑ
)( 00000 BAΑ
)( 00 BAΑ
Small amplitudes
2| eff
| )(~ 0 BAΑ
)(~ 00000 BAΑ
000000 ~
2
~~
2
ΑΑ
ΑΑΑΑ
June 8, 2005 Georges Vasseur 8
Asymmetry measurement
• Exclusive B meson reconstruction.• Time measurement: z ≈ 250 m, z ≈ 170 m.• B-flavor tagging: Q = (1-2)2 ≈ 30%.
– with efficiency and mistag rate.
t =0
(4S)
tagB 0l (e-, -)
z = t c
fully reconstructed B
B 0Coherent B0B0
production
June 8, 2005 Georges Vasseur 9
Common features of the analyses
• Kinematical signal identification with– Beam energy substituted mass– Energy difference
• Hadron ID (separation /K).• Event-shape variables combined in a neural
network (NN) or Fisher discriminant to suppress jet-like continuum event.
2*2*BbeamES pEm
**beamB EEE
June 8, 2005 Georges Vasseur 10
B0→ρ+ρ- analysisB→B→ρρ++ρρ-- not historically favored for measuring α:
2 π0s in the final state.
3 amplitudes (VV decay): A0 (CP-even longitudinal), A|| (CP-even transverse), A┴ (CP-odd transverse).
But turned out to be the best mode:
Large branching fraction.
Penguin pollution much smaller than in B→ππ.
~100% longitudinally polarized! Pure CP-even state.
2
21
22
21
2
21
2
coscossinsin14
1
4
9
coscos
1 LL ff
dd
d
021.0029.0014.0978.0)(
Lf
BaBarBaBar
PreliminaryPreliminary
signal
bkgd
BaBar, hep-ex/050349, submitted to PRL
)89( 10)5430()( 60BBMBB
BaBar, Phys.Rev.Lett 93, 231801 (2004)
232 MBB
June 8, 2005 Georges Vasseur 11
Details of the B0→ρ+ρ- analysis
• Unbinned extended maximum likelihood fit on a data sample of 68703 events.
• Efficiency on signal: 7.7%.• 8 observables: mES, E, t, NN, m (x2), cos
hel (x2).
• Modelisation of signal (1% of fit sample), continuum (92% of fit sample), and 38 different modes of B-background (7% of fit sample).
• Extract signal yield, longitudinal polarization fraction, cosine and sine coefficients.
232 MBB
June 8, 2005 Georges Vasseur 12
ACP(t) in B0 decays
tags0B
tags0BPreliminaryPreliminary
09.018.003.0
24.033.0
52617)(08.014.0
long
long
C
S
BN
BaBar, hep-ex/0503049, submitted to PRL
signal
bkgd
232 MBB
June 8, 2005 Georges Vasseur 13
B+→ρ+ρ0 analysis
• For isospin analysis, need other B→ rates.
• B+→ρ+ρ0 was measured two years ago by both BaBar and Belle.
04.097.0)(
10)8.55.22()(
:BaBar
003.0007.0
0
67.54.5
0
Lf
BB
02.011.095.0)(
10)1.77.31()(
:Belle
0
68.37.6
0
Lf
BB
Phys.Rev.Lett 91, 171802 (2003) Phys.Rev.Lett 91, 221801 (2003)
89 MBB 85 MBB
005.0007.0
060 96.0)( 10)4.64.26()( :average World
LfBB
June 8, 2005 Georges Vasseur 14
B0→ρ0ρ0 analysis
• Limiting factor in the isospin analysis.
• Tree is color suppressed.• No significant signal:
– Penguin are smalls.
• Dominant systematic comes from the potential interference from B→a1
±± (~22%).1233)( 22
20000
BN
C.L.%90101.1
10)19.054.0()(6
636.032.0
000
BB
)M227( BB
%27Eff.Rec.
BaBar, Phys.Rev.Lett 94, 131801 (2005)
June 8, 2005 Georges Vasseur 15
Isospin analysis with B→ρρ
)%90(101.1)(
10)4.64.26()(
10)5430()(
6000
60
60
CLBBF
BBF
BBF
Phys.Rev.Lett 94, 131801 (2005)
Phys.Rev.Lett 91, 171802 (2003) Phys.Rev.Lett 91, 221801 (2003)
Phys.Rev.Lett 93, 231801 (2004)
|eff |< 11°
]123,79[:range %90
13100
CL
BaBar, hep-ex/050349, submitted to PRL
Error dominated by measurement
June 8, 2005 Georges Vasseur 16
B0→(ρ)0 analysis• Unlike , is not a CP eigenstate
– Must consider 4 configurations– Equivalent "isospin analysis" not viable.
• However, a full time-dependent Dalitz plot analysis can constrain
0B 0B
0B 0B
–+
+–00
Snyder, Quinn : PRD 48, 2139 (1993)Snyder, Quinn : PRD 48, 2139 (1993)
Interference at equal masses-squared gives information on
strong phases between resonances
02m
02m
June 8, 2005 Georges Vasseur 17
Time-dependent Dalitz analysis• Extract and strong phases using interferences between
amplitudes of decay.
003
003
AfAfAfA
AfAfAfA
0 B
0
0
for
for
B
B
3
3
A
A
• Assuming amplitude is dominated by ,and resonances
– The "f"s are functions of the Dalitz-plot and describe the kinematics of B→(S→VS).
– The "A"s are the complex amplitudes containing weak and strong phases. They are independent of the Dalitz variables.
script {} refers to {}
June 8, 2005 Georges Vasseur 18
Result with B→ • Hint of direct CP-violation
.)(6.)(113 2717 syststat
Mirror solution not shownWeak constraint at C.L.<5%
2.9
• Likelihood scan of using:
PeTA
PeTAi
i
{}
T =tree amp. P =penguinB
B
04.011.021.0
A
06.047.0 14.015.0
A B
B
213 MBB
June 8, 2005 Georges Vasseur 19
Combined α measurement
• The best individual measurement comes from .
• Mirror solution are disfavored, thanks to .
• Good agreement with global CKM fit.
• Combined value:
http://ckmfitter.in2p3.fr
)103( 10
9
June 8, 2005 Georges Vasseur 20
Summary
• CP violation has entered a phase of precision measurements thanks to the B-factories.
• The angle of the unitarity triangle has been measured with an uncertainty of ~10°.
• Will still improve.
)103( 10
9
http://ckmfitter.in2p3.fr