03/27/22 Attila Mihalyi - Wisconsin 1 Recent results on the CKM angle from BaBar DAFNE 2004, Frascati, Italy Attila Mihalyi University of Wisconsin-Madison
Dec 18, 2015
04/18/23 Attila Mihalyi - Wisconsin 1
Recent results on the CKM angle from BaBar
DAFNE 2004, Frascati, Italy
Attila MihalyiUniversity of Wisconsin-Madison
04/18/23 Attila Mihalyi - Wisconsin 2
The CKM matrix and Unitarity TriangleThe CKM mixing matrix relates the quarks in the weak interaction basis (d’,s’,b’)
and the quark mass eigenstates (d,s,b): (d’,s’,b’)=VCKM (d,s,b)
tbtstd
cbcscd
ubusud
CKM
VVV
VVV
VVV
V
Wolfenstein parametrization:
1)1()1(2
11)1(
)(2
11
223
2242
32
iAiA
AiA
iA
VCKM
=sinC (Cabibbo angle)
Independent parameters: , A
Unitarity leads to:
0 tbtdcbcdubud VVVVVV
*
*
cbcd
tbtd
VV
VV
*
*
cbcd
ubud
VV
VV
1
(,)
The angles of the triangle are related to CP–violation.
Measure from CP-asymmetries in b→uud processes.
B→B→B→
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B-decay modes sensitive to Time dependent asymmetry of a B-B system (h=):
Decay amplitudes: PeTeAPeTeA iihh
iihh
,
Due to the presence of both tree and penguin amplitudes we have:
effi
i
ii
hh eeTP
eTPe
22
1
1
The extraction of is complicated by penguins!
)sin()cos())(())((
))(())(()(
00
00
mtSmtChhtBNhhtBN
hhtBNhhtBNtA hhhhCP
21
Im2
hh
hhhhS
2
2
1
1
hh
hhhhC
hh
hhhh A
A
p
q ie
p
q 2where
eff directly related to Shh
T=TreeP=penguin
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Isospin analysis for B→ and B→Two triangular (isospin) relations can be constructed from the decay amplitudes.
M. Gronau, D. London, Phys. Rev. Lett., 65, 3381 (1990)
00 hhhh~ BABA
hh~
2
1 0BA
hh2
1 0BA
000 hhBA
000 hh~
BA
if no penguins
One can set a limit on the shift from penguins, -eff (useful only if the
B→ h0h0 BR is small):Gronau-London-Sinha-Sinha Phys. Lett. B514, 315 (2001)0
2000
0
00
4
)22(21)22cos(
BB
BBB
B
Beff
Y. Grossman, H. R. Quinn, Phys. Rev., D58, 017504 (1998)
Unknowns: Decay amplitudes
Observables: Branching ratios, CP asymmetries
Solvable but a 4-fold ambiguity on remains:
21)2sin( CS
Common base: EW penguins neglected
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Prospects of from B0→+-
The B0→ 00 BR was recently measured at BaBar, PRL 91 241801 (2003), and also at Belle.
60 10)5.090.1()( BBR
05.019.019.0
03.022.040.0
C
S113 fb-1 of data Preliminary,LP03
02.003.0
10)6.05.5()(
10)2.06.07.4()(
18.017.0
60.19.0
0
60
A
BBR
BBR
From 81fb-1 of data, taken in 1999-2001: PRL 89 281802 (2002), PRL 91 021801 (2003)
Implies large penguin contributions: eff | at 90% c.l. Not easy to get from B→
0B
0B
BR comparable to B0→ +- and B+→ +0 but not large enough to measure the B0 - B0 asymmetry.
0B
HFAG average:
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Prospects of from B→Both tree and penguin processes contribute.
Time dependent decay rate:
S: CPV in interference between mixing and decay
C: direct CPV
C, S: parameters related to not being a CP eigenstate.
ACP: asymmetry between and
Babar Results from 113 fb-1 with a quasi-2-body approach. (Select the bands on the Dalitz plot)
03.006.011.0
05.013.020.0 , 03.018.033.0
05.013.035.0 , 04.018.013.0
CPA
CS
CS
0B
0B
is not a CP eigenstate:
))cos()()sin()(1)(1()( 0 tmCCtmSSAB CP
PRL 91 201802 (2003)
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Isospin Analysis
0000 221 AAAAA
00000
00
00
)(
)( , )(
)( , )(
ABA
ABAABA
ABAABA
Neutral and charged B decay amplitudes:
0000 )()( ABAABA ,
Construct an SU(2) pentagon relationship to solve for :
Lipkin, Nir, Quinn, Snyder, PRD 44, 1454,1991
Even in the absence of penguins there’s an eightfold ambiguity on
2
effˆ1 sin 2S S C C
*ˆ arg A A
Analysis is complicated by penguins (eff) and the non-CP eigenstates )ˆ(
No model independent constraints yet on from B→ The next step is a full Dalitz analysis. (Quinn-Snyder, PRD 48, 2139, 1993)
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Prospects of from B→Both tree and penguin amplitudes contribute.
If no penguins:
)2sin(
0
S
C
With penguin contributions:
)2sin(1
)sin(
2effCS
C
.
0
.
000
2
)(
)()(sin
Long
Long
BBR
BBR
Using the Grossman-Quinn bound to limit =|-eff|
B0→ branching ratio is small compared to B+→ !
61.64.6
0
672.060.0
000
10)4.26()(
10)12.063.0()(
BBR
BBR
)%68(9.12
)%90(7.14
CL
CL
eff
eff
Decay is penguin dominated.
Penguin
Tree
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The B→ decay B0 + - is a VV-decay The decay can proceed through 3 partial waves:
S (L=0, CP even), P (L=1, CP odd), D( L=2, CP even) 3 helicity amplitudes:
=0 → longitudinal polarization. Pure CP even eigenstate. =±1→ transverse polarization. Mix of CP even and odd eigenstates.
The decay B0 + - has been observed at BaBar and its BR and polarization measured: (PRD 69, 031102 (2004) and hep-ex/0404029, submitted to PRL)
B0 + - is an excellent candidate for measuring
§ Longitudinally saturated
§ Relatively large BR
§ Small penguin pollution
§ Two charged tracks in the decay for vertexing
03.003.099.010)5430( 6 longfBR ,
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Analysis Strategy
In a simultaneous fit we measure: signal yield, polarization, Clong and Slong..Use a Maximum Likelihood fit to model: True-signal, Misreconstructed
signal (42% long., 15% trans.), Continuum and 17 B-background modes.
B-background: 209 decay modes simulated. Dominant modes:
,
, , 0
BB
aBaBcharmB0
11,
Simple assumptions
§ We neglect interference with other decays to final states (includes non-resonant contributions).
§ I=1 decay amplitudes are also neglected. I=1 absent due to Bose statistics but reintroduced by the finite (Falk, Ligeti, Nir, Quinn, Phys. Rev. D69:011502,2004)
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B→Signal Selection
Also use the -mass and -decay angle (helicity) to distinguish signal from background.
B-decay: isotropic Continuum qq: jet-like
Combine event shape variables into a Neural Network.
Events with clean tags.
2*2beamES
*BpEm B-mass: *
beam* EEE B Missing energy:
Full likelihood Background
Data
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Results:)(14.0)(27.017.0
)(14.0)(42.042.0
syststatC
syststatS
long
long
Babar result from 81fb-1 of data (taken between 1999-2001)
Submitted to PRL
hep-ex/0404029
Recent preliminary Babar result from 113fb-1 of data (presented at Moriond EW):
penguinsyststat 1341096
)(14.0)(24.023.0
)(11.0)(33.019.0
syststatC
syststatS
long
long
0B
0B
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Global CKM FitsMore plots at: http://ckmfitter.in2p3.fr
Can’t exclude a large region with .Includes the Belle B→result.
The B→system provides the most stringent constraint on !
Other B→used in the SU(2) analysis.
(assumed) 0.1)(
6.0)(
96.0)(
4.26)(
0
8.06.0
000
05.007.0
0
1.64.6
0
Bf
BBR
Bf
BBR
L
L
Includes Belle
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Summary
No significant constraint on from B→ Non optimal B0→BR (large penguins).
B→ quasi-2-body analysis performed but no model-independent constraints on Non-CP eigenstate and penguins not under control.
B→provides the most stringent constraint on . This analysis has been carried out at BaBar, and the result is (with some simple assumptions):
penguinsyststat 1341096