measurements related to the ckm angle α from...
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Measurements related to the CKM angle α from BABARLYDIA ROOSLPNHE-Paris
Rencontres de MoriondEW04
B → ππB → ρπB → ρρ
will cover:
α from B → hh (h=π,ρ)
Tree diagram:Tree diagram:
ubV ∗∗∗∗
d
Penguin diagram:Penguin diagram:
ααα
αλ λ
−
+
−= = =
−22
1
1eff
i
iihh i
P eq A Te ePp A eT
α + β + γ = π
β−= 2iqe
p
,i i
i i
A e T e P
A e T e P
γ β
γ β
+ −
− +
= +
= +
0 0
0 0
( ( ) ) ( ( ) )( )
( ( ) ) ( ( ) )
sin( ) cos( )
CP
hh hh
N B t h h N B t h hA t
N B t h h N B t h h
S mt C mt
+ − + −
+ − + −
→ − →=→ + →
= ∆ − ∆ 2
2
1
1hh
hh
hh
Cλλ
−=
+2
2 Im
1hh
hh
hh
Sλ
λ=
+
π ρ,+ ++ ++ ++ +
tdV
d ++++ππ ρ,+ ++ ++ ++ +
π ρ,− −− −− −− −
π ρ,− −− −− −− −
In the usual phase convention:
g
3
B0
B0
hhhh+h-
A+-
A+-
Time-dependent CP asymmetriesin B → ρπ
ππππ +
ρρρρ -
d
S: CPV in decay/mixing interferencesC: direct CPV
Usual CP parameters
h++++
( ) ( ) ( ) ( )( )+ −Γ → ∝ ± − ± ∆ ∆ ∆ + ± ∆ ∆ ∆0 1 1 sin( ) cos( )CPB h h A S S m t C C m t( ) ( ) ( ) ( )( )ρ π±Γ → ∝ ± − ± ∆ ∆ ∆ + ± ∆ ∆ ∆m0 1 1 sin( ) cos( )CPB A S S m t C C m t( ) ( ) ( ) ( )( )ρ π±Γ → ∝ ± − ± ∆ ∆ ∆ + ± ∆ ∆ ∆m0 1 1 sin( ) cos( )CPB A S S m t C C m t
∆S: from strong phase δ=arg(A-+/A+-)∆C: W→ρρρρ vs. spectactor→ρρρρ asymmetry
ACP: ρρρρ++++ππππ−−−− vs. ρρρρ−−−−ππππ++++ asymmetry Direct CPV
No CPVDILUTION factors
h−−−−
π++++
d
B0
B0
ρρρρ+ππππ-A+-
A-+
ρρρρ-ππππ+
A-+
A+-≠≠≠≠
ρ++++
ρ−−−−π−−−−
Extraction of α: Isospin Analysis
0 000
2 2
A A A AA
+− −+ + ++− −+ + ++− −+ + ++− −+ + ++ ++ ++ ++ ++ =+ =+ =+ =
B → hh': 2 pentagonal relations between amplitudes from strong isospin symmetry [LNQS]:
0 000
2 2
A A A AA
+− −+ + ++− −+ + ++− −+ + ++− −+ + ++ ++ ++ ++ ++ =+ =+ =+ =
12 unknowns and 13 observables : in principle, solvable
LNQS: Lipkin, Nir, Quinn, Snyder, PRD44, 2193 (1991)
00 0 0 00 2
2 0 2
1 2 / ( 2 2 )cos(2 2 )
1 4 1eff
hh hh
B B B B B
C B B Cα α
+ +− +
+− +
− − +− ≥ +− −
If C00 is not measured, one has the bound [GLSS]:
GL: Gronau, London, Phys.Rev.LettD65:3381,1990 GLSS: G,L,Sinha,Sinha, Phys.Lett.B514:315- 320,2001
6 unknowns and 7 observables (or 6: no measure ofS00 in B → ππ)
B → hh: 2 triangular relations [GL]
00 0/ 2A A A+− ++− ++− ++− ++ =+ =+ =+ = 00 0/ 2A A A+− ++− ++− ++− ++ =+ =+ =+ =+ += +0 0 ( )EWA A O Pwith
Common experimental aspectsB candidate mass and energycontinuum background
e- e+ e- e+
§Kinematical variables: cos(PB,z), cos(TB,z)
Combined using Fisher or NN
( )θ∉ ∉
= =∑ ∑2
0 2 , L , L cosBi i T i
i B i B
p p
§Topological variables in CMS, e.g.
θ , BT i
BB qq
Moriond EW04 LYDIA ROOS LPNHE-Paris 6
more rejection of B background Particle Identification
Common experimental aspects
All channels but π+π− suffer fromB background. Useful variables are:§∆E§ρ mass, helicity angle
B0 → ρ+ π−
Unbinned likelihood fitLikelihood function includes time dependence
Moriond EW04 LYDIA ROOS LPNHE-Paris 7
B0 → h+ h- (h=π,K)
π ππ
+ −
+ −
+ −
→ ± ±→ ± ±
→
0 -6
0 -6
0 -6
( ) = (4.7 0.6 0.2) 10
( ) = (17.9 0.9 0.6) 10
( ) < 0.6 10 (90% CL)
Br B
Br B K
Br B K K
π
ππ
ππ
= − ± ±= − ± ±
± ±
0.40 0.22 0.03
0.19 0.19 0.05
= -0.107 0.041 0.013KCP
S
C
A
81 fb-1
113 fb-10B
0B
all
bkg
PRL 89 281802 (2002); PRELIMINARY LP03
Moriond EW04 LYDIA ROOS LPNHE-Paris 8
B± → π±π0 and B0 → π0π0
Yield: 46 ± 13 ± 3
Significance: 4.2σ
113 fb-181 fb-1
0 1.0 60.9
0 1.2 61.1
BR( ) (5.5 0.6)10
BR( ) (12.8 1.0)10K
π ππ
± + −−
± + −−
= ±
= ±0 0 6BR( ) (2.1 0.6 0.3)10π π −= ± ±
PRL 91 021801 (2003); PRL 91 241801 (2003)
0π π ±
0 0π π
B0 → ρ+ π−
ρπ
ρπ
ρπ
ρπ
ρπ
= − ± ±
= ± ±
∆ = ± ±
∆ = ± ±
± ±
0.13 0.18 0.04
0.35 0.13 0.05
0.33 0.18 0.03
0.20 0.13 0.05
= -0.114 0.062 0.027CP
S
C
S
C
A
113 fb-1
0B
0B
PRL 91 201802 (2003)
Significance for direct CPV: 2.5σ
• Isospin analysis needs ~10 ab-1 to disentangle multiple solutions;• More promising: perform full Dalitz plot analysis;• Powerful but model-dependent constraint from QCD FA [BN]: σ(α) ∼9°
Quasi two-body approach:
BN: Beneke, Neubert, Nucl. Phys. B675(2003) 333
B0 → ρ+ ρ−
Three helicity states:longitudinal (CP+) and tranverse (CP+/-)
Mis-reconstructed signal events:39% (longitudinal), 16% (transverse)
B background in signal region:§~350 B0, B± → charm;§ charmless B modes (~65 events), mainly:
ρ+π0, a1ρ, a1π, ρ+ρ0,(higher K res)π
= − ± ±
= − ± ±
0.42 0.42 0.14
0.17 0.27 0.14long stat syst
long stat syst
S
C
ρ ρ −
+−
+ − = ± ±
= ±
6
0.040.03 ( )
( ) (30 4 5 )10
0.99 0.03
stat syst
long (stat) syst
BR
f
81 fb-1
Submitted to PRL
θcos H
New result on B0 → ρ+ ρ−
113 fb-1
0B
0B
= − ± ±
= − ± ±
0.19 0.33 0.11
0.23 0.24 0.14long stat syst
long stat syst
S
C
§Main systematics: CPV in B bkg §Detailed study of B background: 209 B decay modes simulated
§ Isospin analysis: interference, NR contributions, I=1 amplitudesneglected
PRELIMINARY
α = ± ± ± o(96 10 4 13 )stat syst peng
More on α from B→ππ,ρρ
Other ingredients in ρρ isospin analysis: (BABAR & Belle),ρ ρ
ρ ρ
−
+−
+ = ±+ =
6
0.0490.065
0
0
( ) (26.4 6.4)10
( ) 0.962long
BR
f
ρ ρ
ρ ρ
+ −−= ±
=
0.72 60.60
0 0
0 0
( ) (0.62 0.12)10
( ) 1.0long
BR
f(BABAR & Belle),Slide from the CKMfitter group incorporating BABAR CP asymmetries and other BABAR & Belle results
(BABAR)(assumed)
BABAR: PRL 91 171802; Belle: PRL 91 221801
(no ππ,ρρ)
Moriond EW04 LYDIA ROOS LPNHE-Paris 13
ConclusionB → ππ: evidence/observation of all decay modes.
No significant constraint on α with present data.B → ρπ: quasi 2-body asymmetries measured.
Next step is the full Dalitz plot analysis.B0 → ρ+ρ− CP asymmetries
§ Constraint on α in perfect agreement with the Standard Fit;
§ low penguin pollution;§ if BR(ρ0ρ0) not too small, measure not only Cρ0ρ0 but also Sρ0ρ0
= − ± ±
= − ± ±
0.19 0.33 0.11
0.23 0.24 0.14long stat syst
long stat syst
S
C
= − ± ±
= − ± ±
0.42 0.42 0.14
0.17 0.27 0.14long stat syst
long stat syst
S
C
81fb-1 submitted 113 fb-1 preliminary
α = ± ± ± o(96 10 4 13 )stat syst peng
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