New EvtGen-compatible model for rare semileptonic
B-mesons decays
Nikolai Nikitin
(SINP, Lomonosov Moscow State University)
Daria Savrina
(ITEP & SINP, Lomonosov MSU)
Nikolai Nikitin, Gauss meeting
CERN, April 03 2009
Outline
1. Introduction
2. Kinematics
3. New model of rare decays for EvtGen
4. Class structure
5. Some distributions
6. Future plans
7. Conclusions
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Nikolai Nikitin, Gauss meeting
CERN, April 03 2009
Introduction
The goal of this talk is to present the new EvtGen decay model
BTOSLLMS for rare semileptonic B-mesons decays. This model is based
on a complete theoretical calculations of these processes in the SM
and allows us to change easily any of the important input parameters.
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Nikolai Nikitin, Gauss meeting
CERN, April 03 2009
Kinematics
B(p1 )
H ef f (b → q)
+ (k1 )
− (k2 )
P (p2 ) or V (p2 , ε)
p1 = k1 + k2 + p2 , = q + p2 ,
p21 = M12 ,
p22 = M22 ,
k12 = k22 = m2 .
Kinematics of three-body dacays can be described in terms of two
independent variables. The first independent variable:
4 m2 ≤ (s ≡ q 2 ) ≤ (M1 − M2 )2 .
In the rest frame of the leptonic pair we define the second independent
variable: the angle θ between − and final P or V meson.
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Nikolai Nikitin, Gauss meeting
CERN, April 03 2009
EvtGen model for rare
semileptonic B-mesons decays
We propose new EvtGen model BTOSLLMS for rare semileptonic Bmesons decays. In this model:
• 14 rare semileptonic B-decays channels are included;
• the form factors are calculated using the dispersion relation of the
QM according to the parametrizations from D.Melikhov, B.Stech,
PRD62, 014006, 2000.;
• the μ-dependence of the Wilson coefficients Ci and the contribution
from ρ, ω , J/ψ, ψ etc. vector resonances in SM are included;
• the “weak annihilation” contribution is included;
• the complex CKM-matrix elements are included.
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Nikolai Nikitin, Gauss meeting
CERN, April 03 2009
The list of supported channels
B + → K + + − ;
Bd0 → K 0 + − ; Bd0 → KS + − ;
B + → π + + − ;
Bd0 → π 0 + − ;
Bd0 → η+ − ;
Bd0 → η + − ;
Bs0 → η+ − ;
Bs0 → η + − ;
B + → K ∗+ + − ;
Bd0 → (K ∗0 → K + π − ) + − ;
B + → ρ+ + − ;
Bd0 → (ρ0 → π + π − ) + − ;
+ −
+ −
Bs0 → (φ
→
K
K
)
;
Bs0 → K̄ ∗0 → K − π + + − .
Bd0 → KL + − ;
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Nikolai Nikitin, Gauss meeting
CERN, April 03 2009
The files, containing
the BTOSLLMS model
The BTOSLLMS model is implemented in the following 14 files:
.../EvtGenModels/EvtbTosllAmpNew.hh
.../EvtGenModels/EvtbTosllScalarAmpNew.hh
.../EvtGenModels/EvtbTosllVectorAmpNew.hh
.../EvtGenModels/EvtbTosllWilsCoeffNLO.hh
.../EvtGenModels/EvtbTosllFFNew.hh
.../EvtGenModels/EvtbTosllMS.hh
.../EvtGenModels/EvtbTosllMSFF.hh
.../src/EvtbTosllScalarAmpNew.cpp
.../src/EvtbTosllVectorAmpNew.cpp
.../src/EvtbTosllWilsCoeffNLO.cpp
.../src/EvtbTosllMS.cpp
.../src/EvtbTosllMSFF.cpp
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Nikolai Nikitin, Gauss meeting
CERN, April 03 2009
The list of the model input
parameters in dec-files
There are 8 BTOSLLMS model parameters to be specified in the dec-files:
• mu is the scale parameter μ (5 GeV by default);
• Nf is the number of “effective” quark flavours (5 by default);
• res swch is the parameter for switching on/off resonant contribution (off ≡ 0 by default);
• ias
ias
ias
ias
defines a choice of the αs (MZ ):
= 0, lower limit of αs (MZ ) value;
= 1 (default), then the mean value of αs (MZ ) is chosen;
= 2, upper limit of αs (MZ ) value.
• A, lambda, barrho and bareta, are the CKM matrix parameters
corresponding to the Wolfenstein parametrisation: A, λ, ρ̄ and η̄.
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Nikolai Nikitin, Gauss meeting
CERN, April 03 2009
Class structure of
the BTOSLLMZS model
The model includes the following basic classes:
• EvtbTosllWilsCoeffNLO class is designed to calculate the Wilson
coefficients of the SM in the NLO approximation with or without
concidering the contribution of the vector J/ψ- and ψ -resonances.
• EvtbTosllFFNew class is intended to calculate the hadronic form
factors for B̄ → P̄ or V̄ transitions .
• EvtbTosllAmpNew class is requiered to calculate the amplitudes of
the rare semileptonic B-decays. It includes several derivative
classes: EvtbTosllScalarAmpNew to calculate the B̄ (B) → P̄ (P ) + −
decays amplitudes and EvtbTosllVectorAmpNew class to calculate
the B̄ (B) → V̄ (V ) + − decays amplitudes.
• EvtbTosllMS classs implements explicitly the BTOSLLMS model. It
is a derivative class of the EvtDecayAmp.
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Nikolai Nikitin, Gauss meeting
CERN, April 03 2009
Example of the q 2 and cos θ distributions for B̄ → P̄
1 dN
N dq 2
0.04
0.035
0.04
0.035
0.03
0.03
0.025
0.025
0.02
0.02
0.015
0.015
0.01
0.01
0.005
0.005
0
0
5
10
15
20
25
q 2 (GeV2 )
0
−1
−0.5
0
0.5
1
cos θ
The normalized q 2 and cos θ distributions for BTOSLLMS (lightblue) and BTOSLLBALL (red) models in the decay B + → K + μ+ μ− .
Figure 1:
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Nikolai Nikitin, Gauss meeting
CERN, April 03 2009
Example of the q 2 -distribution for B(B̄) → V (V̄ )
1 dN
N dq 2
0.1
0.1
0.08
0.08
0.06
0.06
0.04
0.04
0.02
0.02
0
0
5
10
15
20
2
25
2
q (GeV )
0
0
5
10
15
20
25
2
q (GeV2 )
The normalized q 2 distributions for BTOSLLMS (light-blue) and
BTOSLLBALL (red) models in the decay B̄d0 → K̄ ∗0 μ+ μ− (left). And the
same distribution for BTOSLLMS (light-blue) and BTOSLLALI (red) models
in the decay B̄s0 → φμ+ μ− (right).
Figure 2:
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Nikolai Nikitin, Gauss meeting
CERN, April 03 2009
Example of the cos θ-distribution for B̄(B) → V̄ (V )
1 dN
N d cos θ
0.04
0.035
0.035
0.03
0.03
0.025
0.025
0.02
0.02
0.015
0.015
0.01
0.01
0.005
0.005
0
−1
−0.5
0
0.5
1
cos θ
0
−1
−0.5
0
0.5
1
cos θ
The normalized cos θ distributions for BTOSLLMS (light-blue) and
BTOSLLBALL (red) models in the decay B̄d0 → K̄ ∗0 μ+ μ− (left) and in the
decay Bd0 → K ∗0 μ+ μ− (right).
Figure 3:
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Nikolai Nikitin, Gauss meeting
CERN, April 03 2009
Example of the cos θ-distribution for B̄ → V̄
In B2SLLBALL model code there are the following lines:
EvtVector4C E1=T1.cont1(eps);
EvtVector4C E2=T2.cont1(eps);
But in B2SLLMS model code these lines are:
EvtVector4C E1=M1*T1.cont2(epsV);
EvtVector4C E2=M1*T2.cont2(epsV);
The convolution of tensor μνp1p2 with polarization vector of the vector
meson should be performed by the ν index. This index is second in
this tensor, that’s why cont2() should be used, not cont1(). The
tensor μνp1p2 is fully antisymmetric by indices μ and ν, that’s why the
sign is changed when we convolute it by the another index.
Using cont1() instead of cont2() results in swap between amplitudes
of particles and antiparticles – and that leads to mirroring of cos θ
distribution.
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Nikolai Nikitin, Gauss meeting
CERN, April 03 2009
Future plans
a) To include in the BTOSLLMS model the Wilson coefficients in the
NNLO approach.
b) To prepare several form factors sets (what sets?).
c) Now we have the model for Bd,s → γ + − in the test mode.
d) The generator for τ → 3 decays is Under construction.
e) We plane to prepare the generators for rare four-leptonic decays.
f ) If it is necessary, it is possible to prepare the models for Λb →
Λ μ+ μ− and for the B → P1 P2 + − decays.
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Nikolai Nikitin, Gauss meeting
CERN, April 03 2009
Conclusion
a) The description of the new BTOSLLMS model is presented.
b) This model allows use to generate events for 14 different channels
for a few semileptonic B-meson decays within the EvtGen package.
c) The model uses the Wilson coefficients in the NLO approximation
and includes the contribution of the vector resonances. The
hadron transitions formfactors are taken from the dispersion quark
model.
d) The angular distributions in the rare B-decays are the most favorite
test for the NP. First results for B(B̄) → V (V̄ )+ − decay modelled
in BTOSLLMS were presented. The comparison between BTOSLLMS
and BTOSLLBALL models was performed.
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Nikolai Nikitin, Gauss meeting
CERN, April 03 2009
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