Search for new physics from
+ −
Bs → f (→ KK )l l
'
2
decays
Cai-Dian Lü （吕才典）
IHEP - 中国科学院高能物理研究所
Based on collaboration with R.H.
Li (李润辉), and W. Wang(王伟),
arXiv: 1012.2129, PRD83, 034034 (2011)
2011/4/5
2
outline
 Introduction

 Angular distribution
 BR, FBA, fL.
in SM
' + −
2
( Bs → f l l )
 Two New Physics scenarios
 Brief introduction
 Parameters obtained by fitting
 Effect on the SM results
 Summary
2011/4/5
3
Flavor changing Electroweak
penguin operators
s
b
t
γ,Z
No tree level flavor changing
neutral current in SM
lCD Lu
l+
4
With QCD corrections from the
u
four quark operators b
GF
=
VCKM ∑ Ci Oi
2
i
H eff
O1 = uγ µ Lu ⋅ sγ µ Lb
µ
O3 = sγ Lb ⋅ ∑ qγ µ Lq
q
µ
O5 = sγ Lb ⋅ ∑ qγ µ Rq
q
CD Lu
s
u
O2 = sγ µ Lu ⋅ uγ µ Lb
O4 = sα γ µ Lbβ ⋅ ∑ q β γ µ Lqα
q
O6 = sα γ µ Lbβ ⋅ ∑ q β γ µ Rqα
q
5
Introduction
 Unlike b  s γ or B  K* γ, which have
only limited physical observables
 b  s l+l-, and especially B K* l+l-, with
a number of observables accessible
(exp. also easier), provides a wealth of
information of weak interactions,
ranging from the forward-backward
asymmetries, isospin asymmetries, and
polarization fractions
2011/4/5
6
About K2*(1430) and f2’(1525)
Γ=
100MeV
 K π
2011/4/5
,
73 MeV
,
 K K
7
* + −
2
' + −
2
B → K l l ( Bs → f l l )
 5 polarization states: Jz= -2, -1, 0, 1, 2
 3 contribute to
, Jz=-1, 0, 1,
because of angular momentum
conservation
 Similar to K* mesons.
formulism can be got by some
substitution in
formulism
in pQCD approach.
2011/4/5
8
Form factors needed for the
exclusive decays
 Definition similar to the BK* case
Non-perturbative variables, difficult to
calculate in QCD
2011/4/5
9
Form factors calculated in pQCD to
leading order of 1/mb
2011/4/5
W. Wang, PRD83,014008
10
Branching ratios are proportional to form
factors, have large uncertainties, but
Angular distribution
is not
Partial decay width
is decomposed into 11 terms
2011/4/5
11
Angular distribution

 Up to one-loop matrix element and resonances taken out,
only
contributes an imaginary part.
Without higher order QCD corrections
They could be chosen as the window to observe those
effects that can change the behavior of the Wilson
coefficients, such as NP effects.
2011/4/5
12
BRs, fL
With the recent pQCD results for
form factors
Branching ratios:
Longitudinal Polarization
fractions:
%
2011/4/5
13
Estimate BRs from exp.
 Experimentally, we have
0
* + −
B( B → K l l ) = (1.09 ± 0.12) × 10
−6
*
*
R
=
B
(
K
)
/
B
(
K
) is the same for
 Assume
2
radiative and semi-leptonic decays, we have
Compare with KC Yang, PRD79:114008,2009
2011/4/5
14
 The forward backward asymmetry varies
from positive to negative as q2 grows up
 The 0-cross point is
sensitive to new
physics
2011/4/5
15
Forward and Backward Asymmetry
The zero-crossing point
the equation
2011/4/5
of FBAs is determined by
Smaller uncertainty
16
Similarly for Bsf2’ l+l-
2011/4/5
17
NP scenario: Vector-like quark model (VQM)
Expanding SM including a SU(2)L singlet down type
quark, Yukawa sector of SM is modified to
This modification brings FCNC for the mass
eigenstates at tree level.
The interaction for b-s-Z in VQM is
free parameter
with which the effective Hamiltonian for
is given as
2011/4/5
18
NP scenario: Vector-like quark model (VQM)
The VQM effects can be absorbed into the
Wilson coefficients C9 and C10
Lepton section in VQM
is the same as in SM.
2011/4/5
19
NP scenario: Family non-universal Z’ model
Expand SM by simply including an additional U(1)’
symmetry. The current is
which couples to a family non-universal Z’ boson.
After rotating to the mass eigen basis, FCNC appears
at tree level in both LH and RH section.
Interaction for b-s-Z’ is given as
The effective Hamiltonian for
2011/4/5
is given as
20
NP scenario: Family non-universal Z’ model
Different from VQM, the couplings in both the
quark and lepton section are free parameters.
Too many free parameters. So we set
in our analysis to reduce freedoms.
Z’ also only affects C9 and C10 phenomenally:
2011/4/5
21
Constrain the model parameters by exp.
Data used for fitting
Heavy Flavor Averaging Group, arXiv:1010.1589;
Particle Data Group, J. Phys. G 37,075021.
Definition of
2011/4/5
22
Constrain the VQM parameters
Phase less constrained
Constrains on the Wilson coefficients
with
2011/4/5
23
Constrain the Z’ model parameters
Assume
Both
as real
and
are complex numbers.
with
has little effect on
with
Combining the above results
2011/4/5
24
New Physics effects in observables
In the NP effects, we choose
and
as the reference points.
Br (10-7) may be
enhanced,
however, large
uncertainties
In this parameter space,
recent measurement.
2011/4/5
SM
C9
C10
is consistent with the
D0 collaboration, PLB 693,539.
25
New Physics effects in observable
Zerocrossing
point of
AFB may
be
changed
significan
tly in new
physics
model.
2011/4/5
SM
C9
C10
26
Polarization fraction fL
some
changes
of
Polarizati
on
fraction fL
in new
physics
model.
2011/4/5
SM
C9
C10
27
Summary

is investigated in SM.
expected to be observed in future Exp.
FBA, polarization fractions, etc, are investigated, with
small uncertainties.
 Two NP scenarios (VQM, Z’ model) are investigated.
Parameter space constrained with data of
and
.
Zero-crossing point of FBA can be changed
dramatically, which are sensitive to NP effects
2011/4/5
28
Thank you
2011/4/5
29