Transcript B→K_1 l^+ l^-Decays in a Family Non

Ying Li
YanTai University
Outline
• Introduction: motivation & history
• Remarks on 𝐾1 (1270) and 𝐾1 (1400)
• Formulae
• Results and Discussion
• Summary
Introduction
• FCNC process 𝑏 → 𝑠𝑙 + 𝑙 − forbidden in the standard model (SM) at
the tree level, are the most sensitive and stringiest test for the
SM. Many processes, such as B->K*𝑙 + 𝑙 − , have been explored by
many groups in SM and extensions beyond of it.
•
Q-S Yan, et.al , PRD’98
•
W-J Li, et.al, EPJC’04
•
G-H Zhu, et.al EPJC, 06
•
T Huang, et.al , PRD’10
•
Y-D Yang, et.al , JHEP’09
•
K-C Yang, et.al , PRD’08
•
Y-M Wang, et.al , PRD’08
•
R-M Wang, et.al, PRD’08
•
R-H Li, et.al, PRD’09
•
Q Chang, et.al , NPB’11
•
C-W Chiang, et.al, CPC,11
• Similar to B->K*𝑙 + 𝑙 − , once 𝐵 → 𝐾1 𝑙 + 𝑙 − could be measured
well, they will offer another useful test of the SM and of
its extensions.
• Generally, in order to find the new physics signals, the
relevant branching ratios, the di-lepton invariant mass
distributions, the forward-backward asymmetries and
lepton polarization asymmetries should be calculated in
the SM and new physics models, before the possible new
particles produce directly at the collides.
• To make predictions of these exclusive decays, one
requires the additional knowledge about form factors.
• PQCD Approach
[Li, PRD,09]
• QCD Sum Rules
[Dig,PRD’10]
• Light front quark model
[Cheng, et.al, PRD’09]
• Light-cone QCD Sum Rules
[Yang, PRD’08; Huang, PRD’11]
• In some new physics models beyond of SM, Z’ could be
naturally derived in certain string constructions , E6 by
adding additional U(1)’ gauge symmetries.
• Among many Z’ models, the simplest one is the family
non-universal Z’ model. It is of interest to note that it
could lead to FCNC at tree level as well as introduce new
weak phases, which play important roles in explaining the
CP asymmetries in the current high energy experiments.
Langacker, PRD’00; Cheung, PLB’07; Chiang, JHEP’06;
Barger, PLB’04,PLB,04; JHEP’09; Chang, JHEP’08, JHEP’09;
Barger, PRD’09; Chen, arxiv:0911.3479; Li, PLB’10, EPJC’10
Chiang, arXiv:1108.3969; Li, CPC’11, ……
Remarks on 𝐾1 (1270) and 𝐾1 (1400)
K1A
K10A
a1
3P
a1
a10 , f1 , f1
K1B
K10B
b1
b1
b10 , h1 , h1
1
K1A
K10A
K1B
1P
1
K10B
 In SU(3) limit, K1A & K1B do not get mixed. However, they have admixture
due to strange and light quark mass difference
 PDG ⇒ |K|  45o
 Strong decays K1(1270), K1(1400) K,K* and their masses
⇒ K= 32,56
add: K 34, [CHY, arXiv:1110.2249]
Sign of K depends on the phase convention of states. It can be inferred
from B→ K1 decays (HYC,Chua, PRD’05)
We will use K=-34 13.
Remarks on 𝐾1 (1270) and 𝐾1 (1400)
[Yang, PRD’08]
Formulae
A. The Effective Hamiltonian for 𝑏 → 𝑠𝑙 + 𝑙 − in SM
•
The effective Hamiltonian responsible for the 𝑏 → 𝑠𝑙 + 𝑙− transitions is
given as
• The quark decay amplitude can also receive additional contributions from
the matrix element of four-quark operators, which are usually absorbed
into the effective Wilson coefficients
B. The Effective Hamiltonian for 𝑏 → 𝑠𝑙+ 𝑙 − in Z’ model
Assuming that the couplings of right-handed quark flavors with Z’
boson are diagonal and ignoring Z-Z’ mixing, the Z’ part of the effective
Hamiltonian for 𝑏 → 𝑠𝑙 + 𝑙− can be written as
• The constraint of the parameters has been done by many groups in the
past few years.
• Combining the constraints from 𝑩𝑺 − 𝑩𝑺 mixing, and 𝐁 → 𝐊𝛑, 𝛒𝐊 decays,
𝑩𝑳𝒔𝒃 have been strictly constrained by Chang et. Al.
• They also give the constraints of 𝑩𝑳𝒍𝒍 and 𝑩𝑹
𝒍𝒍 from 𝐁 → 𝑿𝒔 𝐥𝐥, 𝑲
∗
𝝁+ 𝝁− and
𝑩𝒔 → 𝝁+ 𝝁− decays.
• Recently, there have been more data from Tevatron and LHC on decay
processes mentioned above. Many of them might afford stronger upper
bounds than before, but the new parameters have not been fitted.
• In the current work, we will adopt the parameters fitted by Chang
et.al ,so as to probe contribution of new physics with the most possibility.
In order to show the maximal strength of Z’, with permitted
range in S1, we choose the extreme values
More details about fitting can be seen in Chang’s talk.
C. Formula of Observables
D. The lepton polarization asymmetry
The lepton polarization asymmetry 𝐏𝐢 (i = L;N;T) can
be obtained by calculating
Results and Discussion
Summary
• We studied the contributions of family non-universal Z’
model at the tree level in semi-leptonic B decays
involving axial-vector meson K1 in the final states.
• We found the 𝐵 → 𝐾1 (1400)𝑙+ 𝑙− is sensitive to the mixing
angle.
• The 𝐵 → 𝐾1 (1270)𝑙+ 𝑙− is not sensitive to mixing angle,
and sensitive to the new physics effect.
• The Zero position of FBA is a good probe of new physics
contribution.
• The ratio of branching ratios could be used to constrain
the mixing angle.