Download R-parity Violating SUSY

B
P
P ,V V decays and R parity Violating SUSY
Rumin Wang
Work done in collaboration with G. R.. Lu & Y. D. Yang
Huazhong Normal University
Henan Normal University
November 15, 2005, Beijing
Outline
 Motivation
Theoretical input
 Polarization anomaly in B VV decays
 Puzzles in B PP decays
Summary
2
Motivation for study
 To solve the polarization anomaly
in B VV decays
 To solve the puzzles
in B   , K deacys
3
B  VV
Decay amplitude of B to VV in helicity basis:
A  f H i  A0  A  A
Decay amplitudes in transversity basis:
A0  A0
A ,||  ( A  A ) / 2
Longitudinal polarization fraction:
| A0 |2
| A0 |2
( ~0.9 in SM )
fL 

2
2
2
2
2
2
| A0 |  | A |  | A | | A0 |  | A |  | A|| |
4
B  VV
Surprise
 Tree + penguin :
B      ,  0   and K *
f L ~ 0.9
 Pure penguin (Sensitive to NP):
B  K * , K *0 and K *0
??
f L ~ 0.5
5
Previous study
B  VV
 Kagan show increasing nonfactorizable contribution of
annihilation diagram to solve anomaly by QCDF(hep-ph/0407076).
But H.n. Li & Mishima: annihilation contribution is not
sufficient to lower fL down to 0.5 by PQCD (PRD 71,054025).
 Polarization anomaly might be due to large charming penguin
contributions and final-state-interactions (FSI) by Colangelo et
al. & Ladisa et al. (PLB 597,291; PRD 70,115014) .
However, H. Y. Cheng et al. have found the FSI effects not
able to fully account for this anomaly ( PRD 71, 014030 ).
 We try to solve this anomaly including RPV SUSY effects.
6
Motivation for study
 To solve the polarization anomaly
in B VV decays
 To solve the puzzles
in B   , K decays
7
?
 puzzle

Br(Bd    ) exp.  Br(Bd    ) SM
0
0
0
1.5x10^(-6)
 Br(B
   ) exp.

d

10^(-7)
1
 Br(B d      ) SM
2
4.6x10^(-6)

8.3x10^(-6)
ACP ( Bd    ) exp . 

dir
0.319
0

 
(
B


 ) SM
ACP d
dir
-0.057
8
?
K puzzle
A
dir
CP
( Bd   K )  ACP ( B   K ) in SM

But -0.120

dir

0
0.063

in Exp.
0
0
Br
(
B


K
)exp. is larger than the SM prediction

11.4x10^(-6)
6.0x10^(-6)
9
B  PP
Previous study
 Buras et al. point out B to pi pi can be nicely accommodated in
the SM through nonfactorizable hadronic interference effects,
whereas B to pi K system may indicate NP in the electroweak
penguin sector (PRL 92,101804; NPB 697,133).
 H. N. Li et al. & Y. D. Yang et al. study the next to leading order
corrections by PQCD & QCDF, respectively. These higher order
corrections may be important for Br(B to pi K), but the can not
explain other experimental data(hep-ph/0508041;PRD72,074007).
NP
 We try to calculate RPV SUSY effects .
10
Outline
 Motivation
Theoretical input
 Polarization in B VV decays
 Puzzles in B PP decays
Summary
11
Theoretical input
 The effective Hamiltonian in SM
 R-parity Violating SUSY
 QCD Factorization
12
The effective Hamiltonian in SM
The effective weak Hamiltonian for B decays:

GF 10 CKM
H eff 
i Ci (  )Qi (  )  C7 (  )Q7 (  )  C8 g (  )Q8 g (  )

2 i 1
SM
Qi are local four-quark operators
The decay amplitude in SM:
A ( B  M 1 M 2 )  M 1 M 2 H eff B
SM
SM
~ M 1 M 2 Qi (  ) B
13

R-parity Violating SUSY
R - parity : R p  (1)
3B L2 S
S is the particle spin
B is the baryon number
L is the lepton number
R-parity violating superpotential:
c
c
c
c
c
1
1
ˆ
W R   i Lˆ i Hˆ u  2 [ij]k Lˆ i Lˆ j Eˆ k   ijk Lˆ i Q j Dˆ k  2  i[ jk ]Uˆ i Dˆ j Dˆ k
L  1
B  1
: Yukawa couplings
i, j,k : generation indices
C : charge conjugate field
14
The four fermion effective Hamiltonians due to the
exchanging of the sleptons:
1  5
1  5
, PR 
2
2
 s (m ~f )
2

,  0  11  n f
 s (mb )
3
PL 
i
The effective Hamiltonians due to the exchanging of
the squarks:
15
R-parity Violating decay amplitude:
A ( B  M 1M 2 )
R
 M 1M 2 H B
R
~ M 1M 2 Q i ( ) B
R
16
The total decay amplitude:
A ( B  M 1 M 2 )  ASM ( B  M 1 M 2 )  AR ( B  M 1 M 2 )
~ M 1 M 2 Qi B
M 1 M 2 Qi B  ?
Naïve factorization, Generalized factorization,
QCD factorization, Perturbative QCD,
Light-cone QCD sum rules, Lattice QCD,
Soft-collinear effective theory, etc.
17
QCD Factorization
BBNS approach:
PRL 83:1914-1917,1999
NPB 591:313-418, 2000
Naïve Factorization:
M 1 M 2 (q2 q3 ) (V  A) (b q1 ) (V  A) B  M 2 (q2 q3 ) (V  A) 0
fM
M 1 (b q1 ) (V  A) B
F
2
B M1
QCD Factorization:
M 1 M 2 (q2 q3 ) (V  A ) (b q1 ) (V  A ) B
 M 2 (q2 q3 ) (V  A ) 0
M 1 (b q1 ) (V  A ) B
1   r 
n
n
s
 ( QCD / mb )
18
Outline
 Motivation
Theoretical input
 Polarization in B VV decays
 Puzzles in B PP decays
Summary
19
Polarization in B VV decays
Based on paper: Phys.Rev.D72:015009(2005)
20
Longitudinal polarization
RPV SUSY ?
B  VV
Polarization
Anomaly !!
21
RPV effects in B  K *
| i23i22* | [1.5  103~Li2 ,2.1 103~Li2 ]
previous bound :  2.3  103

~  

f 
 100 Gev 
2
m ~f
2
22
RPV effects in B  ρK *
23
Bounds by B  K
*
24
RPV effects in Β  ρρ
25
The polarization anomaly could be
solved by RPV effects.
26
Outline
 Motivation
Theoretical input
 Polarization in B VV decays
 Puzzles in B PP decays
Summary
27
Puzzle in B  K decays
Based on paper: hep-ph/0509273
28
B  PP
Branching ratios
Puzzle !!
29
B  PP
ACPdir 
Direct CP asymmetries
Br ( B  f )  Br ( B  f )
Br ( B  f )  Br ( B  f )
(B is Bd0 or B-u )
RPVPuzzle
SUSY
!! ?
30
The allowed parameter spaces constrained by B  
31
Bounds by B  
32
The allowed parameter spaces constrained by B  K
33
Bounds by B  K
34
B   , K puzzles could be
solved by RPV effects
35
Outline
 Motivation
Theoretical input
 Polarization in B VV decays
 Puzzles in B PP decays
Summary
36
Summary
 Employed QCDF to study RPV SUSY effects in following modes:
o Polarization in B to VV .
o Branching ratios & direct CP asymmetry in B to pi pi, pi K.
 RPV couplings can give a possible solution to the puzzles.
Obtain the ranges of RPV couplings, but these are very narrow.
 The allowed spaces constrained by B to PP are consistent with
these by B to VV decays.
 An explanation is need:
o SM is in no way ruled out.
o Existence of New Physics.
o Many more measurement are in progress.
37
38
39
SM particles & Higgs bosons : R P  1
Squarks, sleptons & higgsinos : R P  1
[ ij ] k : ijk   jik
i[jk ] : ijk  ikj
1
for Q i
3
1
B   for u i , d i
3
B  0 for other
B
L  1 for L i
L  -1 for ei
L0
for other
40
R-parity Violating decay:
~
Not d , for i[jk ]
is antisymmet ric in
e 

p


0
" j"
and
" k"
e K 0
  0

41
Ratios of branching ratios
B
 1.069
B
u
d
42
Branching ratios
B  VV
43