Rumin WangRumin Wang
Work done in collaboration with G. R.. LuG. R.. Lu & Y. D. & Y. D. YangYang
Huazhong Normal University
Henan Normal University
November 15, 2005, Beijing
SUSYViolatingparityRanddecaysVVPPB ,
2
Motivation Theoretical input Summary
decaysVVBinanomalyon Polarizati
Outline
decaysPPBinPuzzles
3
To solve the polarization anomaly
To solve the puzzles
decaysVVBin
deacysK ,Bin
Motivation for study
4
Decay amplitude of B to VV in helicity basis:
Decay amplitudes in transversity basis:
Longitudinal polarization fraction:
( ~0.9 in SM )
AAAiHfA 0
2
||
22
0
2
0
222
0
2
0
||||||
||
||||||
||
AAA
A
AAA
AfL
VVB
2/)(||, 00 AAAAA
5
Tree + penguin :
Pure penguin ((Sensitive to NPSensitive to NP)):
????
Surprise
5.0~, 0*0**LfKandKKB
9.0~, *0LfKandB
VVB
6
Previous study
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.
VVB
7
To solve the polarization anomaly
To solve the puzzles
decaysVVBin
decaysK ,Bin
Motivation for study
8
1.5x10^(-6) 10^(-7)
4.6x10^(-6) 8.3x10^(-6)
0.319 -0.057
puzzle
SM)Br(B)Br(B 00
dexp.
00
d
SM)Br(B2
1)Br(B dexp.d
SMd
dir
CPd
dir
CPBB AA )()( .exp
?
9
ButBut -0.120 0.063 in Exp.
11.4x10^(-6) 6.0x10^(-6)
puzzleK
prediction SM n thelarger tha )(exp.
00 isKBBr
SMin )()( 0 KBAKBA dir
CPd
dir
CP
?
10
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 .
PPB
11
Motivation Theoretical input Summary
decaysVVBinonPolarizati
Outline
decaysPPBinPuzzles
12
Theoretical input
The effective Hamiltonian in SM
R-parity Violating SUSY
QCD Factorization
13
The effective Hamiltonian in SM The effective Hamiltonian in SM
The effective weak Hamiltonian for B decays:
Qi are local four-quark operators
The decay amplitude in SM:
BQMM
BHMMMMBA
i
SM
eff
SM
)(~
)(
21
2121
)()()()()()( 2
H8877
10
1
SM ggiii
CKM
i
F
effQCQCQC
G
14
S is the particle spinB is the baryon numberL is the lepton number
R-parity violating superpotential:
R-parity Violating SUSY R-parity Violating SUSY
)1(23
:parity-R
SLB
pR
DDUDQLELLHLWc
k
c
j
c
ijki
c
kjiijk
c
kjikijuiiR ˆˆˆˆˆˆˆˆˆˆˆ ][][ 2
1
2
1
1B
: Yukawa couplingsi, j,k : generation indicesC : charge conjugate field
1L
15
The four fermion effective Hamiltonians due to the exchanging of the sleptons:
The effective Hamiltonians due to the exchanging of the squarks:
f
bs
fs
RL
nm
m
PP
i
3
211,
)(
)(2
1,
2
1
0
~
55
16
BQMM
BHMM
MMBA
iR
R
R
)(~
)(
21
21
21
R-parity Violating decay amplitude:
17
BQMM
MMBAMMBAMMBA
i
RSM
21
212121
~
)()()(
The total decay amplitude:
?21
BQMMi
Naïve factorization, Generalized factorization, QCD factorization, Perturbative QCD, Light-cone QCD sum rules, Lattice QCD, Soft-collinear effective theory, etc.
18
BBNS approach: PRL 83:1914-1917,1999 NPB 591:313-418, 2000 Naïve Factorization:
QCD Factorization:
)/(1)(0)(
)()(
)(11)(322
)(1)(3221
bQCD
n
snAVAV
AVAV
mrBqbMqqM
BqbqqMM
QCD FactorizationQCD Factorization
1
2
MB
MFf
BqbMqqMBqbqqMMAVAVAVAV )(11)(322)(1)(3221
)(0)()()(
19
Motivation Theoretical input Summary
decaysVVBinonPolarizati
Outline
decaysPPBinPuzzles
20
decaysVVBinonPolarizati
Based on paper: Phys.Rev.D72:015009(2005)
21
Longitudinal polarizationLongitudinal polarization
Polarization
Anomaly !!
VVB
RPV SUSY ?
22
*KB in effects RPV
32323*
2223103.2 :bound previous ]~101.2,~105.1[||
LiLiii
2
~2
100~
Gev
mff
23
*ρKBin effects RPV
24
*Bby KBounds
25
ρρΒin effects RPV
26
The polarization anomaly could be
solved by RPV effects.
27
Motivation Theoretical input Summary
decaysVVBinonPolarizati
Outline
decaysPPBinPuzzles
28
Based on paper: hep-ph/0509273
decaysKBinPuzzle
29
Branching ratiosBranching ratiosPPB
Puzzle !!
30
Direct CP asymmetriesDirect CP asymmetriesPPB
Puzzle !!)Bor B is B( )()(
)()( -
u
0
dfBBrfBBr
fBBrfBBrAdir
CP
RPV SUSY ?
31
Bby dconstraine spacesparameter allowed The
32
BbyBounds
33
KBbydconstrainespacesparameterallowedThe
34
KBbyBounds
35
effects RPVby solved
be could puzzlesK ,B
36
Motivation Theoretical input Summary
decaysVVBinonPolarizati
Outline
decaysPPBinPuzzles
37
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.
38
39
40
otherfor 0L other for 0B
efor -1L d,ufor 3
1B
Lfor 1L Qfor 3
1
iii
ii
B
ikjijkjki
jikijkkij
:
:
][
][
1R :higgsinos & sleptons Squarks,
1R :bosons Higgs & particles SM
P
P
41
p
0
0
0
Ke
ek"" and" j"
in ricantisymmet is
,~
][ jkifordNot
R-parity Violating decay:
42
Ratios of branching ratios
069.1d
u
B
B
43
Branching ratiosBranching ratiosVVB
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