rumin wang work done in collaboration with g. r.. lu & y. d. yang
DESCRIPTION
Rumin Wang Work done in collaboration with G. R.. Lu & Y. D. Yang. Huazhong Normal University Henan Normal University November 15 , 200 5 , Beijing. Outline. Motivation Theoretical input Summary. Motivation for study. To solve the polarization anomaly To solve the puzzles. - PowerPoint PPT PresentationTRANSCRIPT
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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 ,
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Motivation Theoretical input Summary
decaysVVBinanomalyon Polarizati
Outline
decaysPPBinPuzzles
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To solve the polarization anomaly
To solve the puzzles
decaysVVBin
deacysK ,Bin
Motivation for study
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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
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Tree + penguin :
Pure penguin ((Sensitive to NPSensitive to NP)):
????
Surprise
5.0~, 0*0**LfKandKKB
9.0~, *0LfKandB
VVB
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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
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To solve the polarization anomaly
To solve the puzzles
decaysVVBin
decaysK ,Bin
Motivation for study
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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
?
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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
?
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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
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Motivation Theoretical input Summary
decaysVVBinonPolarizati
Outline
decaysPPBinPuzzles
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Theoretical input
The effective Hamiltonian in SM
R-parity Violating SUSY
QCD Factorization
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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
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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
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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
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BQMM
BHMM
MMBA
iR
R
R
)(~
)(
21
21
21
R-parity Violating decay amplitude:
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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.
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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)()()(
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Motivation Theoretical input Summary
decaysVVBinonPolarizati
Outline
decaysPPBinPuzzles
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decaysVVBinonPolarizati
Based on paper: Phys.Rev.D72:015009(2005)
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Longitudinal polarizationLongitudinal polarization
Polarization
Anomaly !!
VVB
RPV SUSY ?
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*KB in effects RPV
32323*
2223103.2 :bound previous ]~101.2,~105.1[||
LiLiii
2
~2
100~
Gev
mff
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*ρKBin effects RPV
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*Bby KBounds
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ρρΒin effects RPV
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The polarization anomaly could be
solved by RPV effects.
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Motivation Theoretical input Summary
decaysVVBinonPolarizati
Outline
decaysPPBinPuzzles
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Based on paper: hep-ph/0509273
decaysKBinPuzzle
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Branching ratiosBranching ratiosPPB
Puzzle !!
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Direct CP asymmetriesDirect CP asymmetriesPPB
Puzzle !!)Bor B is B( )()(
)()( -
u
0
dfBBrfBBr
fBBrfBBrAdir
CP
RPV SUSY ?
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Bby dconstraine spacesparameter allowed The
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BbyBounds
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KBbydconstrainespacesparameterallowedThe
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KBbyBounds
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effects RPVby solved
be could puzzlesK ,B
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Motivation Theoretical input Summary
decaysVVBinonPolarizati
Outline
decaysPPBinPuzzles
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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.
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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
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p
0
0
0
Ke
ek"" and" j"
in ricantisymmet is
,~
][ jkifordNot
R-parity Violating decay:
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Ratios of branching ratios
069.1d
u
B
B
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Branching ratiosBranching ratiosVVB