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