mixing and decays

within supersymmetry

Seungwon Baek (Korea Univ.)

S.B, D. London, J. Matias, J. Virto, JHEP0602, 027(2006);S.B, JHEP0609, 077(2006); S.B, D. London, J. Matias, J. Virto, JHEP0612, 019(2006); S.B, D. London, work in progress

In collaboration with D. London, J. Matias, J. Virto

S SB B

SB KK

Outline

• Motivation: “B→πK puzzle”

• SUSY model with large isospin violation- Grossman-Neubert-Kagan (GNK) scenario

• Strong constraint from Δms

• Bs → KK decays in GNK scenario

• ConclusionsBs-Bsbar mixing and Bs->KKSeungwon Baek 2

B→πK puzzle

0 '

0 ' ' ' '

0 ' '

0 0 0 ' ' '

( )

2 ( )

( )

2 ( )

i iEW

i

iEW

A B K P

A B K P T e P C e

A B K P T e

A B K P P C e

Bs-Bsbar mixing and Bs->KKSeungwon Baek 3

In the SM,

• In the SM:

P’ T’≈ P’≫ EW C’≫

c nR R

0 0( ) ( )CP CPA B K A B K

0 0 0( ) sin 2CPS B K

Bs-Bsbar mixing and Bs->KKSeungwon Baek 4

[G. Hou’s talk]

• problem has disappeared!! Buras, Fleischer, Recksiegel, Schwab

(04,05,06)

• ACP(π0K+) = 0.047±0.026

ACP (π-K+)=-0.093±0.015

[G. Hou’s talk]

• S(π0K0) = 0.33±0.21 sin(2β)(charmonium)=0.675±0.026

/c nR R

Bs-Bsbar mixing and Bs->KKSeungwon Baek 5

• |C’/T’|=1.6±0.3 mainly due to ACP, S(π0K0) SB, London, hep-ph/0701181

cf. In b →d transition, |C/T|=0.28±0.15 (Combined analysis of B→ππ, B→KK). SB, arXiv:0707.2838

→can be solved by NP in the EW-penguin

Bs-Bsbar mixing and Bs->KKSeungwon Baek 6

GNK scenario• Z-mediated EW-peguin in SUSY is suppressed.

• “Trojan penguin?” Grossman, Neubert, Kagan(99)

b S

q qq

b S

g% g

q

b S

q q

b S

• Large enhancement in EW-peguin sector:2 2

2 2

/

/s SUSY

ew W

M

M

Bs-Bsbar mixing and Bs->KKSeungwon Baek 7

Squark mass matrix:

2 2

, ,|L Rd RR d LL

M M

Squark mixing:

K K d dB B

( )SB B X

Oversimplified but useful in constraining 2-3 mixing.

Structure of squark mass matrix

Large 2-3 mixing motivated by SUSY GUT.S.B., T. Goto, Y. Okada, K. Okumura(01), Chang, Masiero, Murayama(02)

0 0

0 0

cos sin

sin cos

L

L

iL L LL L

iL L LL L

s s e b

b e s b

Bs-Bsbar mixing and Bs->KKSeungwon Baek 8

Bs-Bsbar mixing and Bs->KKSeungwon Baek 9

• Large SUSY contribution is possible when– small gluino mass– – – cf. by SU(2)

• can get large SUSY contributions ( ).

Bs-Bsbar mixing and Bs->KKSeungwon Baek 10

mixing

• mass difference:

• Consistent with the SM CKM fits.• Constrains NP models sensitive to

Δms

S SB B

S SB B(D0)

(CDF)

Bs-Bsbar mixing and Bs->KKSeungwon Baek 11

[G. Hou’s talk]

Effective Hamiltonian

Sensitive to mass splitting of and their mixing.

and s b

Only is generated if only LL(RR) exists.MSSM MSSM1 1( )C C

Bs-Bsbar mixing and Bs->KKSeungwon Baek 12

Bs-Bsbar mixing and Bs->KKSeungwon Baek 13

Results for xxxxxxxxx

B→XSγ constraint

0.5 (TeV), 0.5 (TeV)L

g bm m

Bs-Bsbar mixing and Bs->KK

δL=0 δL=π/2

Seungwon Baek 14

Seungwon Baek Bs-Bsbar mixing and Bs->KK 15

Seungwon Baek Bs-Bsbar mixing and Bs->KK 16

and

Bs-Bsbar mixing and Bs->KK

sB K K+ -® 0 0sB K K®

In the SM,

Seungwon Baek 17

• The SM amplitudes are fixed by B→KK modes by flavor-SU(3) symmetry, including factorizable SU(3)-breaking effect

• 1. 2. : QCDf, free of IR divergence and can be safely calculated

3. cf.

Bs-Bsbar mixing and Bs->KKSeungwon Baek 18

0 0.180.17( ) 0.12dirA B K K+ + +

-® =-

S. Descotes-Genon, J. Matias, J. Virto (06)

Seungwon Baek Bs-Bsbar mixing and Bs->KK 19

Bs-Bsbar mixing and Bs->KKSeungwon Baek 20

Bs-Bsbar mixing and Bs->KKSeungwon Baek 21

Bs-Bsbar mixing and Bs->KK

Isobreaking terms: PEW

Seungwon Baek 22

Seungwon Baek Bs-Bsbar mixing and Bs->KK 23

Seungwon Baek Bs-Bsbar mixing and Bs->KK 24

Conclusions• NP in the EW-penguin sector of B→πK is a

promising possibility.

• GNK scenario can give large enhancement to EW penguins in SUSY.

• Δms gives a strong constraint.

• Large CPVs are possible in Bs → K+K– and/or Bs → K0K0. The differences between

the two modes signal NP in the EW-penguin.

Bs-Bsbar mixing and Bs->KKSeungwon Baek 25