Flavor Violation　　　　 in SUSY SEESAW models

　　　　　　　　 8th International Workshop on Tau-Lepton Physics 　　

　　　　　　 Tau04

　　　　　　 Junji Hisano (ICRR, U of Tokyo)

1, Introduction

Lepton-flavor Violation (LFV) in neutrino sector : Neutrino oscillation experiments

, 3 , Tau LFV decays ( ⇔ Atmospheric neutrino ? )Muon LFV decays ( ⇔ 　 Solar neutrino ?)

48 4( ) 10 ( /1 )Br e m eV However,

Charged LFV depends on the physics beyond the SM and origin of the neutrino masses.

How large is LFV in charged lepton sector?

, 3e e

⇒

Neutrino oscillation: Finite, but small neutrino mass

Baryon in Universe: Leptogenesis(B-L violation by Majorana mass )

Unification of Matterin SO(10) GUT:

, , ,(16) ( )

, , ,L R L R

RL R L

u u d d

e e

22( )

0 ( )N

NM

f hm M

NM

1 2l R R R RNL f fLh Me Lh

Seesaw model (Introduction of right-handed neutrinos )R

Superheavy : We need Supersymmetry (SUSY)NM

42

2

2

2

6 (100

( ) 10 ( ) t n) ai

ijL

L

jSUSY

m

m

GeVBr l l

m

Charged Lepton-Flavor Violation in SUSY seesaw model

Non-vanishing LFV slepton masses by radiative correction

202

2 20

†1( lo3 )

8gijL

Nij

G

m AM

f fM

m

And then,

(Borzumati&Masiero)

The charged LFV, 　　 , may be observed in near future experiments.

, e

Flavor-violating Yukawa coupling

1 2 3

1 1 3

( )

( )

R R R L L

R R R L L

s s s

b b b

SUSY GUT with right-handed neutrinos

Matter unification: GUT relation in flavor physics

* ( )2 2 i j

R

iijLd ij

m m e

( :generic CP phase in GUT)i

0d sB K

Flavor-violating right-handed current might predict deviation of and so on.

(moroi)

Colored HiggsFlavor Higgs

SU(5)

Contents of my talk

Introduction Tau LFV in SUSY seesaw model Mixing between 2nd and 3rd generations in SUSY GUT model Summary

2, Tau LFV in SUSY seesaw model

' ' '' '', l l l l l l Radiative decay processes:

Non-vanishing LFV slepton masses by radiative correction

2 20 0 0

22 2

1 1(3 )

8 8ij e ijij ijeLH Hm m AA f A

Sizable effect

2 0Re ijm and where

† log Nij ij

G

MH f f

M

New bounds and future for tau LFV processes

.

11

6 7 7 8

6 7 7 8

6 7 7 8 9

6 7 7 8 9

6 7

2000 ( ) 100 3

1.1 10 3.2 10 10 10

2.7 10 3.6 10 10 10

9.6 10 4.4 10 10 10 10

8.2 10 6.9 10 10 10 10

10 10 1

PDG Belle current L fb L ab

e

e

lll a few a few

7 8 90 10 10

Further improvements of one or two orders may be expected in super B factory.

Bounds on Tau LFV processes are being improved in B factory experiments.

Degrees of freedom of physical observables

In (Hermitian)Real: 6,Phase:3

ijHIn light mass matrix M:3, :3, CP:1(mixing)+ 2(Majorana)

In Seesaw model,M:3+3, :6,CP:4(mixing)+2(Majorana)

† log Nij ij

G

MH f f

M

2

2( ) Tij ij

N

hm f f

M

( )ijm

We can take and for parameterization of seesaw model, and neutrino and charged lepton experiments give independent information of seesaw model.

( )ijm ijH

Bottom-up approach to seesaw model

( )Br ( )Br e comes from , and from .23H 13H

Question: How large they can be?

e 12, 13 32/ 0.H and or H H is generated if .

(1)

* 0 0

0 * *

0 * *

H

(2)

* 0 *

0 * 0

* 0 *

H

( )Br ( )Br e

We assume

Model-building may favor with , not . (1)H (2)H

(Observed large mixings of neutrino come from Yukawa coupling in a case of , but Majorana mass in .)(1)H (2)H

Maximum prediction is fixed by only validity of perturbation, and it Is larger than the experimental bound. These observations give independent information from neutrino oscillation. Even inverted ordering cases for neutrino masses　 give similar results.

0( 200 , 0 , tan 10 30, ( ) 1)wm GeV A GeV or sign

Normal ordering for neutrino mass

(2)H

BELLE result BELLE result

( )Br ( )Br e

(Ellis, JH,Raidal,Shimizu)

(1)H (2)H

Other tau LFV processes: Normal case

One-shell photon contribution is dominant,

since dipole operator contribution is proportional to

Furthermore, 3lepton processes is enhanced by

2tan .log

l

mm

( 3 ( 2 )) / ( ( ) ) 1/ 4

( (3 )) / ( ( )

4

)

0

1/ 94,

B

Br ee e Br

r e Br e

e

If we find the LFV, we can examine non-trivial tests!

( (100) )l

m O GeV

Even if the slepton is so heavy , the anomalous LFV Yukawa coupling for Higgs boson

may be generated radiatively and not be suppressed by the SUSY scale. In this case, the tau LFV processes may be generated by Higgs mediation, and 3mu, mu eta, mu gamma are comparable.

24 2

7 32

2

6tan

( 3 ) (4 10 )60

( ) : ( 3 ) : ( ) 5 :

100

1: 0.5

A

L

L

mBr

m

GeV

Br Br Br

m

( )l

m TeV

(Babu&Kolda;Shar)

In SUSY SU(5) GUT, the neutrino Yukawa induces the flavor violating right-handed currents.

2 3( )2 223 23( ) ( )

R L

i

d lm m e

3, Hadron and tau physics in SUSY GUT model

0

0

0 0

1) ,

.

2) .

3) .

d S

d s

s s

CPasymmetry in b s penguin processes

such as B K

mixing induced CPassymmetry in B M

B B mixing

These processes are correlated with and hadronicEDMs, such as Hg and neutron EDMs, in SUSY GUTs.

( )Br

b-s penguin processes in SUSY GUTNon-negligible may lead to the deviation of CP asymmetry in b-s penguin processes, such as since and are radiative processes.

2.4 and 2.7 sigma deviations in the b-s penguin processes are observed in Belle and Babar experiments, respectively.

223( )

Rdm

0d SB K b sss

b sdd

(Talks in ICHEP04)

b-s penguin v.s.

1 2( )2 2

23 23( ) ( )R L

i

d lm m e GUT relation:

Thus, b-s penguin processes and are correlated in the SUSY GUTs.

CP asymmetry in 0d SB K

2

3

14

5 10 ,

1/ 2,

5 10 ,

tan 30

N

m eV

U

M GeV

This is non-trivial test for the SUSY GUTs.

Hadronic EDM induced by in SUSY GUT

2( )Rd

m If the off-diagonal term in has a CP phase, it contributes to choromoelectric dipole moments (CEDM) for quarks in the cooperation with the left-handed squark. The off-diagonal terms are induced by the top quark Yukawa coupling with CKM.

Here,

2( )Rd

m

2 2 2 2( ) / ( ) /

LR R L

dR dLij ij ij ijdd d d

m m m m

Enhanced by heavier fermion mass

In typical models, the left-handed squark mixings are induced by top quark as

2 3 523 13 13, , ( ~ 0.2)dL dL dL

dLij

dRji

( )L Ld s ( )R Rd s( ) ( )L RL L L Lbd bs d s

Hadronic EDMs

Current bounds on Mercury and neutron EDMs constrain the SUSY models.

28 26| | 2.1 10 , | | 6.3 10 .Hg nd ecm d ecm

5( )2CP

Cq

sq

L i qg G qd

| | 4.8, | | | | 2, ..1 84p uu p p dd p p ss p

Choromoelectric dipole moments (CEDM) generate CP violating hadronic interaction, which leads to EDMs of Mercury and neutron.

Strange quark component in necleon is not negligible. Frombaryon mass and sigma term in chiral perturbation theory,

Thus, hadronic EDMs depend on the strange quark CEDM via K or eta meson interaction, in addition to up and down CEDMs. Using the QCD sum rule, ex,

2 2 20 0

2| | , ( 0.8 ).

3 3CP Cpp sg p ss p m d m GeV

f

(Falk et al)

(Zhitnitsky)

b-s penguin v.s. strange quark CEDM

Csd 8

RC

2 823(1 3) Im12

dLs

bC Rd Cm

CP asymmetry in b-s penguin processes and strange quark CEDM are strongly correlated.

28 ( )8

R sb L

gH m s G P bC

The effective operator for induced by :b sg2

23( )Rd

m

23 82

11Im

4 21C dL Rbs

md C

Assuming and

The neutron EDM bound is one order of magnitude stronger for a sizable deviation in b-s penguin processes. The discrepancy might come from QCD uncertainties. New technique for deuteron EDM may reach to

(JH, Shimizu)

223 0.04dL

CP asymmetry in 0d SB K

2610 .Csd cm

Summary

After discovering neutrino oscillation, flavor violation inducedby neutrino Yukawa coupling gives new interesting phenomena,charged LFV and CP violating hadron phenomena.

Now B factory starts to access interesting region for tau->mu(e) gamma. It may give new information about structure of seesawmechanism.

In the SUSY GUTs, tau LFV is related with other hadronic processes, such b-s penguin processes and hadronic EDMs. It is important to check the correlation. The recent result for b-s penguin processes suggest large Br(tau->mu gamma) in the SUSY GUTs.

EDMs are also a good probe in the SUSY GUTs since non-vanishing mixings for both left-handed right-handed sfermions are predicted in this model. We show constraints from hadronic EDMs induced by strange qaurk CEDM. Since the QCD uncertainties are big, the further experimental and theoretical improvements are very important.

Slepton oscillation

( ) ( )e e ll e X

22( ) / sin 2m m

.

150 , 500

180 , tan 3

L fb s GeV

m GeV

(Arkani-hamed et al)

If sleptons are produced in future collider experiments, LFV slepton mass leads to slepton oscillation, and then

The cross section behaves as

( )Br

e e collider

collider

(JH, Nojiri, Shimizu, Tanaka)

( )e e X

Constraints on the flavor violation in squark mass term

32

31

2

3

3

1

| Im( ) | 4.8(98)

| Im( ) | 4.7(2.5)

| Im( ) | 4.5( 4

0

2.

1

)

10dR

dR

dR

From neutron (Hg atom) EDM

Constraints on (1-3) and (2-3) mixing for the right-handed squark mixings are stringent. (1-2) mixing is constrained by .K

421

131

32

| Im( ) | 2 10 ,

| | 1 10 ,

| | 0

( )

( )

(6 ). ,

K

Bd

dR

dR

dR

M

b s

2 3 523 13 13, , ( ~ 0.2)dL dL dL

tan 10, 500SUSYm GeV for

Here, are assumed.

Hg atom EDM

Hg is a diamagnetic atom, and the EDM is sensitive to CP-violating nuclear force induced by pion and eta exchange, whichgenerates T-odd EM potential (Shiff momentum).

199

CP violating 0 0 mixing

38.7 10 ( 0.005 )C C CHg u d sd e d d d

1.6 ( 0.81 0.16 )C C Cn u d sd e d d d

CP violating CP violating

Neutron EDM