Flavor and CP violation in SUSY seesaw models

Junji Hisano (ICRR, Univ. of Tokyo)

The 12th International Conference on Supersymmetry and Unification of Fundamental InteractionsJune 17-23, 2004, Tsukuba, Japan

Neutrino oscillation: Finite, but small neutrino masses

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 de e

22( )

0 ( )NM

f hm M

M

1 2l R R R RNL f fLh Me Lh

Seesaw model (Introduction of right-handed neutrinos )R

Superheavy : We need Supersymmetry (SUSY) M

42

2

22

6 ( 100( ) 10 ( ) t n) aiijL

L

jSUSY

m

mGeVBr l l

m

Charged Lepton-Flavor Violation in SUSY seesaw modelNon-vanishing LFV slepton masses by radiative correction

2 20 02

†2 1 (3 ) l8

ogijN

ijLpl

Mf fAM

m m

Then,

(Borzumati&Masiero)

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

, e

(These are reviewed by Dr. Illana.)

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 neutrinosMatter unification: GUT relation in flavor physics

* ( )2 2 (log / log )/ i j

R

GUT Niij Ld

pl plij

M MM

mM

m e

( :CP phase in GUT)i

0d sB K

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

(moroi)

Colored HiggsFlavor Higgs

Contents of my talk

Introduction

CP and flavor violation in SUSY GUT model Summary

JH and Shimizu, hep-ph/040691 JH, Kakizaki, Nagai, and shimizu, in preparation.

2, CP violation in SUSY SU(5) GUT

the neutrino Yukawa induces the flavor violating right-handedcurrents, ex,

( )2 2 *( ) ( (log ) /(lo) g )i j

R L

pl piij ijd l

l

GUT N

M Me

Mm

Mm

i

(2.7 sigma deviation observed in Belle experiment.)

0 0 0 0

0 223

1) mixing

( Im( ( ) ) 0)

3)

Rd S d

K K B B

B K m2) CP asymmetry in the decay

CP asymmetry in

EDMs of neutron and atom.

and

(1,2) mixing and (2,3) and (1,3) mixings are constrained by and hadronic EDMs, respectively.

K

Here, is the CP phase in colored Higgs interaction. CP and flavor violation in the RH currents give rich hadron physics

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 hadron interaction, which generates 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. Using the QCD sum rule, ex,

2 2 20 0

2 | | , ( 0.8 ).3 3

CP Cpp sg p ss p m d m GeV

f

(Falk et al)

(Zhitnitsky)

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

38.7 10 ( 0.005 )C C CHg u d sd e d d d (JH, Shimizu)

CP violating

0 0 mixing

Recent evaluation of Shiff momentum by Dmitriev and Sen’kov reveals that contribution to EDM from isoscalar channel for meson exchange is suppressed by 0.01 compared with previous estimate. From it, it is found that the strange quark CEDM contribution comes from pi-eta mixing.

Previous result: 23.2 10 ( 0.012 )C C CHg u d sd e d d d (Falk et al)

Neutron EDM

This evaluation is a difficult task. The QCD sum rule is useful for evaluation of only contribution from valence quarks. Here, we present our result by a traditional calculation of the loop diagrams.

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

Strange quark contribution to neutron EDM is not suppressed Compared with up and down quarks.

Here, Peccei-Quinn symmetry is assumed. Axion suppresses strange quark CEDM contribution for valence quarks, whileabove formula is not so changed even if no PQ symmetry.

(JH, Shimizu)

CP violating CP violating

Compare with the sum rule result: 0.55 ( 0.5 )C Cn u dd e d d

(Pospelov&Ritz)

Deuteron EDM

Recently new technique for measurement of deuteron EDM by using storage ring is proposed and the sensitivity may reach to

27(1 3) 10 .Dd ecm This system is relatively simple and the EDM is given as

( ) ( 5.1 2.1 0.32 )

( 11 11 0.063 )

C C Cp n u d s

NN C C Cu d s

d d e d d d

d e d d d

CP violating nuclear forceEach components are

( ) NND p nd d d d

New technique for deuteron EDM may reach toThis corresponds to and

2710 .Dd ecm2810C C

u dd d cm 2610Csd cm

Hadronic EDM constraint on in SUSY GUT

2( )Rd

m If the off-diagonal term in has a CP phase, it contributes to CEDM in the cooperation with the left-handed squark. Theoff-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 mixing induced by topquark are

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

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

412

113

13

| Im( ) | 2 10 , ( )

( )| |

(

1 10 ,

| | , )2

dR

d

K

R

dR

BdM

b s

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

tan 10, 500SUSYm GeV for

Here, are assumed.

CEDMs in SUSY SU(5) GUT with right-handed neutrinos

0 0500 , 0 500 , tan 10gm GeV a m GeV For

Here, diagonal right-handed neutrino mass matrix is assumed, and then parameters in neutrino sector are given by oscillation data.

New technique for deuteron EDM may reach toThis corresponds to and

Csd

Cdd

2710 .Dd ecm2810C

dd cm 2610Csd cm

(JH, Kakizaki, Nagai, Shimizu)

Deuteron EDM reach Deuteron EDM reach

CP asymmetry in v.s. Strange quark CEDM

Csd 8

RC

2 823(1 3) Im12

dLs

bC Rd Cm

CP asymmetry in and strange quark CEDM are strongly correlated.

0d SB K

0d SB K

23 82

11 Im ,4 21

C dL Rbs

md C

Assuming

The neutron EDM bound is one or two orders of magnitudestronger for a sizable deviation in 0 .d SB K

(JH, Shimizu)

Belle BaBar

Summary

In the extension of SUSY GUT, right-handed squark mixings aregenerated by the neutrino Yukawa interaction. The hadronic EDMs have big potential to probe for (1-3) and (2-3) mixing of the right-handed squark mixing, though they may suffer from theoretical uncertainties.

The neutron EDM is more sensitive to strange quark CEDM, andthe constrain the deviation of CP asymmetry in . New technique for the deuteron EDM measurement may give more stringent constraints on them or find the signal.

It is important to take a correlation among various hadronic EDMs,such as those of diamagnetic atom and neutron. The latter is more sensitive to the strange quark CEDM.

0 .d SB K

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

⇒

Other tau LFV processes:

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)

01/ 94,

BBr ee e Brr e Br e

e

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

Normal case

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.

76 4

tan( ) (8 10 )60

( ) : ( 3 ) : ( ) ~ 5 :1

100

: 0.5A

GeVm

Br

Br Br Br

(Babu&Kolda;Brignole&Rossi;JH&Shimizu)

Even if the slepton is so heavy , ( )lm TeV

' ' '' '', 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 ij e ij ie jLm m A H HAA f

Sizable effect

2 0Re ijm and where † log N

ij ijpl

MH f f

M

2, Tau LFV in SUSY seesaw model

Belle’s new bounds and future

.

11

6 7 7 8

6 7 7 8

6 7 7 8 9

6 7 7 8 9

6 7

2000 ( ) 100 31.1 10 3.1 10 10 102.7 10 3.6 10 10 109.6 10 4.4 10 10 10 108.2 10 6.9 10 10 10 10

10 10 1

PDG Belle current L fb L ab

e

elll a few a few

7 8 90 10 10

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

Belle and BaBar experiments are improving the bounds on Tau LFV processes significantly.

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 fM

22( ) T

ij ijN

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 13HQuestion: How large they can be?

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

(1)

* 0 00 * *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

in SUSY GUT0d SB K

Non-negligible may lead to the deviation of CP asymmetry since is a radiative processes.

223( )

Rdm

0d SB K

The effective operator for induced by :

b sss

b sg

28 ( )8

R sb L

gH m s G P bC

223( )

Rdm

The dominant contribution comes from the gluon penguin diagram in the broad parameter space.

Observation of CP asymmetry in 0 :d SB K

0.96 0.50 ( ), 0.47 0.34 ( )K KS Belle S BaBar (SM prediction: )0.731 0.056KS

The largest values are fixed by only validity of perturbation, and they are larger than the experimental bound. These observations give independent information about seesaw model of neutrino oscillation. Even inverted ordering cases 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

Slepton oscillation

( ) ( )e e ll e 2

2( ) / sin 2m m

.

150 , 500180 , tan 3

L fb s GeVm 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)