EDMs in the SUSY GUTs

Junji Hisano (ICRR, Univ. of Tokyo)

NuFact046th International Workshop on Neutrino Factories and Superbeams,Osaka University, Japan26 July - 1 August 2004

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 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) M

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 modelNon-vanishing LFV slepton masses by radiative correction

2 20 02

†2 1(3 ) l

8ogij

NijL

pl

Mf fA

Mm m

Then,

(Borzumati&Masiero)

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

, e

(This topic was reviewed by Prof. Okada.)

In MSSM with right-handed neutrinos,

In SUSY SU(5) GUT with right-handed neutrinos, quarks and leptons are unified, and then

SUSY SU(5) GUT with right-handed neutrinos

CKM mixing Left-handed sdown mixing⇒Neutrino mixing Left-handed slepton mixing⇒

CKM mixing Right-handed slepton mixing⇒Neutrino mixing Right-handed sdown mixing⇒

Relative phases between left- and right-handed sfermion mixing contributes to EDMs

When both left-handed and right-handed squark and slepton mixings are predicted, the EDMs are generated. The hadronic and leptonic EDMs are good probes for the SUSY GUTs.

Contents of my talk

Introduction

Hadronic CP violation in SUSY GUT model Leptonic EDMs in SUSY GUT model Summary

JH and Shimizu, hep-ph/040691 JH, Kakizaki, Nagai, and shimizu, hep-ph/0407169

2, Hadronic CP violation in SUSY SU(5) GUT

The neutrino Yukawa induces the right-handed sdown mixing, as

( )2 2 *( ) ( ) i j

R L

iij ijd l

m m e

i

(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 m

2) CP asymmetry in the decay

CP asymmetry in

EDMs of neutron and atoms.

and

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

K

Here, comes from GUT inteaction. CP and flavor violation in the RH mixing gives 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 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)

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 C

Hg 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.

This is sensitive to UV cut off, which appears in log as the baryon mass in above equation.

(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

Reach of deuteron EDM 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 mixings are induced by top quark as

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

dLij

dRji

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.

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

in SUSY GUT0d SB K

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

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

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

11Im

4 21C dL Rbs

md C

Assuming and

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

(JH, Shimizu)

Belle BaBar

223 0.04dL

0 0100 , 0 72 , tan 10B

m GeV a m GeV For

2, EDMs in SUSY SU(5) GUT

Electron and muon EDMs are generated by the left- and right-handed slepton mixings, again. Neutrino mixing Left-handed slepton mixing⇒ GUT CKM mixing Left-handed slepton mixing⇒

Br( ) v.s. Leptonic EDMs in SUSY GUTs

e

( )( )R L L RH e F A PAP

RA ( )ed d

Effective operator for is e

26 311

3

26 253211

31

( )3 10 ,

1.2 10

( )3 10 1 10

1.2 10

ee

CKM

CKM

UBr ed

U

VBr ed

V

Br( ) gives bounds on leptonic EDMs.

e

Summary

In the extension of SUSY GUT, the left- and right-handed squark and slepton mixings are predicted, and the relative phases contribute to the hadronic and leptonic EDMs. Thus, the EDMs are good probes for the SUSY GUTs.

The right-handed squark mixings are generated by the neutrino Yukawa interaction. The hadronic EDMs have big potential to probe for (1-3) and (2-3) mixings of the right-handed squarks, though they may suffer from theoretical uncertainties.

The neutron EDM is more sensitive to strange quark CEDM, andit constrains the deviation of CP asymmetry in

0 .d SB K

New technique for the deuteron EDM measurement may give more stringent constraints on the models or find the signal. It is important to take a correlation among various hadronic EDMs, such as those of diamagnetic atom and neutron, after discovering them. The latter is more sensitive to the strange quark CEDM.

Leptonic EDMs are sensitive to the GUT scale parameters, such as GUT CKM and MNS matrixes. If we use the low energy CKM parameters for the GUT CKM, we get upper bound on the electron and muon EDMs as from 27 257 10 , 1 10ed d

.e

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 (log / log )/ i j

R

GUT Niij Ld

pl plij

M M

Mm

Mm 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