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Lepton Electric Dipole Moments in Supersymmetric Type II Seesaw Model

Toru Goto, Takayuki Kubo and Yasuhiro Okada,

“Lepton electric dipole moments in supersymmetric type II seesaw model,” [arXiv:1001.1417].

Takayuki Kubo

(KEK, Graduate University for Advanced Studies)

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Outline

Introduction: electric dipole moment (EDM) SUSY type II seesaw model A new source of CP violation Lepton EDMs: previous study Lepton EDMs: our results Summary

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Introduction(1)

The electric dipole moments (EDMs) of leptons ,

nucleons and atoms are important probe for new

physics. Until now no EDM has been observed.

Upper limits on EDMs strongly constrain CP violating parameters.

cmede27106.1

cmed 19107

Fi

dL 52EDM

4

The ratio of the muon EDM to electron EDM is

important in order to suggest necessary sensitivity for

future experiments of muon EDM. The previous study for lepton EDMs in SUSY type II

seesaw model (Chun, Masiero, Rossi and Vempati, phys. Lett. B 62

2 (2005) 112) suggest

This implies that if the electron EDM lies just below the present limit, muon EDM is given by

Introduction(2)

410ed

d (for the normal hierarchy of neutrino masses)

cmed 2310

5

Introduction(3)

However we found additional contributions which should be taken into account.

We will show that the ratio is given by

in a wide region of parameter space. The ratio does not depend on the neutrino

parameters or unknown parameters.

200ee m

m

d

d

6

Superpotential of the model

Exchange of heavy SU(2)L triplets generates small neutrino masses: the seesaw mechanism.

SUSY Type II Seesaw Model (1): superpotential

)(2

1

2

1)(

2

121222221121112 TTMHTiHHTiHLTiLYW T

TTj

TiijTT tr

10

1

11

1

2

12

1

TT

TTT

22

022

2

2

12

1

TT

TTT

SU(3)c SU(2)L U(1)Y

T1 1 3 +1

T2 1 3 -1

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Integrating out the heavy SU(2)L triplets, we obtain neutrino masses as follows:

The matrix mνis diagonalized by the MNS matrix and we have

YT is directly related to mν and UMNS.

SUSY Type II Seesaw Model (2): neutrino masses

ijTT

ij Yv

Mm )(

2)(

2

22

23

*22

13

2

2

22

2

*

10

)(

10tan

tan101.0)(

eVGeV

MNSMNS

k

jkikk

TijTT

UUmM

YY

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SUSY Type II Seesaw Model (3): soft SUSY breaking terms and assumptions

Soft SUSY breaking terms of the model

Soft SUSY breaking squared-mass parameters are universal (m0

2) at MG=2×1016GeV.

Gaugino masses are also universal (m1/2) at MG. A-terms are proportional to corresponding Yukawa

couplings (AE=a0YE) at MG.

)(2

1

2

1~~)(

2

121222221121112 TTBMHTiHAHTiHALTiLAL TT

TTj

TiijTsoft tr

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BT as a new source of CP violation(1)

There still remains three CP violating phases, namely μ, a0 and BT.

Effects of μ and a0 have been studied very well.

Here we study the effects of BT as a new source of CP violation and assume that μand a0 are real.

10

h.c. wwMbbMeLHAL Rjbi

aijEabsoft

~~2

1~~

2

1~~)( 21

*1

BT as a new source of CP violation(2)

The BT contribute to the scalar trilinear couplings and the gaugino masses through the threshold correction at MT.

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BT as a new source of CP violation(3)

ETTTE YYYBA *216

3

ETE YBA

2

1216

3

ETTTE YYYBA2

1*

216

3

TBgM 221 '

16

6

TBgM 222 16

4

The BT contribute to the scalar trilinear couplings , the gaugino masses and soft squared-masses through the threshold correction at MT.

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Lepton EDMs: previous study

In the previous study (Chun, Masiero, Rossi and Vempati, phys.

Lett. B 622 (2005) 112), the contributions from δM1 and δM

2 are missing.

They estimate lepton EDMs di as follows:

TiiTTeiiEi BYYmAvdi

Im)()(Im *1

tan)(2

1)( *

1*2

ieiiEiiLR mAvm

ETTTE YYYBA2

1*

216

3

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Lepton EDMs: previous study

In the previous study (Chun, Masiero, Rossi and Vempati, phys.

Lett. B 622 (2005) 112), the contributions from δM1 and δM

2 are missing.

They estimate lepton EDMs di as follows:

Their result implies

TiiTTeiiEi BYYmAvdi

Im)()(Im *1

4

11*

22*

10)(

)(

TTe

TT

e YYm

YYm

d

d

14

EAi

MiiiLR ddmM ImIm2

11)(Im

TTTeA

i BYYMmdi

E ImRe2

1*

1Im

TeM

i Bgmdi

Imtan'2Im 1

Lepton EDMs: previous study

But we must include contributions from δM1 and δM2.

ex) Diagram shown below contribute to EDMs:

TBgM 221 '

16

6

TBgM 2

22 16

4

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Lepton EDMs: our results(1)

de dμ

dtau 2T

T

MY

GeV/TM

2

1210 1310 1410

λ2 blows up

YT blows up

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Lepton EDMs: our results(2)

200ee m

m

d

d

We can see that the ratio is around 200 except for the lower end of λ2 .

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Summary

We studied lepton EDMs in the SUSY type II seesaw model.

All contributions generated by one-loop threshold corrections at MT through the BT term are included.

We showed that the ratios of lepton EDMs are given by those of the lepton masses:

Since the upper bound of de is at the level of 10-27 ecm, muon EDM search at the level of 10-24-10-25 are important.

200ee m

m

d

d

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Note

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Lepton EDMs: our results(2) Next we fix the λ2 and MT.

λ2=0.03

MT=1012 GeV

Other parameters are fixed at λ1=0 tanβ=3, 30 a0=0 GeV

m1/2=300, 600 GeV

ReBT=ImBT=100 GeV

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Lepton EDMs: our results(2-1)

de dμ

dtau

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Lepton EDMs: our results(2-2)

200ee m

m

d

d

We vary m0 with in 100GeV < m0 < 1000GeV. The horizontal axis represents mass of the lightest charged slepton.

We can see that the ratio is around 200, independent of the values of tanβ, m1/2 and mass of the lightest charged slepton.

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Lepton EDMs: our results(3)

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m

m

d

d

We can see that the ratio is around 17 except for the lower end of λ2 .

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In the numerical calculation, we evaluated the following diagrams:

We fix the parameters as follows: tanβ= 3 , 30 λ1= 0

m0 = m1/2 = 300 GeV

a0= 0 GeV

ReBT= ImBT= 100 GeV

Lepton EDMs: our results(1)

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Comments on EDMs(1)

grow at small values of λ2 (large valus of YT).

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Comments on EDMs(2)

mass of the lightest slepton which couples to muon rather than electron rapidly decrease due to the large YT.

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Comments on LFV decays Branching ratios of LFV decays are given by

Ratio between the branching ratios is

BR:BR:BR ee

4002.0117.0)(18.0)()(2

23*2

13*2

12* :::: TTTTTT YYYYYY

jiji

ijL

Fji m

m

G BRBR

SUSY

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22~

2

3

tan

for s13=0, δ=0

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Comparison with SUSY type I seesaw

iiTNNi

jjTNNj

i

j

YYm

YYm

d

d

)(

)(*

*

type II type I

i

j

i

j

m

m

d

d

2

,*,

,*,

)(

)(

klTNTNT

ijTNTNT

jilk

jiji

lk

ji

YY

YY

BR

BR

BR

BR

†MNS

diag*MNS UmU

v

MY TT

2

22

2

†MNS

diagUmRMviY N

TN

2

2

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SUSY seesaw models

SUSY type I seesaw model

SUSY type II seesaw model

U(1)B-L extended MSSM

…. ….

...)(2

1)(

2

1212222212 TTMHTiHLTiLYW T

Tj

TiijT tr

...2

1)( 2 jiijj

bi

aijNab NNMNLHYW

...2

1)( 12 jiijj

bi

aijNab NNfNLHYW

SU(3)c SU(2)L U(1)Y

Ni 1 1 0

SU(3)c SU(2)L U(1)Y U(1)B-L

Ni 1 1 0 +1

Δ1 1 1 0 -2

Δ2 1 1 0 +2

SU(3)c SU(2)L U(1)Y

T1 1 3 +1

T2 1 3 -1

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Electric dipole moments as probes of new physics

Non-relativistic Hamiltonian for the interaction of an electric dipole moment (EDM) with an electric field:

The relativistic generalization:

Until now no EDM has been observed. ex) electron and muon EDM

F

idL 52

EDM

cmede27106.1 cmed 19107

ES

SdHEDM

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electron EDM

...585 eddTl

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Motivation(2): seesaw mechanism

Seesaw mechanism explains the observed tiny neutrino masses: