Effects of Large Threshold Corrections in SUSY type-I Seesaw Model

IV International Workshop on the Interconnection between Particle Physics and

CosmologyNational University Library

Torino, Italy 12-16 July 2010

Sin Kyu Kang(Seoul National University of

Technology)Based on arXiv :1005.1354 in

collaboration with Morozumi and Yokazaki)

Outline

Introduction

Threshold corrections to soft SUSY breaking terms in SUSY type-I seesaw

Effects of the threshold corrections on

Numerical calculation and results

Summary

- Relic abundance of neutralino dark matter- Lepton flavor violation

I. Introduction

• Smallness of neutrino masses • Stabilizing EW scale without fine-tuning• Providing a natural candidate for a dark matter• Grand unification of SU(3)xSU(2)xU(1)• introducing gauge singlet RH neutrino superfields

- Brs of LFV radiative decays

- the relic abundance of Neutralino dark matter can be significantly affected by large threshold corrections mediated by gauge singlet neutrino superfields in SUSY type-I Seesaw Model

SUSY version of type I seesaw model :

Main purpose of this talk : to show how

Issue on this work

• In SUSY type I seesaw model with hierarchical RH neutrino mass spectrum,

we allow the B-term , to be large, which leads to large mass splitting of RH sneutrinos• Effects of B-term have been studied by Farzan ’03,

Kato,SKK,Morozumi, Yokozaki ‘09, Giudice, Paradisi, Strumia, ‘10

• Large mass splitting leads to large threshold corrections to affect the minimization condition for the Higgs potential

the fine-tuning can be reduced(Kato, SKK, Morozumi, Yokozaki)

• Such a large mass splitting affects relic abundance of the DM and leads to additional source of LFV slepton masses as well

• While large threshold corrections give rise to large LFV, they lower the abundance of the neutralino DM

hcNNMB RN *~~

~ *

22 HH

II. Threshold corrections

• Superpotential of type-I SUSY seesaw

• Soft SUSY breaking terms :

• Mass spectrum of RH neutrinos & sneutrinos

3,2,1, RRR MMM

• For heavy RH neutrinos NRi :

• For heavy RH sneutrinos :

~ ~

Without threshold corrections• RGEs for slepton masses and H2 mass

• Assuming that soft SUSY breaking parameters are universal at high energy scale like GUT scale.

• Integrating RGEs between

ik ,

RG corrections

Decoupling RH neutrino superfields at threshold scales, terms of RGEs leading to threshold corrections

• Integrating those RGE terms for , and using the relations,

• we can obtain threshold corrections :

• Assuming universal soft breaking terms,

2,

22, khkl MQM

•Similarly, the threshold corrections to up-type Higgs mass

• There also exist finite contributions of threshold corrections calculable by diagrammatic method, but

they are much smaller than the above contributions.

• The above results are consistent with the results obtained by the method of analytic continuation into superspace

(Giudice, Paradisi, Strumia ‘10, see aslo Arkani-Hamed, Giudice, Luty, Rattazzi ‘98, Matssura, Nakano, Yoshioka ’06)

III. Effects of threshold corrections

Parameter via Higgs mass

• Minimization condition of the Higgs potential :

• Corrections to

• When the threshold corrections become large, compensates large top-stop corrections, then the size

parameter becomes small.

• This lowers the relic abundance of neutralino dark matter compared to that of MSSM

thresholds

RG effects

2

2Hm

2

2Hm

• In SUSY seesaw based on mSUGRA, the radiative corrections drive more negative than that in MSSM if we do not include the threshold corrections.

• However, if we include large threshold corrections, is driven less negative which leads to smaller ||.

• So, the portion of higgsino in the lightest neutralino state becomes large,

the allowed parameter space leading to right amount of relic density of neutralino DM becomes shifted compared to MSSM.

2

2Hm

2

2Hm

EW symmetry breaking requires || to be larger than that in MSSM.

• The radiative LFV decays

Branching ratios

The : proportional to

Including the threshold corrections

Both contributions cancel each other when they are comparable.

thresholds

Lepton Flavor Violation

As BN becomes large, threshold corrections get dominant over RG effects.

Giving rise to large lepton flavor violation

Lowering the relic abundance of neutralino dark matter

So, it is possible to obtain right amount of even in the parameter space excluded by WMAP in MSSM

2h

IV. Numerical calculation and Results

• Soft breaking parameters are universal at the high E scale like GUT scale

• Deriving weak scale values of SSB parameters by using RGEs.

• Software : SuSpect, micrOMEGAs with appropriate modifications.

• The upper bounds on

• WMAP result for relic abundance of the cold DM :

)( ji llBR 11

8

8

102.1)(

103.3)(

104.4)(

eBR

eBR

BR

)2( 111.0 011.0015.0

2 hCDM

Assumptions in the Neutrino Sector

• No LFV in charged Lepton sector

• MR are hierarchical

• Yand MR can be diagonalized simultaneously

(A) Normal hierarchical spectrum of light neutrinos

• Thanks to 0sin 13

)()( BReBR

)( ji llBR

2h

as a function of BN

GeV 300

GeV, 300 TeV, 1

2/1

00

m

Am

)( ji llBR as a function of universal soft scalar mass m0

(B) Inverted hierarchical spectrum of light neutrinos

Comparing to NH :

Therefore, threshold corrections to up-type Higgs mass are muchsmaller than in the NH case, which lead to large relic abundance

• In the case of

• even other cases,

it is difficult to satisfy the constraints on BR and relic density

(C) Quasi-degenerate spectrum of light neutrinos

• is larger than that in NH, which makes the prediction of substantially enhanced compared to NH, and thus the constraint of becomes more severe when we consider the constraint of the relic abundance simultaneously.

)( eBR )( eBR

V. Summary

• In type-I SUSY seesaw model, large mass splitting of heavy sneutrinos leads to large threshold corrections to slepton masses and up-type Higgs mass.

• Large threshold corrections affect the relic abundance of neutralino dark matter and give rise to large BRs of the LFV decays.

• Large threshold corrections can reduce fine-tuning in MSSM and make the allowed region of the soft parameter space shifted.

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