Moduli stabilization and flavor Moduli stabilization and flavor structure in 5D SUGRA with mstructure in 5D SUGRA with m

ulti moduliulti moduliYutaka Sakamura (RIKEN)

in collaboration with

Hiroyuki Abe (Yukawa Inst.)

June 17, 2008@SUSY08

Introduction

Problems in Standard Model

• gauge hierarchy problem

• Yukawa hierarchy

• Charge quantization

• Anomaly cancellationGUT?

SUSY?

…

flavor sym., extra dim., …

0 R y

f (0)i

Yukawa hierarchy from extra dimension

e.g.)

zero-mode:

5D mass

(Arkani-Hamed & Schmaltz, PRD61(2000)033005;…)

(4D Yukawa) = (overlap integral)

In 5D SUGRA,

: Radion (chiral) multiplet

Flavor-dependent SUSY breaking

(e.g. Scherk-Schwarz SUSY breaking)

Yukawa hierarchy

SUSY flavor problem

5D SUGRA with Multi moduli

Yukawa hierarchy

SUSY breaking

cf.) In string context, “Mirror mediation”, Conlon, JHEP0803 (2008) 025

5D (off-shell) SUGRA on S /ZField content

• Weyl multiplet:• Vector multiplet:

(One of them is the graviphoton multiplet.)

• Hypermultiplet:

12

compensator physical

(Kugo & Ohashi, 2000-2002)

where

Norm function

5D Lagrangian

bulkpart

(bulk mass)(gauge coupling) =

T = zero-mode of

Single modulus case:

I I

T is the radion multiplet.

Radius:

Moduli:

5D SUGRA with multi moduli

Field contentVector multiplet:

Hypermultiplet:

Orbifold parity

Yukawa hierarchy

SUSY

gauging

matter

4D effective theory

Soft SUSY parameters

physical Yukawa coupling

(cf. H.Abe & Y.S. , PRD75 (2007) 025018)

Single modulus case

tachyonic soft masses from FX

(cf. H.Abe’s talk)

Multi moduli case

If the second term of dominates and ,

No SUSY flavor problem

e.g.)

All moduli are stabilized.

Vacuum

In this case,

When the second term dominates.

• Positive soft squared masses• No SUSY flavor problem

from KK vector multiplets

Integration out for

5D gauge coupling

When ,

R y

Integration out for

When ,

R y

Integration out for

Integration out for

Physical vector multiplets Vecter multiplets (I=1,2,…,n)

: parity-odd: parity-even

Superconformal gauge-fixing

…(# of physical vector multiplets) = n-1

Single modulus case: no KK vector multiplets

R0 y

Single modulus case: sequesteredMulti moduli case: not sequestered

When

Summary

5D SUGRA with multi moduli

Yukawa hierarchy

SUSY breaking

Radius:

Additional contribution to the Kahler potential can save

• Tachyonic sfermion masses at tree level• SUSY flavor problem