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

ulti moduliulti moduliYutaka Sakamura (RIKEN)

with Hiroyuki Abe (Yukawa Inst.)

Aug. 1, 2008@YITP

arXiv:0807.3725

Problems in Standard Model

• gauge hierarchy problem

• Yukawa hierarchy

Introduction

SUSY?

… flavor sym., extra dim., …

We consider effective theories of SUSY extra-dimensional models, focusing the flavor structure.

0 R y

f (0)i

Yukawa hierarchy from extra dimension

e.g.)

zero-mode:

5D mass

(Arkani-Hamed & Schmaltz, 2000 ;…)

(4D Yukawa) = (overlap integral)

In effective theories of 5D SUGRA,

: Radion (chiral) multiplet

(Luty & Sundrum, 2000)

Purpose

Study the flavor structure of the effective theory for more general 5D SUGRA.

In general, the radius is given by

chiral multiplets

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.

Moduli

5D SUGRA with multi moduli

Field contentVector multiplet:

Hypermultiplet:

Orbifold parity

Yukawa hierarchy

SUSYmatter

gauging

4D effective theory

Yukawa couplings and Soft SUSY parameters

(cf. 　 H.Abe & Y.S. , 2007)

(physical Yukawa coupling)

where

If , the soft scalar masses are

Single modulus case

tachyonic soft masses from FX

Multi moduli case

If the second term of dominates,

No SUSY flavor problem

e.g.)

All moduli are stabilized.

Vacuum

In this case,

When the second term dominates.

• non-tachyonic • flavor universal

Soft masses are

R0 y

Single modulus case: sequesteredMulti moduli case: not sequestered

When

Integration out for

5D gauge coupling

R y

Integration out for

When 　　 ,

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

Summary

5D SUGRA with multi moduli

Radius:

Additional contribution to the Kahler potential exist, and it can save

• Tachyonic sfermion masses at tree level• SUSY flavor problem