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
