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Moduli stabilization and flavor structure in 5D SUGRA with multi moduli. Yutaka 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 - PowerPoint PPT Presentation
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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