moduli stabilization and flavor structure in 5d sugra with multi moduli yutaka sakamura (riken) with...
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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)
with Hiroyuki Abe (Yukawa Inst.)
Aug. 1, 2008@YITP
arXiv:0807.3725
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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.
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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)
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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
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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
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5D Lagrangian
bulkpart
(bulk mass)(gauge coupling) =
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T = zero-mode of
Single modulus case:
I I
T is the radion multiplet.
Moduli
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5D SUGRA with multi moduli
Field contentVector multiplet:
Hypermultiplet:
Orbifold parity
Yukawa hierarchy
SUSYmatter
gauging
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4D effective theory
Yukawa couplings and Soft SUSY parameters
(cf. H.Abe & Y.S. , 2007)
(physical Yukawa coupling)
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where
If , the soft scalar masses are
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Single modulus case
tachyonic soft masses from FX
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Multi moduli case
If the second term of dominates,
No SUSY flavor problem
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e.g.)
All moduli are stabilized.
Vacuum
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In this case,
When the second term dominates.
• non-tachyonic • flavor universal
Soft masses are
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R0 y
Single modulus case: sequesteredMulti moduli case: not sequestered
When
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Integration out for
5D gauge coupling
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R y
Integration out for
When ,
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When ,
R y
Integration out for
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Integration out for
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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
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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