Sliding Singlet Mechanism and E6 Unification

繰り込み不可能な超対称
SU(5)模型における
繰り込み群方程式による
フレーバーの破れ
山下敏史 (名古屋大学)
２００９年１１月２７
@ICRR
based on arXiv:0903.2793[hep-ph]
with F. Borzumati （台湾国立大学）
Introduction & Conclusion
LFV vs. QFV in SUSY-GUTs
LFV
RGE
Yukawa
Seesaw mechanism
F. Borzumati &
A. Masiero (1986)
Introduction & Conclusion
LFV vs. QFV in SUSY-GUTs
LFV
RGE
Yukawa
Seesaw mechanism
QFV
Grand Unification
Baek, Goto, Okada
& Okumura (2001)
realistic??
Moroi
(2000)
•Fermion Spectra
•Proton Decay
New Physics above GUT
Introduction & Conclusion
Fermion Spectrum
Wrong GUT relation:
• Non-Renormalizable Operators
affects only 1st
& 2nd
generations
GUT breaking effects
Proton Decay
NRO can suppress
only Yukawa of
.
is allowed.
D.E. Costa & S. Wiesenfelds (2003)
Introduction & Conclusion
LFV vs. QFV in SUSY-GUTs
LFV
RGE
Yukawa
Seesaw mechanism
QFV
Grand Unification
•Fermion Spectra
NROs
•Proton Decay
New Physics above GUT
Introduction & Conclusion
How to deal?
infinite divergences
NRO
RGE
infinite new operators
Approximation
Higher-dim terms : higher suppression by
and/or
We can neglect the higher terms!
An O(s^2) analysis was done.
S. Baek, T. Goto, Y. Okada
& K. Okumura
(2001)
Introduction & Conclusion
Setup
MSSM + …
references
SU(5) w/ NROs
MSSM +
• S. Baek, T. Goto, Y. Okada & K. Okumura (2001)
study with a dim.5 NRO.
generalized
Bolzumati &
T.Y. (2009)
• N. Arkani-Hamed, H. C. Cheng & L. J. Hall (1996)
• J. Hisano, D. Nomura, Y. Okada, Y. Shimizu & M. Tanaka (1998)
RGE w/ effective couplings.
Introduction & Conclusion
conclusion
: not affected
• leading effect :
superCKM
basis
• approximation :
S. Baek et.al. (2001)
P.Ko, J.h.Park & M.Yamaguchi (2008)
Plan
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Introduction & Conclusion
RGEs in renormalizable models
RGEs in non-renormalizable models
Effective couplings
Universality of B.C.
Summary
RGEs in renormalizable models
general setup
field redefinition
RGEs in renormalizable models
Feynman rule
: propagator
field
redefinition
RGEs in renormalizable models
Feynman diagram
RGEs in renormalizable models
corrections
field redefinition
superpotential terms :
Plan
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Introduction & Conclusion
RGEs in renormalizable models
RGEs in non-renormalizable models
Effective couplings
Universality of B.C.
Summary
RGEs in NR models
general setup
field redefinition
RGEs in NR models
Feynman diagram
RGEs in NR models
Approximation
neglect O(s^3) contributions
dim.
tree
loop
Q-dep.
5
B.C.
6
B.C.
neg.
neg.
7<
neg.
neg.
neg.
neg.
one-step approximation :
S. Baek, T. Goto, Y. Okada
& K. Okumura
(2001)
Plan
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Introduction & Conclusion
RGEs in renormalizable models
RGEs in non-renormalizable models
Effective couplings
Universality of B.C.
Summary
Effective couplings
definition
SU(5) example
forgotten in some
literatures
used in the matching to MSSM.
These can be used also at loop level!
Effective couplings
Feynman diagram
<24H>
<X>
Anom. dim.s are given as in renormalizable model,
by using the effective couplings.
Effective couplings
loop corrections
ignored in the
literatures
???
• Note also the running of the VEV.
Bolzumati &
T.Y. (2009)
These holds in general.
Effective couplings
 flows of VEVs
Field redefinition:
if no vertex corrections :
independent of the Kahler Potential
def. of VEVs:
H
Vacuum structure
general setup
independent
depends onofKahler?
Kahler
EOM :
Effective couplings
loop corrections
ignored in the
literatures
• Note also the running of the VEV.
Bolzumati &
T.Y. (2009)
These holds in general.
Effective couplings
used approximation
does not
cancel 1/Mcut
O(E/Mcut )?
remark
Colored Higgs Yukawa has peculiar contributions,
of O(s^2), affecting FVs at O(s^3), via add. loop.
Plan
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Introduction & Conclusion
RGEs in renormalizable models
RGEs in non-renormalizable models
Effective couplings
Universality of B.C.
Summary
Universality of B.C.
in MSSM
• The universal B.C. is often used, at a high scale.
in non-renormalizable models
How should it be generalized?
field-independence
for each dimensionality?
“weak” universality
Universality of B.C.
weak universality
• This does not ensure
.
• This is not stable under the field redefinition
to minimize the Kahler potential :
Universality of B.C.
weak universality
Universality of B.C.
strong universality
Universality of B.C.
strong universality in superpotential
This does ensure
!
Universality of B.C.
strong universality in Kahler potential
impose this minimized by the field redefinition
w/
Universality of B.C.
minimal SUGRA
strong universality in Kahler potential
The SUSY should couple to the overall potentials.
• # parameters : 3
(apart from the gaugino mass
)
Summary
We discuss RGEs in NR models are.
• O(s^2) contributions can be controlled.
S. Baek, T. Goto, Y. Okada & K. Okumura (2001)
• We propose (formulate) another treatment
via effective coupling is
Cf. N. Arkani-Hamed et.al. (1996), J. Hisano et.al. (1998)
• We see how universality is generalized.
In paper
F. Borzumati & T. Y. (2009)
• Non-universal B.C. are also investigated.
• Some discussion on Proton decay is given.
• All the relevant RGEs are given for type I, II, III.

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