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

based on arXiv:0903.2793[hep-ph]based on arXiv:0903.2793[hep-ph]　　 with F. Borzumati with F. Borzumati （台湾国立大（台湾国立大学）学）

山下　敏史 　 ( 名古屋大学 )２００９年１１月２７　 ２００９年１１月２７　

@ICRR@ICRR

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

Introduction & Conclusion

LFV vs. QFV in SUSY-GUTs

LFVSeesaw mechanism

F. Borzumati & A. Masiero (1986)

YukawaRGERGE

Grand Unification

Introduction & Conclusion

LFV vs. QFV in SUSY-GUTs

LFV Yukawa

QFV realistic??•Fermion Spectra•Proton Decay

New Physics above GUT

affected

? Baek, Goto, Okada & Okumura (2001)Moroi (2000)

Seesaw mechanism

RGERGE

RGERGE

NRO can suppress only Yukawa of .

Introduction & Conclusion

Fermion Spectrum

Wrong GUT relation:

• Non-Renormalizable Operators

GUT breaking effects

Proton Decay

is allowed.D.E. Costa & S. Wiesenfelds (2003)

affects only 1st & 2nd

generations

Grand Unification

Introduction & Conclusion

LFV vs. QFV in SUSY-GUTs

LFV Yukawa

QFV•Fermion SpectraFermion Spectra•Proton Decay

New Physics above GUT

Seesaw mechanism

NROs

RGERGE

RGERGE

affected

?

Introduction & Conclusion

How to deal?

NRO

RGE

infinite divergences

infinite new operators

ApproximationHigher-dim terms : higher suppression by

and/or

We can neglect the higher terms!

An (s^2) analysis was done. S. Baek, T. Goto, Y. Okada & K. Okumura (2001)

• S. Baek, T. Goto, Y. Okada & K. Okumura (2001)

• N. Arkani-Hamed, H. C. Cheng & L. J. Hall (1996)• J. Hisano, D. Nomura, Y. Okada, Y. Shimizu & M. Tanaka (1998)

study with a dim.5 NRO.study with a dim.5 NRO.

Introduction & Conclusion

Setup

MSSM + … SU(5) w/ NROs

references

RGE w/ RGE w/ effective couplingseffective couplings..

generalizedBolzumati & T.Y. (2009)

MSSM +

superCKM basis

Introduction & Conclusion

conclusion

: not affected

• leading effect :

• approximation :

P.Ko, J.h.Park & M.Yamaguchi (2008)S. Baek et.al. (2001)

Plan• Introduction & ConclusionIntroduction & Conclusion• RGEs in renormalizable modelsRGEs in renormalizable models• RGEs in non-renormalizable modelsRGEs in non-renormalizable models• Effective couplingsEffective couplings• Universality of B.C.Universality of B.C.• SummarySummary

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• Introduction & ConclusionIntroduction & Conclusion• RGEs in renormalizable modelsRGEs in renormalizable models• RGEs in non-renormalizable modelsRGEs in non-renormalizable models• Effective couplingsEffective couplings• Universality of B.C.Universality of B.C.• SummarySummary

RGEs in NR models

general setup

field redefinition

RGEs in NR models

Feynman diagram

RGEs in NR models

Approximation

neglect (s^3) contributions

dim. tree loop Q-dep.

5 B.C. neg.

6 B.C. neg. neg.

7< neg. neg. neg.

one-step approximation : S. Baek, T. Goto, Y. Okada & K. Okumura (2001)

Plan• Introduction & ConclusionIntroduction & Conclusion• RGEs in renormalizable modelsRGEs in renormalizable models• RGEs in non-renormalizable modelsRGEs in non-renormalizable models• Effective couplingsEffective couplings• Universality of B.C.Universality of B.C.• SummarySummary

Effective couplings

definition

SU(5) example

These can be used also at loop level!

used in the matching to MSSM.

forgotten in some literatures

Effective couplings

Feynman diagram

Anom. dim.s are given as in renormalizable model, by using the effective couplings.

<24H>

<X>

Effective couplings

loop corrections

???

• Note also the running of the VEV.

These holds in general.

ignored in the literatures

Bolzumati & T.Y. (2009)

independent of the Kahler Potential

Effective couplings

flows of VEVs

Field redefinition:

if no vertex corrections :

def. of VEVs:

H

Vacuum structure

general setup

depends on Kahler?

EOM :

independent of Kahler

Effective couplings

loop corrections

• Note also the running of the VEV.

These holds in general.

ignored in the literatures

Bolzumati & T.Y. (2009)

Effective couplings

used approximation

Colored Higgs Yukawa has peculiar contributions,

of (s^2), affecting FVs at (s^3), via add. loop.

remark

does not cancel 1/Mcut (E/Mcut )?

Plan• Introduction & ConclusionIntroduction & Conclusion• RGEs in renormalizable modelsRGEs in renormalizable models• RGEs in non-renormalizable modelsRGEs in non-renormalizable models• Effective couplingsEffective couplings• Universality of B.C.Universality of B.C.• SummarySummary

Universality of B.C.

in MSSM

• The universal B.C. is often used, at a high scale.

How should it be generalized?

field-independence

for each dimensionality?“weak” universality

in non-renormalizable models

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.

strong universality in Kahler potential

The SUSY should couple to the overall potentials.

• # parameters : 3

(apart from the gaugino mass )

minimal SUGRA

Summary

• (s^2) contributions can be controlled.

• We propose (formulate) another treatment via effective coupling is

• We see how universality is generalized.

S. Baek, T. Goto, Y. Okada & K. Okumura (2001)

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.

Cf. N. Arkani-Hamed et.al. (1996), J. Hisano et.al. (1998)

We discuss RGEs in NR models are.

In paper