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 affected? RGE Baek, Goto, Okada & Okumura (2001) Moroi (2000) Grand Unification QFV realistic?? Fermion Spectra Proton Decay New Physics above GUT

Introduction & Conclusion Fermion Spectrum affects only 1st & 2nd generations Wrong GUT relation: Non-Renormalizable Operators 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 affected? RGE Grand Unification QFV Fermion Spectra Proton Decay NROs New Physics above GUT

Introduction & Conclusion How to deal? NRO infinite divergences 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 + … SU(5) w/ NROs references MSSM + 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) Bolzumati & T.Y. (2009) study with a dim.5 NRO. generalized RGE w/ effective couplings.

Introduction & Conclusion : not affected leading effect : superCKM basis approximation : S. Baek et.al. (2001) P.Ko, J.h.Park & M.Yamaguchi (2008)

Plan 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 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. neg. 6 7< one-step approximation : S. Baek, T. Goto, Y. Okada & K. Okumura (2001)

Plan Introduction & Conclusion RGEs in renormalizable models RGEs in non-renormalizable models Effective couplings Universality of B.C. Summary

forgotten in some literatures 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.

ignored in the literatures 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: def. of VEVs: if no vertex corrections : independent of the Kahler Potential def. of VEVs: H

Vacuum structure general setup independent of Kahler depends on Kahler? EOM :

ignored in the literatures Effective couplings loop corrections ignored in the literatures Note also the running of the VEV. Bolzumati & T.Y. (2009) These holds in general.

O(E/Mcut )? Effective couplings used approximation remark 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 Introduction & Conclusion RGEs in renormalizable models RGEs in non-renormalizable models Effective couplings Universality of B.C. Summary

Universality of B.C. in MSSM in non-renormalizable models The universal B.C. is often used, at a high scale. in non-renormalizable models How should it be generalized? field-independence “weak” universality for each dimensionality?

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