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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: [hep-ph] with F. Borzumati （台湾国立大学）
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Introduction & Conclusion
LFV vs. QFV in SUSY-GUTs LFV RGE Yukawa Seesaw mechanism F. Borzumati & A. Masiero (1986)
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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
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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)
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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
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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)
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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.
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Introduction & Conclusion
: not affected leading effect : superCKM basis approximation : S. Baek et.al. (2001) P.Ko, J.h.Park & M.Yamaguchi (2008)
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Plan Introduction & Conclusion RGEs in renormalizable models
RGEs in non-renormalizable models Effective couplings Universality of B.C. Summary
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RGEs in renormalizable models
general setup field redefinition
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RGEs in renormalizable models
Feynman rule : propagator field redefinition
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RGEs in renormalizable models
Feynman diagram
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RGEs in renormalizable models
corrections field redefinition superpotential terms :
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Plan Introduction & Conclusion RGEs in renormalizable models
RGEs in non-renormalizable models Effective couplings Universality of B.C. Summary
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RGEs in NR models general setup field redefinition
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RGEs in NR models Feynman diagram
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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)
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Plan Introduction & Conclusion RGEs in renormalizable models
RGEs in non-renormalizable models Effective couplings Universality of B.C. Summary
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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!
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Effective couplings Feynman diagram
<24H> <X> Anom. dim.s are given as in renormalizable model, by using the effective couplings.
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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.
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Effective couplings flows of VEVs Field redefinition: def. of VEVs:
if no vertex corrections : independent of the Kahler Potential def. of VEVs: H
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Vacuum structure general setup independent of Kahler
depends on Kahler? EOM :
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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.
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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.
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Plan Introduction & Conclusion RGEs in renormalizable models
RGEs in non-renormalizable models Effective couplings Universality of B.C. Summary
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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?
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Universality of B.C. weak universality This does not ensure .
This is not stable under the field redefinition to minimize the Kahler potential :
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Universality of B.C. weak universality
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Universality of B.C. strong universality
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Universality of B.C. strong universality in superpotential
This does ensure !
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Universality of B.C. strong universality in Kahler potential
impose this minimized by the field redefinition w/
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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 )
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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.
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