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

1. 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）

2. Yukawa LFV Introduction & Conclusion • LFV vs. QFV in SUSY-GUTs RGE Seesaw mechanism F. Borzumati & A. Masiero (1986)

3. Yukawa LFV QFV RGE Introduction & Conclusion • LFV vs. QFV in SUSY-GUTs RGE Seesaw mechanism affected? Baek, Goto, Okada & Okumura (2001) Moroi (2000) Grand Unification realistic?? Fermion Spectra Proton Decay New Physics above GUT

4. Wrong GUT relation: NRO can suppress only Yukawa of . Introduction & Conclusion • Fermion Spectrum affects only 1st & 2nd generations Non-Renormalizable Operators GUT breaking effects • Proton Decay is allowed. D.E. Costa & S. Wiesenfelds (2003)

5. Yukawa LFV QFV Introduction & Conclusion • LFV vs. QFV in SUSY-GUTs RGE Seesaw mechanism affected? RGE Grand Unification Fermion Spectra Proton Decay NROs New Physics above GUT

6. RGE Introduction & Conclusion • How to deal? infinite divergences NRO infinite new operators • Approximation Higher-dim terms : higher suppression by and/or We can neglect the higher terms! S. Baek, T. Goto, Y. Okada & K. Okumura (2001) An O(s^2) analysis was done.

7. MSSM + Introduction & Conclusion • Setup MSSM + … SU(5) w/ NROs • references 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) generalized study with a dim.5 NRO. RGE w/ effective couplings.

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

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

10. RGEs in renormalizable models • general setup field redefinition

11. RGEs in renormalizable models • Feynman rule : propagator field redefinition

12. RGEs in renormalizable models • Feynman diagram

13. RGEs in renormalizable models • corrections field redefinition superpotential terms :

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

15. RGEs in NR models • general setup field redefinition

16. RGEs in NR models • Feynman diagram

17. RGEs in NR models • Approximation neglect O(s^3) contributions one-step approximation : S. Baek, T. Goto, Y. Okada & K. Okumura (2001)

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

19. Effective couplings • definition • SU(5) example forgotten in some literatures used in the matching to MSSM. These can be used also at loop level!

20. Effective couplings • Feynman diagram <24H> <X> Anom. dim.s are given as in renormalizable model, by using the effective couplings.

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

22. H Effective couplings • flows of VEVs Field redefinition: if no vertex corrections : independent of the Kahler Potential def. of VEVs:

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

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

25. 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.

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

27. 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 “weak” universality for each dimensionality?

28. This does not ensure . Universality of B.C. • weak universality • This is not stable under the field redefinition to minimize the Kahler potential :

29. Universality of B.C. • weak universality

30. Universality of B.C. • strong universality

31. This does ensure ! Universality of B.C. • strong universality in superpotential

32. Universality of B.C. • strong universality in Kahler potential impose this minimized by the field redefinition w/

33. The SUSY should couple to the overall potentials. Universality of B.C. minimal SUGRA • strong universality in Kahler potential # parameters : 3 (apart from the gaugino mass )

34. Summary • We discuss RGEs in NR models are. • O(s^2) contributions can be controlled. • We propose (formulate) another treatment via effective couplingis • 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.