Phenomenology of Generation Twisted SUSY-GUT

1. July 31, 2006, PPP2006 @ YITP Kentaro Kojima Department of Physics, Kyushu University Phenomenology of Generation Twisted SUSY-GUT Collaborate with Kenzo Inoue, Koichi Yoshioka

2. Contents of the talk • Introduction • SO(10) unification with twisted generation structure • Fermion masses and radiative electroweak symmetry breaking • Phenomenological implications • Summary

3. Introduction

4. Key to the SUSY and GUT: neutrino • Tiny mass scale: • Large generation mixing angles in the lepton sector ? (bi-)large mixing VMNS (all) small mixing VCKM naively conflict with GUT (quark-lepton unification) Several models have been proposed focusing on fermion mass structure It is not sufficient in large/moderate tanβ : fermion masses strongly depends on sparticle spectrum

5. Radiative EWSB Sparticle spectrum Threshold corrections • B.C. for soft terms • Soft mass renormalization evolution Fermion masses Fermion mass structure with ν GUT models Important for moderate or large tanβ Radiative EWSB should be examined with neutrino properties We examined radiative EWSB and phenomenological constraints including neutrino properties in SO(10) scenario, where tanβ naturally takes large values.

6. SO(10) unification with twisted generation

7. MSSM+RHν(assuming the seesaw mechanism) VCKMversus VMNS in GUT hierarchical SU(5) realtion Highly asymetric, so-called lopsided forms same order [Babu, Barr 95] Symmetric contribution to Yukawa matrices Non-trivial extension is needed to explain the asymmetry

8. Twisted flavor structure In generally, there are many candidates for SU(5) 5* in SO(10) (or higher as E6) multiplets: We are naturally led to the case that 5* ’s in each generation does not hold parallelism between these SO(10) origins. twisted 5* Naturally explain large 2-3 asymmetric coupling e.g. contribute to VMNS; contribute to VCKM; [Sato, Yanagida. (98), Bando, Kugo, Yoshioka (99)]

9. Small VCKM Large VMNS In the following, we consider the SO(10) scenario where • Large top Yukawa coupling mainly comes from • Observed flavor structure is the result of twisted 5* Twisted 5* structure Lopsided Yd and Ye

10. Fermion masses and radiative electroweak symmetry breaking

11. The angle θ parametrizes 5* Higgs twisting • Nearly maximal atmospheric mixing angle comes from Ye Yukawa structure at the GUT scale Considered Yukawa matrices (up to relatively small entries) • SU(5) relation is modified by Includes SU(5)

12. Fermion masses in the MSSM Depend on SUSY spectrum In large tanβ, Δb can easily be large as [Hall, Rattazzi, Sarid (94); Blazek, Raby, Pokorski (95)] Sign of μ　⇔　Sign of Δｂ (PQ sym. limit) (R sym. limit)

13. Bottom mass prediction without the correction tanβ and θ are correlated Input parameters Experimental range

14. Implications for superparticle spectrum Bottom mass prediction and allowed range of Δb strong correlation; due to the lopsided Yd SU(5) breaking factor xd Various SUSY spectra are expected depends on xd and θ(tanβ) e.g. μ<0 and relatively hierarchical spectrum are expected for a large value of tanβ xd=1 μ>0 and scalars cannot be much heavier than gauginos and higgsisnos xd=-1/3

15. Inclusion of radiative EWSB μ andB are fixed by the following two equations at MSUSY GUT scale SUSY breaking parameters Solving the MSSM (+RHν)RGE

16. SO(10) motivated boundary conditions for SUSY breaking parameters To fix GUT scale SUSY breaking parameters, we consider explicit model: Independent SUSY breaking parameters at the GUT scale: Includes SU(5) Remant of mixed Hd

17. Radiative EWSB conditions at MSUSY Solving the RGE • positive D-term reduce the size of μ • increasing θ, CP-odd Higgs mass tends to be large

18. Bottom quark mass prediction green: excluded by b→sγ decay blue: excluded by τ→μγ decay gray: excluded by Higgs mass bound for xd=1 case, μ should be more suppressed and scalars should be heavier than for xd=-1/3 case

19. Phenomenological implications • b  s γ decay • τ μγ decay • neutralino relic density

20. Xd=1 case: Suppressed Xd case: b  s γ rare decay process When tanβ is not small, three diagrams give important contributions: Consistent with exp. The both must be suppressed or Each of them must be canceled out (allowed only for μ>0; suppresed Xd case)

21. Lepton flavor violating process RGE between induces irreducible 2-3 mixing in the mass matrix for scalar lepton doublet Large 2-3 entry of Ye D-term contributions amplify non-degeneracy of the scalar leptons: Non-zero D-term contributions enhances B(τμγ) For suppressed Xd case, where relatively light scalars are allowed, sizable B(τμγ) is expected

22. Neutralino relic density In our scenario, LSP is neutralino; Contribution tends to be too large Xd=1 case: Rχ can be small (small μ is consistent with mb) Suppressed Xd case: Rχ should be nearly 1. s-channel pole can suppresses the density

23. Xd = 1 case (preliminary) [Calculated byDarkSUSY] • Higgsino-like LSP suppresses • The s-channel pole also suppresses the • density, but where correct mb cannot be achieved.

24. WMAP result 3000GeV, 400GeV 4000GeV, 400GeV 3000GeV, 500GeV 4000GeV, 500GeV the lightest neutralino should have negligible higgsino component Relatively large m0 is required by b→sγ, this suppresses τ→μγ θ，D are scanned for Xd = 1. Experimental constraints for bsγ, bottom mass, Higgs mass, and sparticle masses are included.

25. Xd = -1/3 case • CP-odd Higgs mass is relatively light and insensitive to m0 • Suppression of the density is enough supplied

26. θ，D are scanned for Xd = -1/3. Experimental constraints for bsγ, fermion masses, higgs masses, and sparticle masses are included. WMAP result Current exp. bound 700GeV, 400GeV 1000GeV, 400GeV WMAP result 700GeV, 600GeV 1000GeV, 600GeV • The relic density have strong correlation to with CP-odd Higgs mass • Sizable lepton flavor violation is expected for relatively light SUSY spectrum

27. : heavy scalars, higgsino-like lightest neutralino : relatively light spectrum is allowed; large LFV ratio; masses of LSP neutralino and CP-odd Higgs are correlated Summary • We studied phenomenological aspects of the SO(10) scenario where 5*’s of SU(5) have generation twisting. • Typical sparticle mass spectrum is dramatically changed depending on the breaking degree of SU(5) relation, • Future collider experiments and flavor violation searches may reveal the validity of the scenario

29. Largely broken SU(5) relation • SU(5) relation must be broken to reproduce observed • mass pattern of 1st and 2nd generation. • In generally the breaking appears in large asymmetrical entries [Georgi, Jarlskog (79); Ellis, Gaillard (79)] • Even if the 3-3 entries are unified, bottom-tau mass ratio has • a large deviation from 1; e.g.

30. Bottom quark mass Bottom mass and threshold corrections In the following we take c= -1/3 as an explicit example. Δb should be positive and sizable • Positive sign of μ • Approximate PQ and R sym. are • weaker than the previous case

31. Sizable Δb is needed • Compared to the previous case: • opposite sign of μ: μ>0 • size of μ should not much • suppressed • relatively light spectrum is allowed Bottom quark mass value small |μ| stau LSP

32. Asymmetrical Yukawa matrices modified

33. g’s and h’s are dimension less functions of Input parameters, which characterizes the dependence on GUT scale SUSY parameters Radiative EWSB conditions Solving the RGE

34. scalar mass is marginal • small cosθ easily rise MA • M1/2 rises |μ| • positive D lowers |μ| Small cosθ and D>0 make PQ and R symmetric REWSB possible Favored by fermion mass spectrum

35. Bottom quark mass Small cosθ　⇒　μ<0, lower tanβ, For large/moderate tanβ　⇒　 Δbshould be suppressed Approximately PQ and R symmetric spectrum is favored

36. Supersymmetric extension of the Standard Model is one of the most attractive candidates for TeV scale physics: Mass scale of the Higgs potential (weak scale) is stabilized against quantum corrections. Minimal supersymmetric extension: MSSM Gauge coupling unification, SUSY-GUT In this work, we focused on neutrino properties, and examined radiative electroweak symmetry breaking in SUSY-SO(10) unified scenarios. Obtained sparticle spectra have distinctive features. We discuss various phenomenological implications.

37. Some high energy scale (depending on the mediation of SUSY breaking) Typical SUSY breaking mass scale (considered to TeV scale) RG evolution Sparticle spectrum and radiative EWSB Correct EWSB can radiatively occur • Boundary conditions for SUSY breaking parameters • RG evolution of SUSY breaking parameters tightly connected with sparticle spectrum

38. “Lopsided ’’ forms of Yukawa matrices VCKM VMNS hierarchical so-called lopsided forms same order contribute to VMNS; contribute to VCKM;

39. PQ and R symmetric limit In the R symmetric limit (M1/2, A0 → 0), PQ symmetry is achieved with Then MA takes are consistent with PQ, R symmetric Radiative ElectroWeak Symmetry Breaking

40. Bottom quark mass value ex. by too samll MA^2 ex. by too samll |μ|^2 ex. by Stau LSP |μ| cannot be small. Large m0/M1/2 suppressΔb Approximate PQ and R symmetric SUSY spectrum suppress Δb

41. WMAP result Current exp. bound 700GeV, 400GeV 1000GeV, 400GeV WMAP result 700GeV, 600GeV 1000GeV, 600GeV Modified SU(5) case (preliminary) • Large 2-3 mixing in Ye • Relatively light sparticle spectrum Sizable lepton flavor violating decay rate

42. Fermion masses Sparticle spectrum Fermion masses strongly depend on sparticle spectrum through the potentially large threshold correction Large threshold correction to the bottom massin large or moderate tanβ regime • Δb can be easily large as O(0.5) for tanβ～50

43. ? Key to the GUT: neutrino • Tiny mass scale: • Large generation mixing angles in the lepton sector

44. Impacts on GUT physics • Fermion mass structure small mixing angles in the quark sector bi-large mixing angles in the lepton sector • Neutrino Yukawa contribution to RGE • Yukawa coupling unification • bottom-tau mass ratio • top-bottom-tau Yukawa unification • Gauge coupling unification (2-loop order) naively conflict with GUT (quark-lepton unification)

45. Bottom quark mass value small |μ| small MA Stau LSP Stau LSP |μ| cannot be small. Large m0/M1/2 suppressΔb Approximate PQ and R symmetric SUSY spectrum suppress Δb

46. Yukawa structure at the GUT scale Considered Yukawa matrices (up to relatively small entries) SU(5) symmetric case SU(5) asymmetric case

47. RG contributions • Gauge coupling unification (2-loop order) • bottom-tau Yukawa unification • lepton flavor violation • … (bi-)large mixing VMNS (all) small mixing VCKM naively conflict with GUT (quark-lepton unification) Several models have been proposed focusing on fermion mass structure Key to the GUT: neutrino • RH neutrinos and neutrino Yukawa coupling • Fermion mass structure

48. Radiative Electroweak Symmetry Breaking To fix GUT scale SUSY breaking parameters, we consider explicit model: Independent SUSY breaking parameters at the GUT scale: Universal scalar mass parameter RG contribution between Mpl to MG Universal gaugino mass parameter Trilinear soft mass parameter D-term contributions arise in SO(10)→SU(5)×U(1) Higgs quadratic coupling

49. Fermion masses Sparticle spectrum Fermion masses strongly depend on sparticle spectrum through the potentially large threshold correction Large threshold correction to the bottom massin large or moderate tanβ regime • Δb can be easily large as O(0.5) for tanβ～50