1. Phenomenological aspects of Generation Twisted Supersymmetric Unification Aug. 30, 2006, SI2006 @ APCTP Kentaro Kojima Department of Physics, Kyushu University Based on Kenzo Inoue, K.K., Koichi Yoshioka, JHEP 0607032; and in preparation Kenzo Inoue, K.K., Koichi Yoshioka, JHEP 0607032; and in preparation

2. 2 SUSY is one of the most promising candidates for TeV scale new physics –solves hierarchy problem in the SM Higgs potential –naturally includes DM candidates –MSSM predicts gauge coupling unification! Supersymmetric GUT is well motivated Neutrino gives important information to the SUSY-GUT very heavy RH neutrinos: SU(3)×SU(2)×U(1) singlets This seems to prefer SO(10) or higher GUT theories But GUTs naively have difficulties about flavor structure

3. 3 Several quarks and leptons are unified into a multiplet: e.g. minimal SU(5) GUT Several types of Yukawa coupling unification are predicted: SU(5) relationSymmetric Yukawa matrices Minimal SO(10) GUT Good for third generation, Completely false for the others; Completely false for the others; SU(5) relation must be modified… SU(5) relation must be modified… Diagonalization matrices Same contributions to CKM and MNS; naively conflict with experimental results Asymmetric matrices are useful… GUTs need nontrivial extensions for the flavor sector Identified to RH ν

4. 4 Contents of the talk SO(10) unification with generation twistingSO(10) unification with generation twisting Third generation fermion masses and sparticle spectrumThird generation fermion masses and sparticle spectrum Radiative EWSB and bottom mass predictionRadiative EWSB and bottom mass prediction b→sγ and τ→μγ processesb→sγ and τ→μγ processes LSP nature and cosmological constraintLSP nature and cosmological constraint Neutralino relic densityNeutralino relic density SummarySummary

5. SO(10) unification with generation twisting

6. 6 hierarchical same order Asymmetric Yukawa matrices seem to be suitable for CKM and MNS in GUTs MSSM+RHν (assuming the seesaw mechanism) SU(5) relaltion Symmetric contribution to Yukawa matrices How can we realize the lopsided forms in SO(10)? But naïve SO(10) GUT cannot accommodate to the asymmetry Highly asymmetric matrices, so-calledlopsided forms, so-called lopsided forms, [Babu, Barr 95]

7. 7 Generation twisting In generally, there are many candidates for SU(5) 5* in SO(10) (or higher as E 6 ) multiplets: e.g. 10+5*+1 5+5* 16 i 10 M... [Sato, Yanagida (98); Bando, Kugo, Yoshioka (99)] SU(2) rotation in E6 Note: Hd ( 5 * H ) should be mixed states of 10 H and others Naturally embedded into E6 GUT 1 27

8. 8 In the following, we consider the scenario where Large top Yukawa coupling mainly comes from Large top Yukawa coupling mainly comes from Difference between CKM and MNS is the result of twisted 5* Difference between CKM and MNS is the result of twisted 5* Small V CKM Large V MNS Lopsided Y d and Y e Twisted 5* structure It is generally difficult to see or test the flavor structure of the GUT since M G is very high. But we may probe into the flavor structure of the GUT through SUSY particle spectrum.

9. Third generation fermion masses and sparticle spectrum

10. 10 Yukawa structure at the GUT scale Considered Yukawa matrices (up to relatively small entries) Nearly maximal atmospheric mixing angle comes from Y e Nearly maximal atmospheric mixing angle comes from Y e The angle θ parametrizes down-type Higgs mixing The angle θ parametrizes down-type Higgs mixing SU(5) relation is modified by SU(5) relation is modified by Includes SU(5) : Contributions to Ye and Yd are different: 1:-1/3 [Georgi-Jarlskog(79)] tanβ is decreased with Increasing θ b-τmass ratio depends on X d

11. 11 Fermion masses in the MSSM In large tanβ, Δb can be very large Depend on SUSY spectrum Sign of μ ⇔ Sign of Δ ｂ (PQ sym. limit) (R sym. limit) [Hall, Rattazzi, Sarid (94); Blazek, Raby, Pokorski (95); Tobe, Wells (03)] << Induced by SUSY (cf. non-renorm. theorem) “Thresholdcorrections”

12. 12 Inclusion of radiative EWSB μ and B are fixed by the following two equations at M SUSY GUT scale SUSY breaking parameters Solving the MSSM (+RHν) RGE

13. 13 IncludesSU(5) SO(10) motivated boundary conditions for SUSY breaking parameters Now, SO(10) representations of the theory are Independent SUSY breaking parameters at the GUT scale: mixed H d

14. 14 Bottom quark mass prediction for different X d green: excluded by b→sγ decay blue: excluded by τ→μγ decay gray: excluded by Higgs mass bound x d = 1 : μ<0, hierarchical spectrum (M 1/2, |μ|<<m 0 ) x d =-1/3: μ>0, hierarchy must be weakened different Xd → different size of Δb→ different sign of μ different sparticle spectrum (X d =1)(X d =-1/3)

15. LSP nature and cosmological constraint

16. 16 Suppression of the neutralino relic density In our scenario, LSP is neutralino; Xd=1 case: R χ can be small R χ can be small (Suppressed μ is consistent with m b ) Contribution tends to be too large Suppressed Xd case: R χ should be nearly 1 R χ should be nearly 1 (only bino-like LSP is allowed) CP-odd Higgs resonance can suppresses the density

17. 17 X d = 1 case X d = 1 case Higgsino-like LSP suppresses Higgsino-like LSP suppresses CP-odd Higgs resonance also suppresses the density, but where correct m b cannot be achieved. CP-odd Higgs resonance also suppresses the density, but where correct m b cannot be achieved. [ Calculated by DarkSUSY ] X d = -1/3 case X d = -1/3 case CP-odd Higgs mass is relatively light and insensitive to m 0 CP-odd Higgs mass is relatively light and insensitive to m 0 Suppression of the density is enough supplied by Suppression of the density is enough supplied by

18. 18 Parameter scan for Xd=1 case: Constraints for bottom mass, b→sγ, superparticle masses are included Relic density has strong correlation with gaugino fraction Higgsino components effectively suppress the density LSP should have negligible higgsino components

19. 19 Parameter scan for Xd=-1/3 case: Constraints for bottom mass, b→sγ, sparticle masses are included The relic density has strong correlation with CP-odd Higgs mass LSP mass should be near the half of the CP-odd Higgs mass: Sizable τ→μγ ratio is expected for relatively light SUSY spectrum; It may be observed near future experimental searches

20. 20 Summary We study low energy remnants of the generation twisting.We study low energy remnants of the generation twisting. Typical sparticle mass spectrum is changed depending on the breaking degree of SU(5) relation,Typical sparticle mass spectrum is changed depending on the breaking degree of SU(5) relation, Future searches of SUSY particles and flavor violations may be the probe into flavor sector of the unified theoryFuture searches of SUSY particles and flavor violations may be the probe into flavor sector of the unified theory : heavy scalars, LSP should have higgsino components : relatively light spectrum is allowed; large LFV ratio; masses of LSP and CP-odd Higgs should be correlated masses of LSP and CP-odd Higgs should be correlated

21. 21

22. Appendix

23. 23 Largely broken SU(5) relation SU(5) relation must be broken to reproduce observed mass pattern of 1 st and 2 nd generation. mass pattern of 1 st and 2 nd generation. In generally the breaking appears in large asymmetrical entries In generally the breaking appears in large asymmetrical entries Even if the 3-3 entries are unified, bottom-tau mass ratio has a large deviation from 1; e.g. a large deviation from 1; e.g. [Georgi, Jarlskog (79); Ellis, Gaillard (79)] due to group-theoretical factor, non-renorm. o.p.

24. 24 Large threshold correction to the bottom mass in large or moderate tanβ regime Δ b can be easily large as O(0.5) for tanβ ～ 50 Sign of μ ⇔ Sign of Δ ｂ (PQ sym. limit) (R sym. limit)

25. 25 Bottom mass prediction without the correction Experimental range tanβ and θ are correlated Input parameters

26. 26 Implications for superparticle spectrum Bottom mass prediction and allowed range of Δ b SU(5) breaking factor x d strong correlation; due to the lopsided Y d Various SUSY spectra are expected depends on x d and θ( tan β) Various SUSY spectra are expected depends on x d and θ ( tan β) e.g. x d =1 μ<0 and relatively hierarchical spectrum are expected for a large value of tanβ x d =-1/3 μ>0 and scalars cannot be much heavier than gauginos and higgsisnos

27. 27 Radiative EWSB conditions Solving the RGE positive D-term reduce the size of μ increasing θ, CP-odd Higgs mass tends to be large at M SUSY

28. 28 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) X d =1 case: Suppressed X d case:

29. 29 Lepton flavor violating process Large 2-3 entry of Y e RGE between induces irreducible 2-3 mixing in the mass matrix for scalar lepton doublet For suppressed Xd case, where relatively light scalars are allowed, sizable B(τ  μγ) is expected D-term contributions amplify non-degeneracy of the scalar leptons: Non-zero D-term contributions enhances B(τ  μγ)

30. 30 X d = 1 case (preliminary) X d = 1 case (preliminary) Higgsino-like LSP suppresses Higgsino-like LSP suppresses The s-channel pole also suppresses the The s-channel pole also suppresses the density, but where correct m b cannot be achieved. density, but where correct m b cannot be achieved. [ Calculated by DarkSUSY ]

31. 31 X d = -1/3 case X d = -1/3 case CP-odd Higgs mass is relatively light and insensitive to m 0 CP-odd Higgs mass is relatively light and insensitive to m 0 Suppression of the density is enough supplied Suppression of the density is enough supplied