1. Probing flavor structure in unified theory with scalar spectroscopy June 21, 2007, Supersymmetry in 2010’s @Conference Hall, Hokkaido University Kentaro Kojima (Kyushu univ.) K. Inoue (Kyushu univ.), K. K, and K. Yoshioka (Kyoto univ.) [arXiv:hep-ph/0703253] “Probing flavor structure in unified theory with scalar spectroscopy” Based on

2. Supersymmetry in 2010’s, K. Kojima 2Introduction Terascale direct searches in near future experiments: LHC, ILC, … Discovery of Superparticles SUSY breaking SUSY breaking Grand Unified Theory Grand Unified Theory Origin of flavor Origin of flavor ・・・ ・・・ e.g. GUT relation for gaugino masses Next step is: Terascale rich observables Higgs particle spectrum Superparticle spectrum SUSY induced flavor ・・・ Extremely high-energy underlying theory scalar mass spectrum Indirectprobe

3. Supersymmetry in 2010’s, K. Kojima 3 MSSM Scalar mass spectrum with universal hypotheses Generation independent negligible for i =1, 2 highly degenerate 1 st and 2 nd generation scalars highly degenerate 1 st and 2 nd generation scalars suppression of sparticle-mediated FCNC contributions suppression of sparticle-mediated FCNC contributions e.g. CMSSM, mSUGRA, etc, … However, non-degenerate spectrum may be discovered b.c. at a high-scale RG induced effects Terascale observables non-degeneracy of MSSM scalar masses high energy physics flavor structure in unified theory D-term of broken gauge sym.

4. Supersymmetry in 2010’s, K. Kojima 4Contents Introduction Introduction Matter embedding into grand unified models Matter embedding into grand unified models Probing unified flavor structure with scalar spectroscopy Probing unified flavor structure with scalar spectroscopy Summary and Discussions Summary and Discussions

5. Supersymmetry in 2010’s, K. Kojima 5 Generation redundancy in GUT models Successful gauge coupling unification in MSSM However, matter unification is not simply realized CKM vs. MNS: CKM vs. MNS: naively conflict with quark-lepton unification Yukawa (mass) unification: Yukawa (mass) unification: possible only for third generation an available approach: un-parallel generation structure [Sato, Yanagida, Nomura, Bando, Kugo, maekawa, et. al] generation dependent matter embedding into GUT multiplets Generation redundancy for anti-decouplets

6. Supersymmetry in 2010’s, K. Kojima 6 Generation redundancy and induced scalar non-degeneracy generation twist angles for φ i different charge have same charge, but have different chargeand Above the GUT scale, generation dependent scalar non-degeneracy is induced through gauge interaction is induced through G U /G SM gauge interaction generation dependent!! b.c. at a high-scale RG induced effects D-term of broken gauge sym.

7. Supersymmetry in 2010’s, K. Kojima 7 D-term corrections D-term corrections [Drees, ’86; Kawamura, Murayama, Yamaguchi, ‘94] multiple D-term correction is spanned by Cartan generators of RG effects above the GUT scale RG effects above the GUT scale [Kawamura, Murayama, Yamaguchi, ‘94, Polonsky, Pomarol, ‘95] (no intermediate scales) characterized by quadratic Casimir invariant induced scalar non-degeneracy is directly connected to G U /G SM charges, which is parametrized by θ i Twist angles can be probed with the observed non-degeneracy

8. Supersymmetry in 2010’s, K. Kojima 8Contents Introduction Introduction Matter embedding into grand unified models Matter embedding into grand unified models Probing unified flavor structure with scalar spectroscopy Probing unified flavor structure with scalar spectroscopy Summary and Discussions Summary and Discussions

9. Supersymmetry in 2010’s, K. Kojima 9 Relations between observables and twist angles three 27-plets as the fundamental matter multiplets (SU(5) decomposition) RHS: observables RHS: observables independent of high-energy mass parameters Dominant U(1) X D-term case Dominant U(1) X D-term case (MSSM gauge dependent RG effects) General case (including D-term corrections and RG effects) General case (including D-term corrections and RG effects) Yukawa dependent MSSM RG effects negligible for small tanβnegligible for small tanβ numerically calculablenumerically calculable

10. Supersymmetry in 2010’s, K. Kojima 10 Probing into unified flavor structure with scalar spectroscopy D-term dominated case D-term dominated case General case General case scalar non-degeneracy ⇒ non-trivial generation twisting A key ingredient of flavor origin in unified theory

11. Supersymmetry in 2010’s, K. Kojima 11Contents Introduction Introduction Matter embedding into grand unified models Matter embedding into grand unified models Probing unified flavor structure with scalar spectroscopy Probing unified flavor structure with scalar spectroscopy Summary and Discussions Summary and Discussions

12. Supersymmetry in 2010’s, K. Kojima 12Summary near future experiments: superparticle spectrum generation dependent matter embedding into GUT multiplets different G U /G SM interaction and scalar non-degeneracy is induced through gauge interactions above M G TeV scale observables MSSM scalar masses high energy physics generation twisting angles: Origin of flavor in unified theory

13. Supersymmetry in 2010’s, K. Kojima 13 Discussion: Implications from FCNC constraints non-degenerate scalars ⇒ superparticle mediated flavor violation would be large slepton mediated flavor violation ⇒ slepton mediated flavor violation ⇒ diagonalizes Ye constraints from FCNC processes rather depend on the forms of Yukawa matrices generation twisting is consistent with FCNC

14. Supersymmetry in 2010’s, K. Kojima 14 generation twisting andlarge 2 nd and 3 rd generation mixing in charged lepton sector enhance τ → μγ process as reachable in near future experiments generation twisting and large 2 nd and 3 rd generation mixing in charged lepton sector enhance τ → μγ process as reachable in near future experiments In general, generation twisting enhances FCNC processes and flavor violation searches may give us implication of generation twisting

15. Supersymmetry in 2010’s, K. Kojima 15

16. Supersymmetry in 2010’s, K. Kojima 16appendix

17. Supersymmetry in 2010’s, K. Kojima 17

18. Supersymmetry in 2010’s, K. Kojima 18 Relation between observations and twist angles three 27-plets as the fundamental matter multiplets e.g. G U =E 6: three 27-plets as the fundamental matter multiplets (SU(5) decomposition) Dominant U(1) X D-term case Dominant U(1) Z D-term case General case (including D-term corrections and RG effects) Yukawa dependent MSSM RG effects negligible for small tanβ numerically calculable gauge dependent MSSM RG effects are canceled out

19. Supersymmetry in 2010’s, K. Kojima 19 Lepton flavor violating process Large 2-3 entry of Y e RGE between induces large 2-3 mixing in slepton mass matrices Relatively light sparticle spectrum leads sizable B(τ  μγ)