Probing flavor structure in unified theory with scalar spectroscopy

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.) Based on K. Inoue (Kyushu univ.), K. K, and K. Yoshioka (Kyoto univ.) [arXiv:hep-ph/0703253] “Probing flavor structure in unified theory with scalar spectroscopy”

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

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

4. Contents • Introduction • Matter embedding into grand unified models • Probing unified flavor structure with scalar spectroscopy • Summary and Discussions

5. Generation redundancy for anti-decouplets Generation redundancy in GUT models Successful gauge coupling unification in MSSM However, matter unification is not simply realized naively conflict with quark-lepton unification • CKM vs. MNS: • 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

6. generation twist angles for φi and have same charge, but have different charge Generation redundancy and induced scalar non-degeneracy Above the GUT scale, generation dependent scalar non-degeneracy is induced through GU/G SM gauge interaction D-term of broken gauge sym. b.c. at a high-scale RG induced effects generation dependent!!

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

8. Contents • Introduction • Matter embedding into grand unified models • Probing unified flavor structure with scalar spectroscopy • Summary and Discussions

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

10. Probing into unified flavor structure with scalar spectroscopy • D-term dominated case • General case scalar non-degeneracy ⇒ non-trivial generation twisting A key ingredient of flavor origin in unified theory

11. Contents • Introduction • Matter embedding into grand unified models • Probing unified flavor structure with scalar spectroscopy • Summary and Discussions

12. Summary generation dependent matter embedding into GUT multiplets and scalar non-degeneracy is induced through gauge interactions aboveMG different GU/GSM interaction near future experiments: superparticle spectrum TeV scale observables high energy physics MSSM scalar masses generation twisting angles: Origin of flavor in unified theory

13. Discussion: Implications from FCNC constraints non-degenerate scalars ⇒ superparticle mediated flavor violation would be large 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. generation twisting andlarge 2nd and 3rd 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

16. appendix

18. Relation between observations and twist angles e.g. GU=E6: 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 gauge dependent MSSM RG effects are canceled out • negligible for small tanβ • numerically calculable

19. Lepton flavor violating process RGE between induces large 2-3 mixing in slepton mass matrices Large 2-3 entry of Ye Relatively light sparticle spectrum leads sizable B(τμγ)