E 6 GUT Models and FCNC Processes

1. E6 GUT ModelsandFCNC Processes with S-G.Kim, N.Maekawa, A.Matsuzaki, T.Yoshikawa (Nagoya Univ.) Kazuki Sakurai Plan I. Introduction II. E6 GUT and Horizontal Symmetry III. Search for E6×Horizontal GUT -- Lepton Flavor Violation -- CPA in rare B meson decay IV. Summary 2007/8/4 SI07@Fujiyoshida

2. Problems in MSSM Supersymmetry is promising candidates of New Physics.However they have some phenomenological problems. Universal sfermion masses SUSY Flavor Problem Generally, SUSY breaking terms brake flavor symmetry. They generate too large FCNCs. Large SUSY breaking scale SUSY CP Problem Suppressed SUSY CP phases Generally, couplings in SUSY breaking terms are complex. Such couplings violate CP and induce too large EDMs. Large SUSY breaking scale Little Hierarchy Problem Up-type Higgs mass get a large quantum correction which proportional to stop mass. Not large stop masses

3. SU(2)H invariance forbid Yukawa interactions in tree level except for top Yukawa. in SO(10), E6 SU(2)H breaking effect generate first two generation Yukawa couplings through higher dimensional terms. SU(2)H Horizontal sym. can explain smallness of Yukawa couplings!! Horizontal Symmetry Flavor symmetry is natural idea, in order to realize the universal sfermion masses. First two generations are identified as SU(2)H (or U(2)H) doublet. Third generation is singlet. :singlet :doublet If SUSY breaking mediation scale is higher than SU(2)H breaking scale, SUSY breaking terms should respect the SU(2)H symmetry. Universality in first two generations is realized due to SU(2)H!!

4. Horizontal Symmetry However, if is lepton doublet… In mass eigenstate basis of fermion, Neutrino oscillation suggest is large mixing. Therefore large off-diagonal entries arise after this unitary transformation. Such large off-diagonal entries induce too large Lepton Flavor Violation.

5. decouple Low energy three5(Dc L) of SU(5) comefrom only first two generation of27not273. Guisey-Ramond-Sikivie, Aichiman-Stech, Shafi, Barbieri-Nanopoulos, Bando-Kugo,… E6 Unification E6 GUT models are interesting, because… -- all one generation quarks leptons are unified into 27. -- realistic Yukawa hierarchies are obtained.

6. up sector: decouple Low energy three5(Dc L) of SU(5) comefrom only first two generation of27not273. Guisey-Ramond-Sikivie, Aichiman-Stech, Shafi, Barbieri-Nanopoulos, Bando-Kugo,… E6 Unification E6 GUT models are interesting, because… -- all one generation quarks leptons are unified into 27. -- realistic Yukawa hierarchies are obtained. Cabibbo angle

7. decouple Guisey-Ramond-Sikivie, Aichiman-Stech, Shafi, Barbieri-Nanopoulos, Bando-Kugo,… E6 Unification E6 GUT models are interesting, because… -- all one generation quarks leptons are unified into 27. -- realistic Yukawa hierarchies are obtained. up sector: down & charged lepton: Cabibbo angle Low energy three5(Dc L) of SU(5) comefrom only first two generation of27 not273.

8. decouple Guisey-Ramond-Sikivie, Aichiman-Stech, Shafi, Barbieri-Nanopoulos, Bando-Kugo,… E6 Unification E6 GUT models are interesting, because… -- all one generation quarks leptons are unified into 27. -- realistic Yukawa hierarchies are obtained. up sector: down & charged lepton: neutrino sector: Cabibbo angle Low energy three5(Dc L) of SU(5) comefrom only first two generation of27 not273.

9. N.Maekawa. 02, N.Maekawa, T.Yamashita 04 Horizontal Symmetry on E6

10. Since contain lepton doublet, Neutrino oscillation suggest is large mixing. No LFV problem due to full universality in !! In above sfermion masses, we can take large SUSY breaking scale with keeping stop masses around weak scale, because correspond to stop masses. N.Maekawa. 02, N.Maekawa, T.Yamashita 04 Horizontal Symmetry on E6

11. Problems in MSSM Some problems in MSSM can be solved in E6×Horizontal GUT models!! SUSY and GUT are promising candidate of New Physics.However they have some phenomenological problems. Universal sfermion masses SUSY Flavor Problem SUSY breaking terms brake flavor symmetry generally. They generate too large FCNCs. Large SUSY breaking scale SUSY CP Problem Suppressed SUSY CP phases SUSY breaking terms have complex coupling. Such couplings violate CP and induce too large CPV observables (EDMs,...). Large SUSY breaking scale Little Hierarchy Problem Up-type Higgs mass get a large quantum correction which proportional to stop mass. Not large stop masses

12. [ Strategy ] It is expected that FCNC processes become large through the sfermions in 10 of SU(5). Lepton Flavor Violation, CP asymmetries in B meson decay Search for E6×Horizontal GUT Next question is, how can we confirm this model experimentally?

13. Lepton Flavor Violation

14. e Left-handed Right-handed e Lepton Flavor Violation Lepton Flavor Violations (LFVs) are good process for search the New Physics, because LFV processes are forbidden in Standard Model. In E6 models, LFV processes take place with picking up the off-diagonal entries respectively. We can get parameter independent prediction, Since 10 of SU(5) contain not , final state lepton have right-handed chirality. We can check this by measuring angular distribution of final state lepton. spin + + spin + +

15. MEG experiment S.-G.Kim, N.Maekawa, A.Matsuzaki, K.S, T,Yoshikawa ‘06 Can we discover the LFVs at future experiments? (exp. bound) (exp. bound) super-KEKB may be discovered in KEKB or super-KEKB, If < 250GeV. may be discovered in MEG, If < 300GeV.

16. CP asymmetries in rare B meson decay

17. In SM, CP violation is contained in only B-Bbar mixing part through a KM phase. gluino: SM predictions may deviate from experiments. chargino: SUSY CP phase can contribute in direct decay parts. So, current deviations may be explained. in this model. 0.68 (SM prediction) Gluino and Chargino are always interfere with same sign! CP asym. of BφKs, Bη’Ks Time dependent CP asymmetry of BφK, Bη’K are composed of two part, B-Bbar mixing part and direct decay part.

18. (preliminary) Numerical Results total total chargino chargino gluino(C8) gluino(C8) gluino(C3-6) gluino(C3-6) Deviations from SM can be large(~±0.15)!!

19. E6×Horizontal GUT models suggest that current deviations can be true! (preliminary) Numerical Results Scanning in SUSY CP phase

20. Summary E6×Horizontal GUT models can solve some problems in MSSM. We analyze the Lepton Flavor Violations. Parameter independent predictions Final state lepton have right-handed chirality. There are large parameter region in which LFV decays can be discovered in near future experiments. < 250 GeV KEKB or super-KEKB < 300 GeV MEG experiment We analyze the CP asymmetry in rare B decays. Gluino and chargino always interfere with same sign, which makes CPA large enough to be able to detect in future experiments. Deviations from SM of Time Dependent CP Asymmetry of Bdφ,η’ Ks:

21. finite decoupling non decoupling (preliminary) Numerical Results total total chargino chargino gluino(C8) gluino(C8) gluino(C3-6) gluino(C3-6) chargino: gluino(C8): Deviations from SM can be large(~±0.15) and non decoupling for m !!

22. Neutrinos Right-handed neutrino masses: Seasaw mechanism: Mass scale: decouple

23. e Left-handed Right-handed e Lepton Flavor Violation Lepton Flavor Violations (LFVs) are good process for search the New Physics, because LFV processes are forbidden in Standard Model. In E6 models, LFV processes take place through the off-diagonal entries respectively. We can get parameter independent prediction, Since 10 of SU(5) contain not , final state lepton have right-handed chirality. We can check this by measuring angular distribution of final state lepton. spin + + spin + +

24. Propagator suppression increase, but also mass difference increase. As a result, both transition rate remain finite, and don’t decouple! Non Decoupling Features If we raise overall SUSY scale m …

25. e Right-handed Left-handed e Characteristic Feature of Decay Chirality flip is required from operator form. Chirality flip take place at first vertex and intermediate state is right-handed.initial lepton=left-handed,final lepton=right-handed spin spin We can check this feature experimentally by measuring the angular distribution of final state lepton for spin direction of initial lepton.

26. Numerical Results Non decoupling features In > 800 GeV region, the Branching ratios are independent of .

27. Time Dependent CP Asymmetry

28. (SUSY) Bd φKs, η’Ks Loop = SM +NP SM (>>SUSY 31 transition.)

29. … OPE

30. Gluino-Chargino Interference Gluino: Chargino: = • Chargino contribution have a same CP phase as gluino’s one. • Strong interference (additive or negative)

31. (preliminary) Numerical Results

32. bsγ constrant Chargino with θSUSY Chargino with CKM Charged Higgs b  sγ constraint requires large SUSY phase.

33. decouple decouple at low energy: Guisey-Ramond-Sikivie, Aichiman-Stech, Shafi, Barbieri-Nanopoulos, Bando-Kugo,… E6 GUT Symmetry Breaking: Fields and Rep.: E6 GUT: MSSM: generation

34. E6 × R parity invariant interactions : SM interactions assumption

35. down charged lepton M.Bando, N.Maekawa. 01 N.Maekawa, T. Yamashita 02 E6 GUT assumption up sector Good :for up sector due to the assumption Bad :for down and charged lepton sectors Desired Yukawa structures are obtained in E6 GUT model !!

36. Up quark mass ? Models: Experiments: eigenvalues Disagreement !? Naïve order of up quark mass is larger than the experimental value about 10.

37. Im Exp. Bounds require < 10-2 . FCNC induced EDM finite Non decoupling !

39. Gauge invariant Interactions SU(5) invariant Yukawa interactions : SU(5) GUT relations : Not Bad at GUT scale (1016GeV)

40. : SO(10) spinor : SO(10) vector SO(10) invariant interaction : SO(10) GUT relation : : at GUT scale SO(10) GUT SU(5) representations: Grand Unified Theories unify not only the forces but also matters and interactions !!