Nobuhiro Maekawa Nagoya Univ KMI with M Ishiduki

Nobuhiro Maekawa (Nagoya Univ. KMI) with M. Ishiduki, S. -G. Kim, K. Sakurai, K. I. Nagao, M. M. Nojiri, H. Kawase, T. Takayama

Grand Unified Theories u Unification of gauge interactions quantitative evidence: Non SUSY GUT u Unification of matters qualitative evidence: have stronger hierarchy than hierarchies of masses and mixings lepton >>quark (in hierarchies for mixings) ups >> downs, electrons >> neutrinos (in mass hierarchies)

Masses & Mixings and GUT u, c, t Strongest Neutrinos Weakest e, μ，τ　　Middle d, s, b Middle CKM small mixings MNS large mixings These can be naturally understood in SU(5) GUT!!

SU(5) SUSY GUT Albright-Barr Sato-Yanagida… have stronger hierarchy than Stronger hierarchy leads to smaller mixings Quark mixings(CKM) Lepton mixing(MNS)

Mass hierarchy and mixings u Stronger hierarchy leads to smaller mixings Stronger hierarchy Smaller mixings

SU(5) SUSY GUT have stronger hierarchy than Stronger hierarchy leads to smaller mixings Quark mixings(CKM) Lepton mixing(MNS) Good agreement with masses & mixings

u

Ｕｎｉｆｉｃａｔｉｏｎ Guisey-Ramond-Sikivie, Aichiman-Stech, Shafi, Barbieri-Nanopoulos, Bando-Kugo, … Three of six become superheavy after the breaking Once we fix , three light modes of six are determined. We assume all Yukawa matrices

Milder hierarchy for Bando-N. M. 01 N. M, T. Yamashita 02 u fields from become superheavy. Superheavy unless Light modes have smaller Yukawa couplings and milder hierarchy than u Suppressed radiative LFV

u

Modified universal sfermion masses

LHC signatures Kim-N. M. -Nagao-Nojiri-Sakurai 09 Sakurai-Takayama 11 u

7 Te. V LHC with low luminosity u

Summary table of E 6 predictions Kim-N. M. -Matsuzaki-Sakurai-Yoshikawa 06, 08 SM E 6 O(0. 04) O(0. 006) 　 <0. 15 0. 006 <0. 01 very small

Old and new type SUSY CP problems can be solved and several bonuses

SUSY CP Problem Old type u EDM constraints => Real SUSY parameters. problem must be solved is solved by anomalous U(1) u Complex Yukawa couplings => CEDM New type Hisano-Shimizu 04 Griffith et. al. 09 in E 6 GUT with SU(2) Complex Yukawa => is complex generically Additional (discrete) symmetry solves both problems

Decoupling features of SUSY CP problem u EDM constraints from 1 loop u CEDM from Hg(neutron) even if Hisano-Shimizu ‘ 04 Contributions through stop loop are not decoupled. Complex Yukawa couplings induce them generically.

Spontaneous CP violatoin in SU(2) model u Doublets under SU(2) family symmetry Real and require non-trivial discrete charge for and .

What happens by the discrete symmetry? real complex SUSY zero mechanism is real , is complex New SUSY CP problem is solved.

A model with a discrete symmetry Bonus 2: small up quark mass is realized. Usually, to obtain the CKM matrix u Too large good value!

Interesting result(perturbation in ) u is obtained Kawase, N. M 10 This cancellation depends on the adjoint VEV. (B factory measured the direction of GUT breaking? ) u

Discussion & Summary u