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Nobuhiro Maekawa (Nagoya Univ. KMI) TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AA

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What I would like to talk today

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Cosmological signature?

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Introduction GUT is attractive!

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Grand Unified Theories Gauge Interactions Matter ２ Ｕｎｉｆｉ ｃａｔｉｏｎｓ Experimental supports for both unifications GUT is promising

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Grand Unified Theories Unification of gauge interactions quantitative evidence: 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) Non SUSYSUSY GUT

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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 realized in SU(5) GUT!!

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

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

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

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Bando-N.M. 01 N.M, T. Yamashita 02

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

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Milder hierarchy for fields from become superheavy. Light modes have smaller Yukawa couplings and milder hierarchy than Superheavy Larger mixings in lepton sector than in quark sector. Small Small neutrino Dirac masses Suppressed radiative LFV unless Bando-N.M. 01 N.M, T. Yamashita 02

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How to obtain various Yukawas?

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SO(10) GUT relations

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Right-handed neutrinos The same hierarchy LMA for solar neutrino problem

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1st Ｓｕｍｍａｒｙ

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Can we discover the LFV at the future experiments? (exclude) MEG experiment τ→μγ μ →eγ Detectable if <400GeV (super-)KEKB Detectable, when tanβ is large and <250GeV

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

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2nd Summary KM theory is naturally realized by spontaneous CP violation in E6 GUT with family symmetry 1, Real and parameters are realized by introducing a discrete symmetry. 2, The symmetry solves CEDM problem. :real :complex 3, Predicted EDM induced by RGE effect is sizable. 4, 5, 6, E6 Higgs sector consistent with the above scenario with natural realization of D-T splitting

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Sizable EDM Ishiduki-Kim-N.M.-Sakurai09

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Nucleon decay N.M.-Y.Muramatsu 13,14

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Natural(Anomalous U(1)) GUT Natural: All the interactions which are allowed by the symmetry are introduced with O(1) coefficients. (incl. higher dimensional int.) We can define the model only by fixing the symmetry of the model(except O(1) coefficients). The parameters for the definition are mainly about 10 charges for the fields. The predictions are expected to be stable under the quantum corrections or gravity effects. This assumption is quite natural. Infinite number of interactions can be controlled. Doublet-triplet splitting problem can be solved. Realistic quark and lepton masses and mixings. Non trivial explanation for gauge coupling unification. Anomalous U(1) gauge symmetry plays an essential role N.M. 01 N.M. T. Yamashita, 02

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Nucleon decay via dim. 6 is enhanced

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two important ratios of partial decay widths to identify GUT model to identify grand unification group to identify Yukawa structure at GUT scale : dimension-6 operators which have anti electron in final state : dimension-6 operators which have anti neutrino in final state

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3rd Summary

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Impact of LHC

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The little hierarchy problem. -Very serious problem must be solved! N.M.-K.Takayama 14 125GeV Higgs→Heavy stop→Instability of EW scale This step is not automatic! Instability strongly depends on the explicit SUSY breaking scenario → 125GeV Higgs must be a hint for finding the true SUSY breaking scenario.

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Little hierarchy problem

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Low mediation scale scenarios

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Cosmological Gravitino Problem SUSY is still promising Decay of gravitino produced in early universe spoils BBN. Kawasaki-Kohri-Moroi-Yotsuyanagi08 One solution O(100TeV) gravitino It decays before BBN! High scale SUSY but destabilizes the weak scale.

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What we would like to show

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Little hierarchy problem

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Important observation

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N.M.-Y.Muramatsu-Y.Shigekami 14 10: 5:5:

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A signature from sizable D-term contributions How large D-term can be allowed? We consider FCNC constraints

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:constraint from Result 1 = D-term can be 1 TeV!

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4 th Summary

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Summary

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Higgsino?

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