The current problems of the minimal SO(10) GUT and their solutions

This talk consists of two parts. In part I we review how the minimal renormalizable supersymmetric SO(10) model, an SO(10) framework with only one 10 and one 126 Higgs multiplets in the Yukawa sector, is attractive because of its highly predictive power. Indeed it not only gives a consistent predictions on neutrino oscillation data but also gives reasonable and interesting values for leptogenesis, LFV, muon g-2, neutrinoless double beta decay etc. However, this model suffers from problems related to running of gauge couplings. The gauge coupling unification may be spoiled due to the presence of Higgs multiplets much lighter than the grand unification (GUT) scale. In addition, the gauge couplings blow up around the GUT scale because of the presence of Higgs multiplets of large representations. In part II we consider the minimal SO(10) model in the warped extra dimension and show a possibility to solve these problems.Comment: 15 pages, 7 figures, Talk given at the International Workshop on Neutrino Masses and Mixings Toward Unified Understanding of Quarks and Lepton Mass Matrices, held at University of Shizuoka on December 17-19, 200

Axion and Right-handed Neutrino in the Minimal SUSY SO(10) Model

The connection between the axion and right-handed neutrinos is explored in the framework of the minimal SUSY SO(10) model. The former is related to the Peccei-Quinn (PQ) solution to the strong CP problem and the latter is to the light Majorana neutrinos through the see-saw mechanism. In this model, a relative phase between $({\bf 10,1,3}) (\equiv {\bf \bar{\Delta}}_R) \subset {\bf \bar{126}}$ and $({\bf \bar{10},1,3}) (\equiv {\bf \Delta}_R) \subset {\bf 126}$ multiplets of ${\rm SU}(4) \times {\rm SU}(2)_L \times {\rm SU}(2)_R \subset {\rm SO}(10)$ becomes a physical degree of freedom identified with the axion. Then, the PQ symmetry breaking scale ($\Lambda_{\rm PQ}$) and the $B-L$ symmetry breaking scale ($\Lambda_{\rm B-L}$) coincide through the VEV of ${\bf \bar{\Delta}}_R$. The scalar partner of the lightest right-handed neutrino is regarded as the inflaton, which gives a consistent density fluctuation for the CMB.Comment: 8 pages, no figure; the version to appear in JHE

Polarization of migrating cortical neurons by Rap1 and N-cadherin: Revisiting the model for the Reelin signaling pathway

Neuronal migration is essential for the development of the cerebral cortex. Mutations leading to defective migration are associated with numerous brain pathologies. An important challenge in the field is to understand the intrinsic and extrinsic mechanisms that regulate neuronal migration during normal development and in disease. Many small GTPases are expressed in the central nervous system during embryonic development. Recent findings have shown that Rap1 and its downstream partners Ral, Rac and Cdc42 are involved in the maintenance of N-Cadherin at the plasma membrane which is necessary for the correct polarization of migrating neurons. The activation of Rap1 is triggered by Reelin, an extracellular protein known for its role in the organization of the cortex into layers of neurons. In the absence of Reelin, neurons exhibit a broader and irregular pattern of positioning. The prevailing model suggests that Reelin signals to neurons during the last step of their migration, a notion that is inconsistent with new data describing an effect of Reelin on early steps of migration. In regard to these recent findings I suggest a revised model, which I call the “polarity model,” that further refines our understanding of the developmental function played by Reelin and its downstream small GTPases

Can The Majorana neutrino CP-violating phases be restricted ?

We reanalyze the constraints in neutrino masses and MNS lepton mixing parameters using the new data from the terrestrial (KamLAND) and astrophysical (WMAP) observations together with the HEIDELBERG-MOSCOW double beta decay experiment. It leads us to the almost degenerate or inverse hierarchy neutrino mass scenario. We discuss the possibility of getting the bound for the Majorana CP violating phase.Comment: 6 pages, 2 figure