Ichiro Aizawa

Bilarge neutrino mixing and mu - tau permutation symmetry for two-loop radiative mechanism

The presence of approximate electron number conservation and \mu-\tau permutation symmetry of S_2 is shown to naturally provide bilarge neutrino mixing. First, the bimaximal neutrino mixing together with U_{e3}=0 is guaranteed to appear owing to S_2 and, then, the bilarge neutrino mixing together with |U_{e3}|<<1 arises as a result of tiny violation of S_2. The observed mass hierarchy of \Delta m^2_{\odot}<<\Delta m^2_{atm} is subject to another tiny violation of the electron number conservation. This scenario is realized in a specific model based on SU(3)_L x U(1)_N with two-loop radiative mechanism for neutrino masses. The radiative effects from heavy leptons contained in lepton triplets generate the bimaximal structure and those from charged leptons, which break S_2, generate the bilarge structure together with |U_{e3}|<<1. To suppress dangerous flavor-changing neutral current interactions due to Higgs exchanges especially for quarks, this S_2 symmetry is extended to a discrete Z_8 symmetry, which also ensures the absence of one-loop radiative mechanism.

Determination of neutrino mass texture for maximal CP violation

We show a general form of neutrino mass matrix (M), whose matrix elements are denoted by Mij (i,j=e,μ,τ) as flavor neutrino masses, that induces maximal CP violation as well as maximal atmospheric neutrino mixing. The masses of Mμμ, Mττ and Mμτ+σMee (σ=±1) turn out to be completely determined by Meμ and Meτ for given mixing angles. The appearance of CP violation is found to originate from the interference between the μ–τ symmetric part of M and its breaking part. If |Meμ|=|Meτ|, giving either Meμ=−σeiθMeτ or Meμ=−σeiθMeτ* with a phase parameter θ, is further imposed, we find that |Mμμ|=|Mττ| is also satisfied. These two constraints can be regarded as an extended version of the constraints in the μ–τ symmetric texture given by Meμ=−σMeτ and Mμμ=Mττ. Majorana CP violation becomes active if arg(Mμτ)≠arg(Meμ)+θ/2 for Meμ=−σeiθMeτ and if arg(Mμτ)≠θ/2 for Meμ=−σeiθMeτ*.

General property of neutrino mass matrix and CP-violation

Abstract It is found that the atmospheric neutrino mixing angle of θ atm is determined to be tan θ atm = Im ( B ) / Im ( C ) for B = M ν e ν μ and C = M ν e ν τ , where M i j is the ij element of M ν † M ν with M ν as a complex symmetric neutrino mass matrix in the ( ν e , ν μ , ν τ )-basis. Another mixing angle, θ 13 , defined as U e 3 = sin θ 13 e − i δ is subject to the condition: tan 2 θ 13 ∝ | sin θ atm B + cos θ atm C | and the CP-violating Dirac phase of δ is identical to the phase of sin θ atm B * + cos θ atm C * . The smallest value of | sin θ 13 | is achieved at tan θ atm = − Re ( C ) / Re ( B ) that yields the maximal CP-violation and that implies C = − κ B * for the maximal atmospheric neutrino mixing of tan θ atm = κ = ± 1 . The generic smallness of | sin θ 13 | can be ascribed to the tiny violation of the electron number conservation.

Neutrino mass textures with maximal CP violation

We show three types of neutrino mass textures, which give maximal CP violation as well as maximal atmospheric neutrino mixing. These textures are described by six real mass parameters: one specified by two complex flavor neutrino masses and two constrained ones and the others specified by three complex flavor neutrino masses. In each texture, we calculate mixing angles and masses, which are consistent with observed data, as well as Majorana CP phases.

Dilatonic Inflation and SUSY Breaking in String-inspired Supergravity

The theory of inflation will be investigated as well as supersymmetry breaking in the context of supergravity, incorporating the target-space duality and the nonperturbative gaugino condensation in the hidden sector. We found an inflationary trajectory of a dilaton field and a condensate field which breaks supersymmetry at once. The model satisfies the slow-roll condition which solves the η-problem. When the particle rolls down along the minimized trajectory of the potential V(S,Y) at a duality invariant point of T=1, we can obtain the e-fold value ~57. And then the cosmological parameters obtained from our model well match the recent WMAP data combined with other experiments. This observation suggests one to consider the string-inspired supergravity as a fundamental theory of the evolution of the universe as well as the particle theory.

Constraints on flavor neutrino masses and sin**2 2 theta(12) >> sin**2 theta(13) in neutrino oscillations

To realize the condition of sin^2(2theta_{12})>>sin^2(theta_{13}), we find constraints on flavor neutrino masses M_{ij} (ij=e,\mu,\tau): C1) c_{23}^2 M_{\mu\mu} + s_{23}^2 M_{\tau\tau} \approx 2 s_{23} c_{23}M_{\mu\tau} + M_{ee} and/or C2) |c_{23}M_{e\mu} -s_{23}M_{e\tau}|>> |s_{23}M_{e\mu} +c_{23}M_{e\tau}|, where c_{23}=cos(theta_{23}) (s_{23}=sin(theta_{23})) and theta_{12}, theta_{13} and theta_{23} are the mixing angles for three flavor neutrinos. The applicability of C1) and C2) is examined in models with one massless neutrino and two massive neutrinos suggested by \det(M)=0, where M is a mass matrix constructed from M_{ij} (i,j=e,\mu,\tau). To make definite predictions on neutrino masses and mixings, especially on sin(theta_{13}), that enable us to trace C1) and C2), M is assumed to possess texture zeros or to be constrained by textures with M_{\mu\mu}=M_{\tau\tau} or M_{e\tau}=\pm M_{e\mu} which turn out to ensure the emergence of the maximal atmospheric neutrino mixing at sin(theta_{13})->0. It is found that C1) is used by textures such as M_{e\mu}=0 or M_{e\tau}=0 while C2) is used by textures such as M_{e\tau}=\pm M_{e\mu}.

Constraints on flavor neutrino masses and sin 22v12»sin 2v13 in neutrino oscillations

To realize the condition of sin^2(2theta_{12})>>sin^2(theta_{13}), we find constraints on flavor neutrino masses M_{ij} (ij=e,\mu,\tau): C1) c_{23}^2 M_{\mu\mu} + s_{23}^2 M_{\tau\tau} \approx 2 s_{23} c_{23}M_{\mu\tau} + M_{ee} and/or C2) |c_{23}M_{e\mu} -s_{23}M_{e\tau}|>> |s_{23}M_{e\mu} +c_{23}M_{e\tau}|, where c_{23}=cos(theta_{23}) (s_{23}=sin(theta_{23})) and theta_{12}, theta_{13} and theta_{23} are the mixing angles for three flavor neutrinos. The applicability of C1) and C2) is examined in models with one massless neutrino and two massive neutrinos suggested by \det(M)=0, where M is a mass matrix constructed from M_{ij} (i,j=e,\mu,\tau). To make definite predictions on neutrino masses and mixings, especially on sin(theta_{13}), that enable us to trace C1) and C2), M is assumed to possess texture zeros or to be constrained by textures with M_{\mu\mu}=M_{\tau\tau} or M_{e\tau}=\pm M_{e\mu} which turn out to ensure the emergence of the maximal atmospheric neutrino mixing at sin(theta_{13})->0. It is found that C1) is used by textures such as M_{e\mu}=0 or M_{e\tau}=0 while C2) is used by textures such as M_{e\tau}=\pm M_{e\mu}.

Constraints on flavor neutrino masses and sin{sup 2}2{theta}{sub 12}>>sin{sup 2}{theta}{sub 13} in neutrino oscillations

To realize the condition of sin^2(2theta_{12})>>sin^2(theta_{13}), we find constraints on flavor neutrino masses M_{ij} (ij=e,\mu,\tau): C1) c_{23}^2 M_{\mu\mu} + s_{23}^2 M_{\tau\tau} \approx 2 s_{23} c_{23}M_{\mu\tau} + M_{ee} and/or C2) |c_{23}M_{e\mu} -s_{23}M_{e\tau}|>> |s_{23}M_{e\mu} +c_{23}M_{e\tau}|, where c_{23}=cos(theta_{23}) (s_{23}=sin(theta_{23})) and theta_{12}, theta_{13} and theta_{23} are the mixing angles for three flavor neutrinos. The applicability of C1) and C2) is examined in models with one massless neutrino and two massive neutrinos suggested by \det(M)=0, where M is a mass matrix constructed from M_{ij} (i,j=e,\mu,\tau). To make definite predictions on neutrino masses and mixings, especially on sin(theta_{13}), that enable us to trace C1) and C2), M is assumed to possess texture zeros or to be constrained by textures with M_{\mu\mu}=M_{\tau\tau} or M_{e\tau}=\pm M_{e\mu} which turn out to ensure the emergence of the maximal atmospheric neutrino mixing at sin(theta_{13})->0. It is found that C1) is used by textures such as M_{e\mu}=0 or M_{e\tau}=0 while C2) is used by textures such as M_{e\tau}=\pm M_{e\mu}.