Teruyuki Kitabayashi

μ–τ symmetry and maximal CP violation

We argue the possibility that a real part of a flavor neutrino mass matrix only respects a mu-tau symmetry. This possibility is shown to be extended to more general case with a phase parameter theta, where the mu-tau symmetric part has a phase of theta/2. This texture shows maximal CP violation and no Majorana CP violation.

Large solar neutrino mixing in an extended Zee model

The Zee model, which employs the standard Higgs scalar (ϕ) with its duplicate (ϕ ′) and a singly charged scalar (h+), can utilize two global symmetries associated with the conservation of the numbers of ϕ and ϕ′, Nϕ, ϕ′, where Nϕ + Nϕ′ coincides with the hypercharge while Nϕ - Nϕ′ (≡ X) is a new conserved charge, which is identical to Le - Lμ - Lτ for the left-handed leptons. Charged leptons turn out to have e–μ and e–τ mixing masses, which are found to be crucial for the large solar neutrino mixing. In an extended version of the Zee model with an extra triplet Higgs scalar (s), neutrino oscillations are described by three steps: (1) the maximal atmospheric mixing is induced by democratic mass terms supplied by s with X = 2 that can initiate the type II seesaw mechanism for the smallness of these masses; (2) the maximal solar neutrino mixing is triggered by the creation of radiative masses by h+ with X=0; (3) the large solar neutrino mixing is finally induced by a νμ - ντ mixing arising from the rotation of the radiative mass terms as a result of the diagonalization that converts e–μ and e–τ mixing masses into the electron mass.

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*.

Charged lepton contributions to bipair neutrino mixing

Abstract The bipair neutrino mixing describes the observed solar and atmospheric mixings; however, it predicts vanishing reactor mixing angle, which is inconsistent with the observed data. We explore the ways of minimally modifying the bipair neutrino mixing by including charged lepton contributions. There are two categories of the bipair neutrino mixing which are referred to as case 1 and case 2. It turns out that, without arbitrary phases, a minimal modification is realized by just considering one e – τ contribution from the charged lepton sector in the case 1. On the other hand, not only e – τ contribution but also μ – τ contribution is required to realize a minimal modification in the case 2.

Bi-pair neutrino mixing

Abstract A new type of neutrino mixing named bi-pair neutrino mixing is proposed to describe the current neutrino mixing pattern with a vanishing reactor mixing angle and is determined by a mixing matrix with two pairs of identical magnitudes of matrix elements. As a result, we predict sin 2 θ 12 = 1 − 1 / 2 ( ≈ 0.293 ) for the solar neutrino mixing and either sin 2 θ 23 = tan 2 θ 12 or cos 2 θ 23 = tan 2 θ 12 for the atmospheric neutrino mixing. We determine flavor structure of a mass matrix M, leading to diagonal masses of m 1 , 2 , 3 , and find that | M μ μ − M e e / t 12 2 | : | M μ τ | : | M τ τ − M e e / t 12 2 | = t 23 2 : | t 23 | : 1 for the normal mass hierarchy if m 1 = 0 , where t i j = tan θ i j ( i , j = 1 , 2 , 3 ) and M i j ( i , j = e , μ , τ ) stand for flavor neutrino masses. For the inverted mass hierarchy, the bi-pair mixing scheme turns out to satisfy the strong scaling ansatz requiring that | M μ μ | : | M μ τ | : | M τ τ | = 1 : | t 23 | : t 23 2 if m 3 = 0 .

Remark on the minimal seesaw model and leptogenesis with tribimaximal mixing

We have studied a leptogenesis scenario in the framework of the minimal seesaw model with tribimaximal mixing. Usually, at least one of the elements in the Dirac mass matrix is fixed to be zero, for example, we denote it by b{sub 2}=0. We have pointed out that the absolute value of the CP asymmetry has several minimums and maximums with nonzero b{sub 2}. Thus one can expect that more rich phenomena, such as an enhanced leptogenesis, are hidden in the b{sub 2}{ne}0 space.

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.

Maximal CP violation in flavor neutrino masses

Since flavor neutrino masses

CP violation in bipair neutrino mixing

M_{mumu,tautau,mutau}

CP violation in modified bipair neutrino mixing and leptogenesis

can be expressed in terms of