Abstract
We study the structure of the neutrino-mass matrix in the minimal gauged hbox {U}(1)_{L_mu -L_tau } model, where three right-handed neutrinos are added to the Standard Model in order to obtain non-zero masses for the active neutrinos. Because of the hbox {U}(1)_{L_mu -L_tau } gauge symmetry, the structure of both Dirac and Majorana mass terms of neutrinos is tightly restricted. In particular, the inverse of the neutrino-mass matrix has zeros in the (mu ,mu ) and (tau ,tau ) components, namely, this model offers a symmetric realization of the so-called two-zero-minor structure in the neutrino-mass matrix. Due to these constraints, all the CP phases – the Dirac CP phase delta and the Majorana CP phases alpha _2 and alpha _3 – as well as the mass eigenvalues of the light neutrinos m_i are uniquely determined as functions of the neutrino mixing angles theta _{12}, theta _{23}, and theta _{13}, and the squared mass differences Delta m_{21}^2 and Delta m_{31}^2. We find that this model predicts the Dirac CP phase delta to be delta simeq 1.59pi –1.70pi (1.54pi –1.78pi ), the sum of the neutrino masses to be sum _{i}m_i simeq 0.14–0.22 eV (0.12–0.40 eV), and the effective mass for the neutrinoless double-beta decay to be langle m_{beta beta }rangle simeq 0.024–0.055 eV (0.017–0.12 eV) at 1sigma (2sigma ) level, which are totally consistent with the current experimental limits. These predictions can soon be tested in future neutrino experiments. Implications for leptogenesis are also discussed.
Highlights
Due to these constraints, all the CP phases – the Dirac CP phase δ and the Majorana CP phases α2 and α3 – as well as the mass eigenvalues of the light neutrinos mi are uniquely determined as functions of the neutrino mixing angles θ12, θ23, and θ13, and the squared mass differences m m231
We find that this model predicts the Dirac CP phase δ to be δ 1.59π –1.70π (1.54π –1.78π ), the sum of the neutrino masses to be i mi 0.14–0.22 eV (0.12–0.40 eV), and the effective mass for the neutrinoless double-beta decay to be mββ 0.024–0.055 eV (0.017–0.12 eV) at 1σ (2σ ) level, which are totally consistent with the current experimental limits
We have studied the structure of the neutrino-mass matrix in the minimal gauged U(1)Lμ−Lτ model
Summary
Offer promising candidates for dark matter in the Universe [18,19,20,21,22]. For other recent studies on gauged U(1)Lμ−Lτ models, see Refs. [23,24,25,26,27,28,29,30,31,32,33,34,35]. It turns out that the observed neutrino mixing structure can be obtained only when the U(1)Lμ−Lτ -breaking scalar field has the U(1)Lμ−Lτ charge ±1 In this case, the (μ, μ) and (τ, τ ) components of the Majorana mass matrix for the right-handed neutrinos remain zero even after the. (e, τ ), (μ, e), and (τ, e) components in Eq (2) can be induced after the scalar field acquires a VEV, while the (μ, μ) and (τ, τ ) can be generated if the scalar has the U(1)Lμ−Lτ charge ± 2 In the latter case, the Majorana mass matrix becomes block-diagonal, which makes it unable to explain the observed neutrino mixing angles.
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