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Register a new userThe renormalization group analysis of the large lepton flavor mixing and the neutrino mass
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The Superkamiokande experiment suggests the large flavor mixing between nu_mu and nu_tau. We show that the mixing angle receives significant corrections from the renormalization group equation (RGE) when both the second and the third generation neutrino masses are larger than O(0.1eV). This means that the mixing angle must be small at the decoupling scale of right-handed neutrinos in the model containing a sterile neutrino nu_s with the mass spectrum of m_nu_s = m_nu_e << m_nu_mu = m_nu_tau.
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We borrow the general idea of renormalization-group equations (RGEs) to understand how neutrino masses and flavor mixing parameters evolve when neutrinos propagate in a medium, highlighting a meaningful possibility that the genuine flavor quantities in vacuum can be extrapolated from their matter-corrected counterparts to be measured in some realistic neutrino oscillation experiments. Taking the matter parameter $a equiv 2sqrt{2} G^{}_{rm F} N^{}_e E$ to be an arbitrary scale-like variable with $N^{}_e$ being the net electron number density and $E$ being the neutrino beam energy, we derive a complete set of differential equations for the effective neutrino mixing matrix $V$ and the effective neutrino masses $widetilde{m}^{}_i$ (for $i = 1, 2, 3$). Given the standard parametrization of $V$, the RGEs for ${widetilde{theta}^{}_{12}, widetilde{theta}^{}_{13}, widetilde{theta}^{}_{23}, widetilde{delta}}$ in matter are formulated for the first time. We demonstrate some useful differential invariants which retain the same form from vacuum to matter, including the well-known Naumov and Toshev relations. The RGEs of the partial $mu$-$tau$ asymmetries, the off-diagonal asymmetries and the sides of unitarity triangles of $V$ are also obtained as a by-product.
The see-saw mechanism to generate small neutrino masses is reviewed. After summarizing our current knowledge about the low energy neutrino mass matrix we consider reconstructing the see-saw mechanism. Low energy neutrino physics is not sufficient to reconstruct see-saw, a feature which we refer to as ``see-saw degeneracy. Indirect tests of see-saw are leptogenesis and lepton flavor violation in supersymmetric scenarios, which together with neutrino mass and mixing define the framework of see-saw phenomenology. Several examples are given, both phenomenological and GUT-related. Variants of the see-saw mechanism like the type II or triplet see-saw are also discussed. In particular, we compare many general aspects regarding the dependence of LFV on low energy neutrino parameters in the extreme cases of a dominating conventional see-saw term or a dominating triplet term. For instance, the absence of mu -> e gamma or tau -> e gamma in the pure triplet case means that CP is conserved in neutrino oscillations. Scanning models, we also find that among the decays mu -> e gamma, tau -> e gamma and tau -> mu gamma the latter one has the largest branching ratio in (i) SO(10) type I see-saw models and in (ii) scenarios in which the triplet term dominates in the neutrino mass matrix.
We study a neutrino mass model based on $S_4$ flavor symmetry which accommodates lepton mass, mixing with non-zero $theta_{13}$ and CP violation phase. The spontaneous symmetry breaking in the model is imposed to obtain the realistic neutrino mass and mixing pattern at the tree- level with renormalizable interactions. Indeed, the neutrinos get small masses from one $SU(2)_L$ doubplet and two $SU(2)_L$ singlets in which one being in $underline{2}$ and the two others in $underline{3}$ under $S_4$ with both the breakings $S_{4}rightarrow S_3$ and $S_{4}rightarrow Z_3$ are taken place in charged lepton sector and $S_4rightarrow mathcal{K}$ in neutrino sector. The model also gives a remarkable prediction of Dirac CP violation $delta_{CP}=frac{pi}{2}$ or $-frac{pi}{2}$ in the both normal and inverted spectrum which is still missing in the neutrino mixing matrix. The relation between lepton mixing angles is also represented.
We construct a class of renormalizable models for lepton mixing that generate predictions given in terms of the charged-lepton mass ratios. We show that one of those models leads, when one takes into account the known experimental values, to almost maximal CP-breaking phases and to almost maximal neutrinoless double-beta decay. We study in detail the scalar potential of the models, especially the bounds imposed by unitarity on the values of the quartic couplings.
We propose two phenomenological scenarios of lepton mass matrices and show that either of them can exactly give rise to tan^2theta_{13} = m_e/(m_e + 2m_mu), tan^2theta_{23} = m_mu/(m_e + m_mu) and tan^2theta_{12} = (m_e m_2 + 2m_mu m_1)/(m_e m_1 + 2m_mu m_2) in the standard parametrization of lepton flavor mixing. The third relation, together with current experimental data, predicts a normal but weak hierarchy for the neutrino mass spectrum. We also obtain theta_{13} approx 2.8^circ for the smallest neutrino mixing angle and J approx 1.1% for the Jarlskog invariant of leptonic CP violation, which will soon be tested in the long-baseline reactor and accelerator neutrino oscillation experiments. A seesaw realization of both scenarios is briefly discussed.
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