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Register a new userMaximal zero textures of the inverse seesaw with broken $mutau$ symmetry
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The inverse neutrino seesaw, characterised by only one source of lepton number violation at an ultralight $O$(keV) scale and observable new phenomena at TeV energies accessible to the LHC, is considered. Maximal zero textures of the $3times 3$ lighter and heavier Dirac mass matrices of neutral leptons, appearing in the Lagarangian for such an inverse seesaw, are studied within the framework of $mutau$ symmetry in a specified weak basis. That symmetry ensures the identity of the positions of maximal zeros of the heavy neutrino mass matrix and its inverse. It then suffices to study the maximal zeros of the lighter Dirac mass matrix and those of the inverse of the heavier one since they come in a product. The observed absence of any unmixed neutrino flavour and the assumption of no strictly massless physical neutrino state allow only eight $4$-zero $times$ $4$-zero, eight $4$-zero $times$ $6$-zero and eight $6$-zero $times$ $4$-zero combinations. The additional requirement of leptogenesis is shown to eliminate the last sixteen textures. The surviving eight $4$-zero $times$ $4$-zero textures are subjected to the most general explicit $mutau$ symmetry breaking terms in the Lagrangian in order to accommodate the nonzero value of $theta_{13}$ in the observed range. A full diagonalisation is then carried out. On numerical comparison with all extant and relevant neutrino (antineutrino) data, seven of these eight combination textures in five neutrino matrix forms are found to be allowed, leading to five distinct neutrino mass matrices. Two of these permit only a normal (and the other three only an inverted) mass ordering of the light neutrinos.
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We investigate Linear and Inverse seesaw mechanisms with maximal zero textures of the constituent matrices subjected to the assumption of non-zero eigenvalues for the neutrino mass matrix $m_ u$ and charged lepton mass matrix $m_e$. If we restrict to the minimally parametrized non-singular `$m_e$ (i.e., with maximum number of zeros) it gives rise to only 6 possible textures of $m_e$. Non-zero determinant of $m_ u$ dictates six possible textures of the constituent matrices. We ask in this minimalistic approach, what are the phenomenologically allowed maximum zero textures are possible. It turns out that Inverse seesaw leads to 7 allowed two-zero textures while the Linear seesaw leads to only one. In Inverse seesaw, we show that 2 is the maximum number of independent zeros that can be inserted into $mu_S$ to obtain all 7 viable two-zero textures of $m_ u$. On the other hand, in Linear seesaw mechanism, the minimal scheme allows maximum 5 zeros to be accommodated in `$m$ so as to obtain viable effective neutrino mass matrices ($m_ u$). Interestingly, we find that our minimalistic approach in Inverse seesaw leads to a realization of all the phenomenologically allowed two-zero textures whereas in Linear seesaw only one such texture is viable. Next our numerical analysis shows that none of the two-zero textures give rise to enough CP violation or significant $delta_{CP}$. Therefore, if $delta_{CP}=pi/2$ is established, our minimalistic scheme may still be viable provided we allow more number of parameters in `$m_e$.
We investigate, within the Type I seesaw framework, the physical implications of zero textures in the Yukawa couplings which generate the neutrino Dirac mass matrix $m_D$. It is shown that four is the maximal number of texture zeroes compatible with the observed leptonic mixing and the assumption that no neutrino mass vanishes. We classify all allowed four-zero textures of $m_D$ into two categories with three classes each. We show that the different classes, in general, admit CP violation both at low and high energies. We further present the constraints obtained for low energy physics in each case. The r^ ole of these zero textures in establishing a connection between leptogenesis and low energy data is analysed in detail. It is shown that it is possible in all cases to completely specify the parameters relevant for leptogenesis in terms of light neutrino masses and leptonic mixing together with the unknown heavy neutrino masses.
We discuss an inverse seesaw model based on right-handed fermion specific $U(1)$ gauge symmetry and $A_4$-modular symmetry. These symmetries forbid unnecessary terms and restrict structures of Yukawa interactions which are relevant to inverse seesaw mechanism. Then we can obtain some predictions in neutrino sector such as Dirac-CP phase and sum of neutrino mass, which are shown by our numerical analysis. Besides the relation among masses of heavy pseudo-Dirac neutrino can be obtained since it is also restricted by the modular symmetry. We also discuss implications to lepton flavor violation and collider physics in our model.
We propose a complex extension of $mutau$ permutation antisymmetry in the neutrino Majorana matrix $M_ u$. The latter can be realized for the Lagrangian by appropriate CP transformations on the neutrino fields. The resultant form of $M_ u$ is shown to be simply related to that with a complex (CP) extension of $mutau$ permutation symmetry, with identical phenomenological consequences, though their group theoretic origins are quite different. We investigate those consequences in detail for the minimal seesaw induced by two strongly hierarchical right-chiral neutrinos $N_1$ and $N_2$ with the result that the Dirac phase is maximal while the two Majorana phases are either 0 or $pi$. We further provide an uptodate discussion of the $betabeta0 u$ process vis-a-vis ongoing and forthcoming experiments. Finally, a thorough treatment is given of baryogenesis via leptogenesis in this scenario, primarily with the assumption that the lepton asymmetry produced by the decays of $N_1$ only matters here with the asymmetry produced by $N_2$ being washed out. Tight upper and lower bounds on the mass of $N_1$ are obtained from the constraint of obtaining the correct observed range of the baryon asymmetry parameter and the role played by $N_2$ is elucidated thereafter. The mildly hierarchical right-chiral neutrino case (including the quasidegenerate possibility) is discussed in an Appendix.
We make an investigation of modular $Gamma^{prime}_5 simeq A^{prime}_5$ group in inverse seesaw framework. Modular symmetry is advantageous because it reduces the usage of extra scalar fields significantly. Moreover, the Yukawa couplings are expressed in terms of Dedekind eta functions, which also have a $q$ expansion form, utilized to achieve numerical simplicity. Our proposed model includes six heavy fermion superfields i.e., $mathcal{N}_{Ri}$, $mathcal{S}_{Li}$ and a weighton. The study of neutrino phenomenology becomes simplified and effective by the usage of $A^prime_5$ modular symmetry, which provides us a well defined mass structure for the lepton sector. Here, we observe that all the neutrino oscillation parameters, as well as the effective electron neutrino mass in neutrinoless double beta decay can be accommodated in this model. We also briefly discuss the lepton flavor violating decays $ell_i to ell_j gamma$ and comment on non-unitarity of lepton mixing matrix.
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