Cai-Chang Li

A bstract: We perform the first comprehensive study of Modular Littlest Seesaw models based on the finite modular group ∆(96). We construct the vector-valued modular forms (VVMFs) for all irreducible representations of modular ∆(96), classify the inequivalent symmetry-preserving fixed points, and derive the corresponding alignments of the lowest-weight and next-to-lowest-weight triplet VVMFs. These results allow an exhaustive scan over the residual symmetries in the charged lepton, atmospheric neutrino, and solar neutrino sectors. We identify 35 phenomenologically viable and inequivalent breaking patterns, including 21 with normal ordering and 14 with inverted ordering. The resulting Dirac neutrino mass matrices go beyond the conventional CSD( n ) structure, yielding new fixed PMNS columns and novel correlations among the lepton mixing parameters beyond the TM ₁ paradigm. The viable models are highly predictive, giving narrow ranges for neutrino masses, mixing angles, and CP-violating phases, and can be stringently tested by upcoming experiments such as JUNO, DUNE and T2HK.

A bstract: Working within the reference three-neutrino mixing framework, we confront the lepton mixing predictions derived using non-Abelian discrete flavour and CP symmetries with the first JUNO data on the solar neutrino mixing parameters sin ² θ ₁₂ and with the results of the latest global neutrino data analysis. We focus on symmetry breaking patterns for which the lepton PMNS mixing matrix depends only on one or two free real parameters. Performing a comprehensive statistical analysis in each of the considered cases, we report the best fit values, the 3 σ C.L. allowed ranges and the χ ² -distributions of the lepton mixing observables — the three mixing angles and the three CP-violation phases. We find that the JUNO measurements can disfavour or rule out a number of the mixing patterns associated with specific types of breaking of the discrete flavour and CP symmetries. The synergy of JUNO, DUNE and T2HK data can provide an exhaustive test of the considered approach to lepton mixing based on non-Abelian discrete lepton flavour symmetries combined with the CP symmetry.

We perform a comprehensive bottom-up study of all the simplest lepton models based on non-holomorphic A ₅ modular flavor symmetry, in which neutrinos are assumed to be Majorana particles and their masses are generated by the Weinberg operator or the type I seesaw mechanism. In the case that the generalized CP (gCP) symmetry is not considered, we find that 21 Weinberg operator models and 174 seesaw models can accommodate the experimental data in lepton sector, and all of them depend on six dimensionless free parameters and two overall scales. If gCP symmetry compatible with A ₅ modular symmetry is imposed, one more free parameter would be reduced. Then only 4 of the 21 Weinberg operator models and 100 of the 174 seesaw models agree with the experimental data on lepton masses and mixing parameters. Furthermore, we perform a detailed numerical analysis for two example models for illustration.

A bstract: We perform a comprehensive analysis of the minimal eclectic flavor group Q ₈ ⋊ S ₃ which is isomorphic to GL(2 , 3), and all its irreducible representations are induced from the irreducible representations of Q ₈ and S ₃ . The consistency conditions between EFG and generalized CP (gCP) symmetry are revisited, and we find the gCP symmetry compatible with the minimal EFG Q ₈ ⋊ S ₃ . The most general forms of Kähler potential and superpotential based on Q ₈ ⋊ S ₃ are discussed, and the corresponding fermion mass matrices are presented. A concrete lepton model invariant under Q ₈ ⋊ S ₃ and gCP is constructed, in which the experimental data of all six lepton masses and six mixing parameters can be successfully described through seven real input parameters. The model predicts a vanishing effective mass m _ββ in neutrinoless double beta decay.