Fermion masses and mixing from the double cover and metaplectic cover of the A5 modular group

We perform a comprehensive study of the homogeneous finite modular group A(5)' which is the double covering of A(5). The integral weight and level 5 modular forms have been constructed up to weight 6 and they are decomposed into the irreducible representations of A(5)'. Then we perform a systematical analysis of the A(5)' modular models for lepton masses and mixing. The phenomenologically viable models with minimal number of free parameters and the results of fit are presented. We find out 15 models with 9 real free parameters which can accommodate the experimental data of lepton sector. After including generalized CP symmetry, 9 viable models with 7 free parameters are found out. We apply A(5)' modular symmetry to the quark sector, and a quark-lepton unification model is given. The framework of modular invariance is extended to include the rational weight modular forms of level 5. The ring of modular forms at level 5 can be generated by two algebraically independent weight 1/5 modular forms denoted by F-1(tau) and F-2(tau). We give the expressions of the rational weight modular forms of level 5 up to weight 3 and arrange them into the irreducible multiplets of finite metaplectic group (Gamma) over tilde (5) congruent to A(5)' x Z(5). A neutrino mass model with (Gamma) over tilde (5) modular symmetry is presented, and the phenomenological predictions of the model are analyzed numerically.

Automated summary

A comprehensive study of the finite modular group A(5)' was conducted, constructing integral weight and level 5 modular forms up to weight 6 and decomposing them into irreducible representations of A(5)'. The study also analyzed A(5)' modular models for lepton masses and mixing, presenting phenomenologically viable models with minimal free parameters. By extending the framework to include rational weight modular forms of level 5, the study explored 15 models accommodating experimental data in the lepton sector.