Double Covering of the Modular $A^{}_5$ Group and Lepton Flavor Mixing in the Minimal Seesaw Model

Abstract

In this paper, we investigate the double covering of modular Γ 5 A 5 group and derive all the modular forms of weight one for the first time. The modular forms of higher weights are also explicitly given by decomposing the direct products of weight-one forms. For the double covering group Γ 5A 5 , there exist two inequivalent two-dimensional irreducible representations, into which we can assign two right-handed neutrino singlets in the minimal seesaw model. Two concrete models with such a salient feature have been constructed to successfully explain lepton mass spectra and flavor mixing pattern. The allowed parameter space for these two minimal scenarios has been numerically explored, and analytically studied with some reasonable assumptions.

Modular Invariant $A_{4}$ Models for Quarks and Leptons with Generalized CP Symmetry

“…The most general form of neutrino mass matrix is given in Eqs. (44,46). Requiring the number of coupling constants in the effective light neutrino mass matrix is less than 4, we can obtain 3 Weinberg operator models W 1,2,3 and 5 seesaw models S 1,2,3,4,5 , they are summarized in table 3.…”

“…The formalism of the homogeneous finite modular group Γ N which is the double covering of Γ N have been explored in [42]. The homogeneous finite modular groups Γ 3 ∼ = T [42,43], Γ 4 ∼ = S 4 [44,45] and Γ 5 ∼ = A 5 [46,47] have been utilized…”

4D modular flavor symmetric models inspired by higher dimensional theory

“…The supersymmetric (SUSY) modular invariant theories give us an attractive framework to address the flavor problem of quarks and leptons. Indeed, finite modular flavor symmetric models have been presented in all these years [1][2][3][4][5][6][7][8][9][10][11][12][13]. The homogeneous modular group Γ = SL(2, Z) and inhomogeneous modular group Γ = SL(2, Z)/Z 2 include S 3 , A 4 , S 4 , A 4 as finite subgroups [14].…”

Radiative neutrino masses from modular $A_4$ symmetry and supersymmetry breaking

“…[73,74], and double covering of A 5 in refs. [75][76][77][78]. Other types of modular symmetries have also been proposed to understand masses, mixings, and phases of the standard model (SM) in refs.…”