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

TL;DR

This paper explores the double covering of the modular group related to $A_5$, deriving modular forms, constructing models for neutrino masses and mixing, and analyzing their parameter spaces.

Contribution

It provides the first explicit derivation of modular forms for the double covering of $A_5$ and applies them to minimal seesaw models for lepton flavor mixing.

Findings

Derived all modular forms of weight one for the double covering group.

Constructed two minimal seesaw models explaining lepton masses and mixing.

Numerically and analytically analyzed the parameter space of these models.

Abstract

In this paper, we investigate the double covering of modular $\Gamma^{}_5 \simeq A^{}_5$ 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 $\Gamma^\prime_5 \simeq A^\prime_5$, 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.