Neutrino masses and mixing from double covering of finite modular groups

By Xiang-Gan Liu, Gui-Jun Ding. Journal of High Energy Physics, 2019

137 citations recorded by the source corpus.

We extend the even weight modular forms of modular invariant approach to general integral weight modular forms. We find that the modular forms of integral weights and level N can be arranged into irreducible representations of the homogeneous finite modular group ΓN′\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {\Gamma}_N^{\prime } $$\end{document} which is the double covering of ΓN. The lowest weight 1 modular forms of level 3 are constructed in terms of Dedekind eta-function, and they transform as a doublet of Γ3′\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {\Gamma}_3^{\prime } $$\end{document} ≅ T′. The modular forms of weights 2, 3, 4, 5 and 6 are presented. We build a model of lepton masses and mixing based on T′ modular symmetry.

Subfields: Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/25d462c04c73ffd9754fc9bcfae3f26361d1f117