Modular $A_5$ Symmetry for Flavour Model Building

Abstract

In the framework of the modular symmetry approach to lepton flavour, we consider a class of theories where matter superfields transform in representations of the finite modular group ${\Gamma }_5\simeq A_5$. We explicitly construct a basis for the 11 modular forms of weight 2 and level 5. We show how these forms arrange themselves into two triplets and a quintet of $A_5$. We also present multiplets of modular forms of higher weight. Finally, we provide an example of application of our results, constructing two models of neutrino masses and mixing based on the supersymmetric Weinberg operator.

34 pages, 3 figures; the model with flavons in subsection 3.3 slightly modified, results unchanged; Appendix C extended with multiplets of weight 6, 8 and 10 modular forms; Appendix D on correspondence with the Dedekind eta function containing one new figure added; one reference added; typos corrected; version to be published in JHEP

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