Modular Symmetry and Flavour

by Arsenii Titov (IPPP)

Friday 1 Mar 2019, 14:00 → 15:00 Europe/London

In this talk, I will review a new and very interesting approach to lepton flavour, based on invariance of the supersymmetric action under the modular group. The couplings in the considered modular-invariant models of lepton masses and mixing are modular forms which, as well as matter superfields, transform in irreducible representations of a finite modular group ${\mathrm{\Gamma }}_N$. I will concentrate on the minimal scenario in which the only source of modular symmetry breaking is the vacuum expectation value of a single complex field, the modulus. In this scenario, there is no need to introduce flavons. After reviewing how to construct the basis for the modular forms of weight 2 and level 4, I will present minimal phenomenologically viable models based on ${\mathrm{\Gamma }}_4\simeq S_4$ in which neutrino masses are generated via the type I seesaw mechanism. While successfully accommodating charged lepton masses, neutrino mixing angles and mass-squared differences, these models predict the absolute neutrino mass scale, the values of Dirac and Majorana CP-violating phases, as well as specific correlations between several observables. Finally, I will comment on construction of the basis for 11 modular forms of weight 2 and level 5, demonstrating how these forms arrange themselves into two triplets and a quintet of the finite modular group ${\mathrm{\Gamma }}_5\simeq A_5$.