Trimaximal TM${}_1$ mixing with two modular $S_4$ groups

Abstract

We discuss a minimal flavour model with twin modular symmetries, leading to trimaximal TM${}_1$ lepton mixing in which the first column of the tri-bimaximal lepton mixing matrix is preserved. The model involves two modular $S_4$ groups, one acting in the neutrino sector, associated with a modulus field value ${\tau }_{SU}$ with residual $Z_2^{SU}$ symmetry, and one acting in the charged lepton sector, associated with a modulus field value ${\tau }_T$ with residual $Z_3^T$ symmetry. Apart from the predictions of TM${}_1$ mixing, the model leads to a new neutrino mass sum rule which implies lower bounds on neutrino masses close to current limits from neutrinoless double beta decay experiments and cosmology.

23 pages, 2 figures, minor improvement, published in PRD

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