Stitching an Asymmetric Texture with ${\mathcal{T}}_{13}\times {\mathcal{Z}}_5$ Family Symmetry

Abstract

We propose ${\mathcal{T}}_{13}={\mathcal{Z}}_{13}⋊{\mathcal{Z}}_3$ as the underlying non-Abelian discrete family symmetry of the asymmetric texture presented in arXiv:1805.10684 [hep-ph]. Its mod 13 arithmetic distinguishes each Yukawa matrix element of the texture. We construct a model of effective interactions that singles out the asymmetry and equates, without fine-tuning, the products of down-quark and charged-lepton masses at a GUT-like scale.

Comments: Major change from previous version: the symmetry ${\mathcal{Z}}_4$ has been changed to ${\mathcal{Z}}_5$ to prohibit a new unwanted vertex, 26 pages, version accepted for publication in Physical Review D