Abstract

Imposing a family symmetry on the Standard Model in order to reduce the number of its free parameters, due to the Schur’s Lemma, requires an explicit breaking of this symmetry. To avoid the need for this symmetry to break, additional Higgs doublets can be introduced. In such an extension of the Standard Model, we investigate family symmetries of the Yukawa Lagrangian. We find that adding a second Higgs doublet (2HDM) does not help, at least for finite subgroups of the U ( 3 ) group up to the order of 1025.

Highlights

  • At currently achievable energies, the Standard Model (SM) of fundamental interactions is a very good working theory

  • One of the signs of this state of things is a large number of free parameters which need to be fitted from experiments

  • Package for constructing representations of finite groups, we have found groups which fulfil the requirements of our model and impose flavour symmetry on the Yukawa Lagrangian

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Summary

Introduction

The Standard Model (SM) of fundamental interactions is a very good working theory. One of several proposals how to restrict number of a free parameters in the SM is to introduce symmetry between Yukawa constants in Yukawa SM interaction in such a way that after spontaneous symmetry breaking get masses and mixing matrix parameters for quarks and leptons which are consistent with experience. Such symmetry is known in the literature as a flavor symmetry [1] (and family or horizontal symmetry). Lepton sector and especially neutrino physics is an attractive area to search for such a symmetry due to the so called lepton mixing matrix [2,3]

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