A new type of CP symmetry, family replication and fermion mass hierarchies

TL;DR

This paper proposes a two-Higgs-doublet model with extended CP symmetries that restricts fermion couplings, leading to specific mass hierarchies and predictions for future collider experiments.

Contribution

It introduces a novel principle of maximal CP invariance extending to the full Lagrangian, constraining fermion-Higgs couplings and explaining fermion mass hierarchies.

Findings

Fermion families cannot all couple to Higgs fields simultaneously.

The model predicts degenerate or hierarchical fermion masses.

Potential experimental signatures at the LHC are discussed.

Abstract

We study a two-Higgs-doublet model with four generalised CP symmetries in the scalar sector. Electroweak symmetry breaking leads automatically to spontaneous breaking of two of them. We require that these four CP symmetries can be extended from the scalar sector to the full Lagrangian and call this requirement the principle of maximal CP invariance. The Yukawa interactions of the fermions are severely restricted by this requirement. In particular, a single fermion family cannot be coupled to the Higgs fields. For two fermion families, however, this is possible. Enforcing the absence of flavour-changing neutral currents, we find degenerate masses in both families or one family massless and one massive. In the latter case the Lagrangian is highly symmetric, with the mass hierarchy being generated by electroweak symmetry breaking. Adding a third family uncoupled to the Higgs fields and thus keeping it massless we get a model which gives a rough approximation of some features of the fermions observed in Nature. We discuss a number of predictions of the model which may be checked in future experiments at the LHC.