Abelian symmetries in the two-Higgs-doublet model with fermions

TL;DR

This paper classifies all abelian symmetries in the two-Higgs-doublet model with fermions, identifying 246 relevant cases and analyzing implications for quark masses, CP violation, and flavor-changing neutral currents.

Contribution

It provides a comprehensive classification of abelian symmetries in the two-Higgs-doublet model with fermions, reducing possibilities to 246 cases with 34 matrix forms.

Findings

Applying Z_n with n ≥ 4 induces a continuous U(1) symmetry.

Certain symmetries allow for spontaneous CP violation.

Some symmetries naturally suppress flavor-changing neutral currents.

Abstract

We classify all possible implementations of an abelian symmetry in the two-Higgs-doublet model with fermions. We identify those symmetries which are consistent with non-vanishing quark masses and a CKM matrix which is not block-diagonal. Our analysis takes us from a plethora of possibilities down to 246 relevant cases, requiring only 34 distinct matrix forms. We show that applying Z_n with n \geq 4 to the scalar sector leads to a continuous U(1) symmetry in the whole Lagrangian. Finally, we address the possibilities of spontaneous CP violation and of natural suppression of the flavour changing neutral currents. We explain why our work is relevant even for non-abelian symmetries.