Fermion number conservation and two Higgs doublet models without tree level flavour changing neutral currents

TL;DR

This paper identifies a class of two Higgs doublet models that conserve fermion number and avoid tree-level flavour changing neutral currents, while introducing new CP-violating phases relevant for B meson mixing.

Contribution

It introduces a novel class of 2HDM models with fermion number conservation and no tree-level FCNC, featuring new CP-violating phases affecting B meson mixing.

Findings

Models can explain B meson CP violation hints

New phases do not affect K meson CP violation

Charged Higgs couplings contain additional CP phases

Abstract

The charged fermion mass matrices are always invariant under $U(1)^3$ symmetry linked to the fermion number transformation. A class of two Higgs doublet models (2HDM) can be identified by requiring that the definition of this symmetry in an arbitrary weak basis be independent of Higgs parameters such as the ratio of the Higgs vacuum expectation values. The tree level flavour changing neutral currents normally present in 2HDM are absent in this class of models but unlike the type I or type II Higgs doublet models, the charged Higgs couplings in these models contain additional flavour dependent CP violating phases. These phases can account for the recent hints of the beyond standard model CP violation in the $B_d$ and $B_s$ mixing. In particular, there is a range of parameters in which new phases do not contribute to the $K$ meson CP violation but give identical new physics contribution to the $B_d$ and $B_s$ meson mixing. Specific model realizations of the above scenario are briefly discussed.