Flavour Invariants of Multi Higgs Models

TL;DR

The paper develops a basis-invariant framework to analyze flavour in general $N$-Higgs-doublet models. It introduces mixing matrices akin to the CKM structure, emphasized by the charged Higgs basis, and constructs a complete set of weak-basis invariant traces to describe physical parameters and RG evolution. A SVD-based approach on the Yukawa-sourced flavour matrices $N_{dk}$ and $N_{uk}$ yields CKM-like and FCNC structures through the $C$ matrices and eigenvalues $E_{dk},E_{uk}$, extending the 2HDM results to arbitrary $N$. The authors prove consistency with SM parameter counting and provide $10+36(N-1)$ independent invariants to extract masses, mixings, and CP phases in a basis-independent way, enabling robust, scale-evolution analyses of flavour in multi-Higgs scenarios.

Abstract

In this work, a systematic way of analyzing the N Higgs Doublet Models flavor sector will be developed. We introduce a complete set of mixing matrices describing the rotation between certain suitably defined bases, akin to the Cabibbo-Kobayashi-Maskawa matrix, which describes the relation between the up-quark and down-quark mass bases. We point out the crucial importance played by the charged Higgs basis. It is also introduced for the first time a complete set of weak basis transformation invariant traces of flavor matrices for the general N doublets case. This will be important for studies of the renormalization group evolution in terms of relevant physical parameters.