Renormalization-group constraints on Yukawa alignment in multi-Higgs-doublet models

TL;DR

This paper derives renormalization-group equations for Yukawa couplings in multi-Higgs-doublet models and identifies conditions under which Yukawa alignment is preserved during running, focusing on two-Higgs and multi-Higgs scenarios.

Contribution

It provides the first detailed analysis of the renormalization-group evolution of Yukawa alignment in multi-Higgs-doublet models, establishing conditions for its stability.

Findings

Yukawa alignment is preserved only in specific 2HDM types (I, II, X, Y).

In multi-Higgs models, alignment persists if and only if each fermion charge couples to a single Higgs doublet.

The results constrain model building by linking Yukawa alignment stability to basis choices.

Abstract

We write down the renormalization-group equations for the Yukawa-coupling matrices in a general multi-Higgs-doublet model. We then assume that the matrices of the Yukawa couplings of the various Higgs doublets to right-handed fermions of fixed quantum numbers are all proportional to each other. We demonstrate that, in the case of the two-Higgs-doublet model, this proportionality is preserved by the renormalization-group running only in the cases of the standard type-I, II, X, and Y models. We furthermore show that a similar result holds even when there are more than two Higgs doublets: the Yukawa-coupling matrices to fermions of a given electric charge remain proportional under the renormalization-group running if and only if there is a basis for the Higgs doublets in which all the fermions of a given electric charge couple to only one Higgs doublet.