Tridiagonal scalar mass matrix in the CP4 3HDM and its implications

TL;DR

This paper demonstrates that the scalar sector of the CP4 3HDM can be parametrized using observable quantities due to the unique tridiagonal form of its neutral Higgs mass matrix, enabling detailed phenomenological analysis.

Contribution

It introduces an observable-driven parametrization method for the CP4 3HDM's scalar sector based on the tridiagonal mass matrix, facilitating potential reconstruction and phenomenological studies.

Findings

A set of input observables and an algorithm for potential reconstruction are proposed.

The scalar sector can be explored beyond previous limitations, with additional Higgses in the 300-600 GeV range.

The method enables a full phenomenological scan of the model.

Abstract

When parametrizing multi-Higgs potentials, it is desirable to express its coefficients via observables. This is routinely done for the 2HDM, but this approach often fails in more elaborate models. Here, we show that the scalar sector of the CP4 3HDM, an intriguing model based on an order-4 $CP$ symmetry, can also be parametrized in an observable-driven manner. The key feature that makes it work is the very special tridiagonal form of the $5\times 5$ neutral Higgs mass matrix. We propose a set of input observables and present an algorithm to reconstruct the coefficients of the potential through linear relations. Equipped with this procedure, we explore the scalar sector of the CP4 3HDM beyond the limitations of previous studies. In particular, we identify a viable and testable regime in which all additional Higgses lie in the 300-600 GeV range. This work offers a key ingredient for a future full phenomenological scan of this model.