# A Simple Method to detect spontaneous CP Violation in multi-Higgs models

## TL;DR

This paper introduces a straightforward and rigorous alternative method to detect spontaneous CP violation in multi-Higgs models, especially useful when dealing with more than two Higgs doublets and continuous symmetries.

## Contribution

The authors propose a new method that simplifies the detection of spontaneous CP violation by analyzing the Higgs potential in the Higgs basis, improving upon the traditional approach.

## Key findings

- Method is effective for models with multiple Higgs doublets.
- Applicable to models with continuous symmetries.
- Simplifies analysis by transforming to the Higgs basis.

## Abstract

For models with several Higgs doublets we present an alternative method to the one proposed by Branco, Gerard and Grimus, in 1984, to check whether or not CP is spontaneously violated in the Higgs potential. The previous method is powerful and rigorous. It requires the identification of a matrix $U$ corresponding to a symmetry of the Lagrangian and verifying a simple relation involving the vacuum expectation values. The nonexistence of such a matrix signals spontaneous CP violation. However, as the number of Higgs doublets increases, finding such a matrix $U$ may not be straightforward and it may turn out to be easier to analyse the potential by going to the so-called Higgs basis. The transformation to the Higgs basis is straightforward once the vacuum expectation values are known. The method proposed in this work is also powerful and rigorous and can be particularly useful to analyse models with more than two Higgs doublets and with continuous symmetries.