# Alignment limit in three Higgs-doublet models

## TL;DR

This paper analyzes the alignment limit in three Higgs-doublet models (3HDMs), showing it has a similar structure to two Higgs-doublet models (2HDMs) and demonstrating how to implement these conditions in realistic scenarios.

## Contribution

It provides an analytic framework for understanding the alignment limit in CP-conserving 3HDMs, extending the known structure from 2HDMs and illustrating practical implementation with a $Z_3$-symmetric example.

## Key findings

- Alignment limit in 3HDMs has the same analytic structure as in 2HDMs.
- Efficient implementation of alignment conditions demonstrated with a $Z_3$-symmetric 3HDM.
- Alignment conditions can be used to achieve SM-like Higgs couplings in BSM models.

## Abstract

The LHC Higgs data is showing a gradual inclination towards the SM result and realization of an SM-like limit becomes essential for BSM scenarios to survive. Considering the accuracy that can be achieved in future colliders, BSMs that acquire the alignment limit with an SM-like Higgs boson coupling can surpass others in the long run. Using a convenient parametrization, we demonstrate that the alignment limit for CP-conserving 3HDMs takes on the same analytic structure as that in the case of 2HDMs. Using the example of a $Z_3$-symmetric 3HDM, we illustrate how such alignment conditions can be efficiently implemented for numerical analysis in a realistic scenario.