Improved unitarity constraints in Two-Higgs-Doublet-Models

TL;DR

This paper refines unitarity constraints in Two-Higgs-Doublet-Models by including finite energy effects, revealing more restrictive parameter space limits and emphasizing the importance of cubic couplings over loop corrections.

Contribution

It introduces a full tree-level calculation at finite energy for unitarity constraints in THDMs, improving upon the large energy approximation commonly used.

Findings

Finite energy calculations tighten unitarity bounds.

The light Higgs window closes for large $|M_{12}|$.

Cubic couplings often dominate over loop corrections.

Abstract

Two-Higgs-Doublet-Models (THDMs) are among the simplest extensions of the standard model and are intensively studied in the literature. Using on-shell parameters such as the masses of the additional scalars as input, corresponds often to large quartic couplings in the underlying Lagrangian. Therefore, it is important to check if these couplings are for instance in agreement with perturbative unitarity. The common approach for doing this check is to consider the two-particle scattering matrix of scalars in the large centre-of-mass energy limit where only point interactions contribute. We show that this is not always a valid approximation: the full calculation including all tree-level contributions at finite energy can lead to much more stringent constraints. We show how the allowed regions in the parameter space are affected. In particular, the light Higgs window with a second Higgs below 125 GeV completely closes for large values of the $Z_2$ breaking parameter $|M_{12}|$. We also compare against the loop corrected constraints, which use also the large $\sqrt{s}$ approximation, and find that (effective) cubic couplings are often more important than radiative corrections.