Light states in real multi-Higgs models with spontaneous CP violation

TL;DR

In multi-Higgs models with spontaneous CP violation, the scalar spectrum cannot be arbitrarily heavy; at least some new scalars remain near the electroweak scale due to perturbativity constraints.

Contribution

This work demonstrates that in models with spontaneous CP violation, the scalar masses are limited and cannot be arbitrarily large, contrary to naive expectations.

Findings

New scalars have masses close to the electroweak scale.

Charged and neutral scalars are constrained by perturbativity.

Heavy scalar regimes are not achievable in these models.

Abstract

In models with extended scalar sectors consisting of multiple Higgs doublets that trigger spontaneous electroweak symmetry breaking, it might be expected that the abundance of dimensionful quadratic couplings in the scalar potential could allow for a regime where, apart from the would-be Goldstone bosons and a neutral Higgs-like state, all new scalars have masses much larger than the electroweak scale. In the case of models where CP invariance holds at the lagrangian level but is broken by the vacuum, we show that such a reasonable expectation does not hold. When perturbativity requirements are placed on the dimensionless quartic couplings, the spectrum of the new scalars includes one charged and two additional neutral states whose masses cannot be much larger than the electroweak scale.