BFB conditions on a class of symmetry constrained 3HDM

TL;DR

This paper investigates the bounded from below conditions in three Higgs doublet models with specific symmetries, developing methods to find sufficient conditions and validating them through phenomenological simulations.

Contribution

It introduces a general strategy using lower bounds to determine BFB conditions in symmetry-constrained 3HDMs and tests their effectiveness through detailed simulations.

Findings

Lower bounds are effective for BFB conditions in certain 3HDMs.

No significant new physical effects found when using these bounds.

Validation shows the bounds are reliable where exact conditions are unknown.

Abstract

We study the bounded from below (BFB) conditions on a class of three Higgs doublet models (3HDM) constrained by the symmetry groups U(1)xU(1), U(1)xZ2 and Z2xZ2. These constraints must be implemented on both the neutral (BFB-n) and charged (BFB-c) directions. The exact necessary and sufficient BFB conditions are unknown in the Z2xZ2 case. We develop a general strategy using lower bounds to find sufficient conditions for BFB-n and BFB-c and apply it to these symmetries. In addition, we investigate the concern that the use of safe sufficient conditions can ignore valid points which would yield distinct physical consequences. This is done by performing a full phenomenological simulation of the U(1)xU(1) and U(1)xZ2 models, where exact necessary and sufficient BFB conditions are possible. We look specifically at the points allowed by exact solutions but precluded by safe lower bounds. We found no evidence of remarkable new effects, partly reassuring the use of the lower bounds we propose here, for those potentials where no exact necessary and sufficient BFB conditions are known.