One-loop considerations for coexisting vacua in the CP conserving 2HDM

TL;DR

This paper examines whether tree-level methods for identifying the global minimum in the CP conserving 2HDM remain valid when considering one-loop quantum corrections, focusing on different types of coexisting minima.

Contribution

It demonstrates that tree-level criteria for determining the global minimum are reliable for regular minima at one-loop, but not for non-regular minima in the CP conserving 2HDM.

Findings

Tree-level formulas generally identify the global minimum for regular minima at one-loop.

For non-regular minima, tree-level expectations fail at one-loop.

The sign of $m^2_{12}$ indicates the global minimum for regular minima even after quantum corrections.

Abstract

The Two-Higgs-Doublet model (2HDM) is a simple and viable extension of the Standard Model (SM) with a scalar potential complex enough that two minima may coexist. In this work we investigate if the procedure to identify our vacuum as the global minimum by tree-level formulas carries over to the one-loop corrected potential. In the CP conserving case, we identify two distinct types of coexisting minima --- the regular ones (moderate $\tan\beta$) and the non-regular ones (small or large $\tan\beta$) --- and conclude that the tree level expectation fails only for the non-regular type of coexisting minima. For the regular type, the sign of $m^2_{12}$ already precisely indicates which minima is the global one, even at one-loop.