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

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 $m_{12}^2$ already precisely indicates which minima is the global one, even at one-loop.