Fate of metastable vacua in the type-II two-Higgs-doublet model

The scalar potential of the Two-Higgs-Doublet Model (2HDM) can admit multiple non-degenerate vacua due to the presence of the two Higgs doublets unlike the Standard Model (SM). For a physically viable parameter point, one of these vacua must correspond to the physical electroweak (EW) symmetry breaking vacuum with the vacuum expectation value of about $246$ GeV. Given the complex structure of the scalar potential, the physical EW vacuum may be metastable in nature rather than the global minimum of the potential. In this work, we delineate regions of the parameter space in the Type-II 2HDM accommodating multiple extrema of the scalar potential and analyze, in a gauge-independent manner, the stability of the EW vacuum there at the tree level and beyond. A Bayesian global fit of the Type-II 2HDM, including next-to-leading-order unitarity constraints and the latest experimental measurements, indicates that parameter space regions leading to metastable EW vacua are excluded at both the tree and one-loop levels.