Further study of the global minimum constraint on the two-Higgs-doublet models: LHC searches for heavy Higgs bosons

The usually considered vacuum of the two-Higgs-doublet model (2HDM) could be unstable if it locates at a local but not global minimum (GM) of the scalar potential. By requiring the vacuum to be a GM, we obtain an additional constraint, namely the GM constraint, on the scalar potential. In this work, we explore the GM constraint on the $CP$-conserving general 2HDM. This constraint is found to put limits on the soft ${\mathbb{Z}}_2$ breaking mass parameter $m_{12}^2$ and also squeeze the heavy $CP$-even Higgs boson mass into larger values for the $m_{12}^2<0$ case. Combined with the current global signal fits from the LHC measurements of the 125 GeV Higgs boson, we discuss the phenomenological implications for the heavy Higgs boson searches at the LHC.