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

Understand

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.