Abstract
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.
Highlights
In the studies of new physics beyond the Standard Model (BSM), it is quite often that one has an extended Higgs sector
The current LHC 13 TeV searches for the Higgs boson pairs, as well as other exotic heavy Higgs boson decay modes, are imposed to the benchmark models with the global minimum (GM) constraint taken into account
Similar situations can be envisioned for the BP-2 and BP-3 cases as well, but for the different decay mode of A → ZH. This suggests that the heavy Higgs boson spectrum involving exotic decay modes may be hidden from the LHC experimental searches, with negative inputs of m212 and the GM constraint taken into account
Summary
In the studies of new physics beyond the Standard Model (BSM), it is quite often that one has an extended Higgs sector. One may encounter the possibilities as follows: (i) one Higgs doublet does not acquire a vacuum expectation value (VEV), (ii) the Higgs VEVs break the CP symmetry, or (iii) the Higgs VEVs even break the Uð1ÞEM symmetry It has previously been studied in Refs. To avoid the vacuum instability, one may impose a global minimum (GM) condition for the desired vacuum This leads to new constraints on the Higgs potential, in addition to the conventional bounded-from-below (BFB) constraints and the unitarity bounds. Since the GM constraint on the m212 parameter will control the Higgs boson self-couplings in the 2HDM, the pair productions of both SM-like and BSM Higgs bosons at the LHC can be relevant to this constraint. The current LHC 13 TeV searches for the Higgs boson pairs, as well as other exotic heavy Higgs boson decay modes, are imposed to the benchmark models with the GM constraint taken into account.
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