^{1}

^{,†}

^{2}

^{,*}

^{3}

^{,‡}

^{4}

^{,§}

Corresponding author.

^{3}.

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

In the studies of new physics beyond the Standard Model (BSM), it is quite often that one has an extended Higgs sector. A simple and well-known example is the two-Higgs-doublet model (2HDM),

See Ref.

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. Recently, the GM condition of the 2HDM potential has been analytically formulated in Ref.

Typically in many BSM models with scalar extensions, the GM conditions of the desired vacua can be nontrivial and deserve further studies. The GM conditions of some models have been studied before, such as the Georgi-Machacek model in Ref.

In this work, we further study the GM constraint on the 2HDM, with the focus on the phenomenological implications at the LHC. It turns out that the GM condition is likely to put constraints on the masses of heavy Higgs bosons and the soft

The layout of this paper is described as follows. In Sec.

The scalar potential of the general 2HDM is written as follows:

The potential in Eq.

In the general 2HDM, there could be tree-level flavor-changing neutral currents (FCNC), which are well-known constraints on such model. To alleviate the tree-level FCNC process constraints, the SM fermions of a given representation are usually assigned to a single Higgs doublet. We focus on the so-called Type I and Type II Yukawa couplings of

Besides, two

The current LHC run I and run II have measured the signal strengths of the SM-like 125 GeV Higgs boson

Throughout the context, we always assume that

The combined LHC run-I and run-II constraints on the 125 GeV Higgs boson signal strengths in terms of 2HDM parameters

As explained in the Introduction, to guarantee the absolute stability of the usually considered vacuum, we shall impose the GM constraint on the potential. First, we will present all the possible minima of the potential at the tree level and discuss the condition of the desired one being a global minimum. We realize that loop corrections can also have important influence on the GM constraint. Subsequently, we will also address the issue of including loop corrections.

At the tree level, by defining the following three

Depending on whether the minima are on one of the boundaries in Eq.

All possible local minima of the scalar potential. “

^{a}

Not required.

The row in Table

The solution of Type A is given by

The Type D minimum is determined by

The potential minima for the Type B, Type C, and Type D cases can be expressed as follows in the physical basis:

Apparently, the minimal values of the 2HDM potential in the Type B and Type C cases are essentially controlled by the input parameters of

The GM constraint requires that the Type D minimum is a GM of the potential in order to protect the corresponding vacuum from decaying to other vacua. To infer whether it is a GM, one can compute all the possible minima listed in Table

Note that the minima summarized in Table

When applying the GM constraint, we shall first impose the BFB

However, as recently shown in Ref.

Given inputs of (

all the heavy Higgs bosons are mass degenerate, i.e.,

two of the heavy Higgs bosons are mass degenerate while the remaining are heavier or lighter than the degenerate mass—see Table

Summary table of the different benchmark planes (BP) with exotic heavy Higgs boson decays in the 2HDM.

For scenario (i), we perform a grid scan of

In Fig.

The GM constraints in the

In Fig.

The GM constraints (excluding yellow) combined with the unitarity and BFB constraints (excluding gray) on some benchmarks tabulated in Table

In this section, we will discuss the implications of the GM constraint on the LHC phenomenology of the heavy Higgs boson searches in the general 2HDM. Since we have found that the GM condition is able to further constrain

We study the resonance productions of the SM-like Higgs boson pair productions for the degenerate heavy Higgs boson scenario. The exact results for the one-loop Higgs pair production processes at the

The decay branching fractions of

We obtain the heavy

The current LHC 13 TeV search limits on the resonance productions of SM-like Higgs boson pairs, for the Type I model (left panel) and Type II model (right panel). The red and blue hatched regions have been excluded by the

In general, the cubic self-couplings control the partial decay widths of heavy Higgs bosons, such as

Currently, the most recent LHC search limits on a heavy Higgs boson decaying into a

The current LHC 13 TeV search limits on the

Similar to Fig.

Similar to Fig.

Similar to Fig.

As shown in Figs.

For the BP-1 and BP-4 cases, a more negative input of

In the scalar potential of the general 2HDM, it is likely that several minima may coexist. The usually considered vacuum can thus become a local minimum, and it may decay into a deeper one. To avoid this vacuum instability at the tree level, we impose the GM condition to the 2HDM potential.

According to our analysis, it turns out that the GM condition can impose a more stringent bound on the

The work of N. C. is supported by the National Natural Science Foundation of China (under Grant No. 11575176) and Center for Future High Energy Physics (CFHEP). The work of Y. C. W. is partially supported by the Natural Sciences and Engineering Research Council of Canada. N. C. thanks Center for High Energy Physics Peking University for their hospitality when part of this work was prepared.