Heavy Higgs bosons at the LHC upgrade

We evaluate the discovery potential for the heavy Higgs bosons at the LHC energy upgrade with TeV. We assume the degenerate mass spectrum and an approximate alignment limit in the Type-II Two Higgs Doublet Model for illustration. We explore the observability of the heavy neutral Higgs bosons by examining the clean signals from via gluon-gluon fusion production. The associated production of a top quark and a charged Higgs boson via is adopted to predict the discovery potential of heavy charged Higgses. We also emphasize the potential importance of the electroweak production of Higgs boson pairs, i.e. and . These are only governed by pure electroweak gauge couplings and can provide complementary information to the conventional signals in the determination of the nature of the Higgs sector.


Introduction
Since the milestone discovery of the Higgs boson at the CERN Large Hadron Collider (LHC) [1,2], much attention has been drawn to the searches for new physics beyond the Standard Model (SM). Most of the theoretical model constructions beyond the SM contain the extended Higgs sector, most notably in the minimal Supersymmetric Standard Model (MSSM) [3] and the composite Higgs model such as the little Higgs theory [4]. Thus, there is strong motivation to search for the new heavy Higgs bosons beyond the SM. Such efforts have been actively carried out, particularly in the LHC experiments.
While the LHC and its luminosity upgrade (HL-LHC) will continue the journey of searching for new physics in the next two decades, future higher energy hadron colliders, such as the energy upgrade for the LHC to 27 TeV C.M. energy (HE-LHC) [5][6][7][8] and the future circular collider of about 100 TeV C.M. energy (FCC-hh) [9], are proposed to perform the direct searches at the energy frontier. In this paper, we set out an initial study for the discovery potential for the new heavy Higgs bosons at the HE-LHC. We take the Type-II Two Higgs Doublet Model (2HDM) for illustration.
The leading search channel for the non-SM neutral Higgses comes from their single production, followed by their conventional decays into pairs of SM particles. We thus study the clean gluon fusion processes and investigate the implication on the parameter space of the Type-II 2HDM model. The channel suffers from major SM backgrounds, such as multijet, , and [8]. For the charged Higgs heavier than the top quark, the typical search channel is the associated production of a charged Higgs boson and top quark. The decay mode is dominant over other decays once kinematically accessible, but also suffers from large SM backgrounds ( + light-flavor jets, + jet(s), + vector boson, + Higgs, single top + W, etc.) [10]. For the subdominant decay , the relevant SM backgrounds involve processes with . The difference between the Yukawa coupling for and the gauge interaction for , in terms of the spin correlation in tau decay, can be used to distinguish the signal from the SM backgrounds.
Although the above conventional signals for searching Higgs bosons benefit from large QCD production cross sections and simple kinematics, they all have a sub-stantial dependence on additional 2HDM parameters, such as and . It is worth emphasizing the potential importance of the electroweak production of Higgs boson pairs, e.g. and . Their production cross sections are only governed by pure electroweak gauge couplings and quite complementary to the conventional signals in the determination of the nature of the Higgs.
The rest of the paper is organized as follows. In Sec. 2, we give a brief overview of the 2HDM and discuss the constraints on the parameters relevant for our study. In Sec. 3, we analyze the single production of neutral Higgs bosons via gluon-gluon fusion and give the implication on the parameters of the Type-II 2HDM model. The prospect of probing single charged Higgs production is presented in Sec. 4. In Sec. 5, we study the signatures of non-SM Higgses pair production through pure electroweak interactions. Finally, in Sec. 6, we summarize our main results.

Two Higgs Doublet Model
(2) L The Two Higgs Doublet Model [11] is a good representative prototype to study the Higgs boson properties beyond the SM. In the 2HDM, the Higgs sector is composed of two SU scalar doublets After the electroweak symmetry breaking (EWSB), there are four more Higgs bosons ( ) besides the SM-like Higgs boson ( ) in the particle spectrum (2) Here, the important parameter is defined as with GeV. Because of the absence of new physics signals from the searches at the LHC, we require that the non-SM Higgses are all heavier than and take their masses as free parameters. Certain discrete symmetries between the two doublets are often imposed to avoid unwanted flavor-changing-neutral currents (FCNC). Motivated by the construction of the minimal Supersymmetric Standard Model (MSSM), we assume the Type-II 2HDM in which only couples to the downtype quarks and leptons and only couples to the uptype quarks. Their couplings to the SM fermions behave as with a normalization factor of for neutral Higgses. The couplings between neutral Higgses and two gauge bosons are and . As such, the parameters involved in our analyses include , , and the relevant Higgs masses under consideration.
As previously intimated, we identify the lighter CPeven scalar as the SM-like Higgs observed at the LHC. This, together with the absence of exotic decays of the 125 GeV Higgs boson, implies the alignment limit [12,13]. We will take the alignment limit or assume the value of near the alignment in the following analysis. The theoretical consideration of vacuum stability [14] and unitarity [15], along with the measurement of the electroweak precision observables, [16] suggest small mass splittings among the four non-SM Higgses. Thus, we assume degenerate heavy Higgs mass spectra (unless otherwise stated) and forbid exotic Higgs decay modes [17][18][19][20][21].
In addition, there are strong constraints on the non-SM Higgs sector from the flavor constraints. In particular, the latest analyses on Br have constrained the charged Higgs to be heavier than 600 GeV at 95% C.L. [22,23]. Precision observables, particularly S and T oblique parameters, also impose correlations between the charged Higgs mass and the neutral ones: or . These limits, however, are typically model dependent and could be relaxed in Type-I 2HDM as shown in Ref. [23], or with additional contributions to the flavor or precision observables from other sectors in the new physics models [24,25]. In this paper, since we focus on the collider aspect of beyond the SM Higgs bosons, we choose the mass spectrum of the non-SM Higgses to be characteristic of the absent exotic decay channels that we analyze and consider the heavy Higgs bosons as they satisfy the current direct collider search limits. The decays that we study in this paper could be applied to those extended models, with possible rescaling of the branching fractions. One should, however, keep those potentially dangerous indirect constraints in mind when considering a specific new physics model with an extended Higgs sector.

Single neutral Higgs production
Just like the Higgs boson discovery, the leading production channel for a heavy neutral Higgs boson is through the gluon fusion These channels benefit from the large gluon luminosity at higher energies and the favorable phase space for a single particle production. We show the production cross sections versus the Higgs mass (from 250 GeV to 2 TeV) at the 14 TeV LHC, 27 TeV LHC, as well as the 100 TeV collider, in Fig. 1. The cross sections are obtained at NNLO in QCD using default SusHi [26] and LHAPDF [27] with the alignment limit or (note that the production does not depend on ). Note that the mixing angle is also constrained through Higgs rate measurements, and is at the edge of the 95% CL exclusion limit by fits to the measured rates of Higgs boson production and decays [28]. For illustration, we take a negative value of here for decays. One should note that a positive value of near the alignment limit is also allowed. We see that the total production cross section at 27 TeV LHC ranges from 4 (2.8) pb at GeV to pb at TeV for in the alignment limit. In addtiion, it increases by four times at GeV and by eight times at TeV from 14 TeV to 27 TeV C.M. energy. The production does not depend on and its production cross section is larger than that of for and . From to , the production cross section of increases and be- comes larger than that of . We explore the observability of the heavy neutral Higgs bosons by examining the specific decay channels. For the channels we consider, we use MadGraph5_ aMC@NLO [29] to generate the signal and backgrounds events, and TAUOLA [30] interfaced with Pythia [31] to simulate the tau lepton decay. To simulate the detector effects in the following analysis, we smear the hadronic/leptonic energy using a Gaussian distribution whose width is parameterized as [32] ∆E The above energy resolution is the expected performance of the ATLAS detector for the LHC. Recently, Delphes-3.4.2 [33] was released for detector simulation and event reconstruction and included the beta card for HL-LHC and HE-LHC studies. Compared with the LHC case, remained almost the same, and and were reduced by 30% and enhanced by three times, respectively. As a values only affect the linear terms in the energy resolution, we expect that the change will not impact our results much.
By far, the cleanest signals for heavy new physics would be the leptonic final states from the decays. We now utilize those channels to search for the CP-even Higgs . The basic requirements for the leptons are and we select the events satisfying The mass of the resonance in the channel can be reconstructed by the transverse mass as shown in Fig. 2. The SM backgrounds are the same as those for channel, but with gauge bosons' leptonic decay to electron/muon. The background has the opposite-sign lepton pairs from Z boson decay and can be further reduced by vetoing the invariant mass of opposite sign leptons if GeV. For the channel, we simply require for the minimal lepton and the invariant mass of the four leptons. The production with pure leptonic decays can also be a reducible background after the two b-jets are vetoed if [34]. The cut efficiencies are given in Tables 1 and 2 for and Table 1. The cut efficiencies for and the SM backgrounds after consecutive cuts at the 27 TeV LHC. We take or 800 GeV.      tan β tan β = 10 (1)

cut efficiencies basic cuts
The exclusion contours for the decay to the SM gauge bosons by the 13 TeV LHC [34,36] are added in the bottom panel of Figs. 3 and 4, assuming . For the decay channel, the LHC has excluded the CP-even Higgs with masses up to 360 (390) GeV and below 1 (3). With realistic branching fractions at , the 27 TeV LHC may discover the CP-even Higgs as heavy as 1 TeV ( TeV) through channels as shown in Figs. 3(c) and 4(c). The loss of sensitivity at the large is mainly due to the reduction of BR . It is known that the Higgs production in association with a pair can enhance the sensit-tan β ≳ 10 ivity for in the Type-II 2HDM [37,38], which is beyond the scope of this article.

Single charged Higgs production
If the charged Higgs boson is heavier than the top quark mass, the conventional production of heavy charged Higgs occurs through . However, in high energy colliders, an ordinary cut (several tens of GeV) on the b-jet in final states is not sufficient as is still very large. Thus, this exclusive contribution is only meaningful when detecting final state b-jet with a sufficiently large cut as a regulator. A more dominant mode would be taking b as a parton and considering "inclusive " production. Thus, the leading production mechanism would be the associated production of H ± with a top quark [39,40] gb → tH ± . (10) Its total cross section is more accurately estimated in [41][42][43].
The production cross sections versus charged the Higgs mass are shown in Fig. 5 at the 14 TeV LHC, 27 TeV LHC, and the 100 TeV colliders. They are the leading order results with a running bottom quark Yukawa coupling at the scale of the pole mass GeV. The total production cross section at 27 TeV LHC ranges from 0.5 pb at GeV to pb at TeV for . We quantify the signal observability according to the leading decay channels.
We consider the clean channel of the charged Higgs boson's leptonic decay, i.e. with , with the branching fraction being , and the hadronic decay of the W boson from the top quark. This channel with the lepton has been studied before and was argued to be a good production mode for the LHC energy upgrade to search [44,45]. Another signal channel is through the leptonic decay to an electron or a muon and two neutrinos [46]. The components of the SM backgrounds for this channel are more complicated as the lepton in final states can be either from tau decay or from gauge boson decay. Also, as there are more missing neutrinos in the events, it is more difficult to reconstruct the tau leptons and extract the Higgs resonance mass. Thus, for simplicity we neglect this channel and make a conservative analysis based on pure hadronic decay of the tau lepton. We adopt the basic acceptance cuts The leading SM backgrounds are given by with . There are more reducible QCD backgrounds, such as the production with one b-jet vetoed if and multijet production with the -fake rate being approximately [46].
Note that, as the charged Higgs only coupled with the right-handed charged lepton, the right-handed decays to a left-handed and . This causes the to move preferentially along the momentum direction. In contrast, the coming from the decay is lefthanded, which has the opposite effect on the . A similar feature holds for the from the and decays. This is a well-known result of spin correlation in the decay [47,48]. Thus, the transverse momentum of from the charged Higgs decay to the tau lepton yields a harder spectrum than that from the W decay in the SM backgrounds [49][50][51], as seen in Fig. 6(a). We thus tighten the missing energy and the of pion Furthermore, Fig. 6(b) indicates that the transverse mass of the pion and missing neutrinos from the charged Higgs should be greater than 100 GeV in order to reduce the backgrounds. One can see that these cuts help reduce the backgrounds significantly from the cut efficiencies shown in Table 3.
If the exotic decay modes (one neutral Higgs with W boson) are absent, the charged Higgs decay is actually dominated by the mode once it is kinematically open. The decay is the secondary significant mode in gb → tH ± tan β = 10 pp tan β gb → tH ±   . As a comparison, the 13 TeV LHC exclusion limit on as a function of is also presented [52].
Chinese Physics C Vol. 44, No. 9 (2020) 093103 the decays to the SM particles and becomes more important as increases. Figure 7(a) and (b) display the reachable limit of BR at the 27 TeV LHC. The HE-LHC with 15 ab luminosity extends the reach of BR to the level for and 4.
The 13 TeV LHC performed the search for charged Higgs bosons through the production of a heavy charged Higgs boson in association with the t and b quarks [52,53]. The results are interpreted in the framework of the hMSSM scenario, which is a Type-II 2HDM [54]. As a comparison, the 95% CL exclusion limit on as a function of is also presented in Fig. 7(c). The charged Higgs boson mass is excluded up to 1.1 TeV for , with the integrated luminosity of 36 fb [52]. With realistic BR , the discovery region in the versus planes is shown in Fig. 7(c) for the channel at the 27 TeV LHC. The region below can not be covered by discovery due to the suppression of the decay branching fraction. The 27 TeV pp collider with 3 ab luminosity can dis-tan β = 10 (60) cover the charged Higgs mass up to 1 TeV (2 TeV) for .

Pair production of Higgs bosons
Besides the above leading production channels of the single Higgs boson, the electroweak production of Higgs boson pairs are potentially important. Their total production cross sections are independent of any model parameters except for the Higgs masses as they exist via pure electroweak gauge interactions. The pair productions of the Higgs bosons through pure gauge interactions are [49,50,[55][56][57] The relevant Higgs couplings to gauge bosons scale is where g is the weak coupling and is the weak-mixing angle with . Figure 8 shows their total cross sections at 14 TeV LHC, 27 TeV LHC and 100 TeV collider. The total cross section of the production at 27 TeV LHC ranges from pb at GeV to pb with 1 TeV Higgs mass. It is approximately twice as large as that of the production. We explore their observability based on the leading decay modes.
The first signal channel we consider is the associated

093103-9
A 0 production of the CP-odd Higgs and the charged Higgs , followed by and decay to and respectively; i.e., . We again adopt the leading 2-body decay channel, i.e.
, with the branching fraction being . The b-jets and the charged pions in final states satisfy the following basic cuts and any b-jets in the events are assumed to be tagged with an efficiency of 70%. The major SM backgrounds are thus from the following irreducible contributions: • the gluon splitting process: , • the single top production: , and the reducible ones • the -gluon fusion process with a forward jet: , • the QCD production: . The last two processes having additional jets or leptons can be vetoed by requiring the extra objects with We display the distributions of signal and backgrounds after the basic cuts at the 27 TeV LHC in Fig. 9 (a) missing transverse energy and (b) transverse pion momentum . The signal exhibits a harder spectrum than the SM backgrounds from the Jacobian peak around . The mass peak of the resonance also leads to an enhanced distribution near . Furthermore, as discussed for the single production with in Sec. 4, the signal has a harder distribution of compared to the SM backgrounds. The charged Higgs mass and the CP-odd Higgs mass can be read from the edge of the transverse mass Fig. 9. (color online) The differential cross section distributions of (a), M bb and the invariant mass of two b-jets , as shown in Figs. 9(c) and (d). We thus apply the following kinematic cuts The cut efficiencies of the signal and backgrounds after imposing the above cuts are summarized in Table 4. One can see that all the SM backgrounds could be sufficiently suppressed and we expect to achieve good signal significance although our signal is induced by a pure electroweak process.
As the production is independent of any model parameters except for the Higgs masses, the only unknown in our signal process can be extracted as the de- cay branching fractions of and . In Fig. 10(a) we show the reach of the product of branching fractions, i.e.
, with the degenerate spectrum and different luminosity assumptions. For GeV with 15 ab luminosity, the discovery limit of the branching fraction product can be as small as . With = 20%, the maximal discovery masses of the degenerate heavy Higgs bosons are approximately 450 GeV and 800 GeV with an integrated luminosity of 3 ab and 15 ab , respectively. We also vary the masses of the charged Higgs and the CP-odd Higgs, and display the discovery region with respect to the two masses in Fig. 10(b) by fixing the branching fraction product to be 20%. The regions to the left of the curves can be covered by 5 discovery.