Heavy Higgs Bosons at the LHC Upgrade

We evaluate the discovery potential for the heavy Higgs bosons at the LHC energy upgrade with $\sqrt{s}=27$ TeV. We take degenerate mass spectrum and assume near the 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 leading decay channel $H^0/A^0\to \tau^+\tau^-$ and the clean signals from $H^0\to W^+W^-, ZZ$ via gluon-gluon fusion production. The associated production of a top quark and a charged Higgs boson via $gb\to t H^\pm$ 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. $pp\to W^\ast \to H^\pm A^0$ and $pp\to Z^\ast/\gamma^\ast \to H^+ H^-$. They 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 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]. It is therefore strongly motivated to search for the new heavy Higgs bosons beyond the SM. Such efforts have been actively carried out, in particular in the LHC experiments.
While the LHC and its luminosity upgrade (HL-LHC) will continue the journey on 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] and the future circular collider of about 100 TeV C.M. energy (FCChh) [8], 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 gluon fusion processes gg → φ → τ + τ − , W + W − , ZZ and investigate the implication on the parameter space of the Type-II 2HDM model. For the charged Higgs heavier than top quark, the typical search channel is the associated production of a charged Higgs boson and top quark. The decay mode H ± → tb may suffer from large SM backgrounds but is dominant over other decays H ± → τ ± ν and cs, once kinematically accessible. For the sub-dominant decay H ± → τ ± ν, the relevant SM backgrounds involve processes with W ± → τ ± ν. The difference between the Yukawa coupling for H ± and the gauge interaction for W ± , 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 are benefitted from large QCD production cross sections and simple kinematics, they all have a substantial dependence on additional 2HDM parameters, such as tan β and cos(β − α). It is worth to emphasize the potential importance of the electroweak production of Higgs boson pairs, e.g. pp → W * → H ± A 0 and pp → Z * /γ * → H + H − . Their production cross sections are only governed by pure electroweak gauge couplings and quite complementary to the conventional signals in the determination of the Higgs nature.
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
Two Higgs Doublet Model [9] 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(2) L scalar doublets After the electroweak symmetry breaking (EWSB), there are four more Higgs bosons (H 0 , A 0 , H ± ) besides the SM-like Higgs boson (h 0 ) in the particle spectrum Here, the important parameter is defined as Because of the absence of new physics signals from the searches at the LHC, we demand that the non-SM Higgses are all heavier than h 0 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 H 1 only couples to the down-type quarks and leptons and H 2 only couples to the up-type quarks. Their couplings to the SM fermions behave as with a normalization factor im u,d,l /v for neutral Higgses. The couplings between neutral Higgses and two gauge bosons are g H 0 V V = cos(β − α) and g A 0 V V = 0. As such, the parameters involved in our analyses include tan β, cos(β − α), and the relevant Higgs masses under consideration. As intimated before, we identify the lighter CP-even scalar h 0 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 [10,11]. We will take the alignment limit cos(β −α) = 0 or assume the value of cos(β −α) not far away from the alignment in the following analysis. The theoretical consideration of vacuum stability [12] and unitarity [13] and the measurement of electroweak precision observables [14] suggest small mass splittings among the four non-SM Higgses. We thus assume degenerate heavy Higgs mass spectrum (unless otherwise stated) and forbid exotic Higgs decay modes [15][16][17][18][19].
In addition, the non-SM Higgs sector is strongly constrained by various flavor physics measurements such as the b → s transitions [20]. The charged Higgs boson in Type-II 2HDM is in particular required to be heavier than about 600 GeV [21]. This constraint can be relaxed by the cancellation between the charged Higgs contribution and new contributions to the flavor observables from other sectors in new physics models [22,23]. As we focus on the collider search of heavy Higgs bosons in this paper, we will not pursue the flavor constraints explicitly. We will individually take into account LHC constraints for the specific decay channels of heavy Higgses we consider in the following.

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 are benefitted 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 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 [24] and LHAPDF [25] with the alignment limit cos(β − α) = 0 or cos(β − α) = −0.1 (note that the gg → A 0 production does not depend on cos(β − α)). We see that the total production cross section at 27 TeV LHC ranges from 4 (2.8) pb at M H 0 (A 0 ) = 250 GeV to 1 (3) × 10 −4 pb at M H 0 (A 0 ) = 2 TeV for tan β = 10 in the alignment limit. It increases by four times at M H 0 /A 0 = 500 GeV and by eight times at M H 0 /A 0 = 1.5 TeV from 14 TeV to 27 TeV C.M. energy. We explore the observability of the heavy neutral Higgs bosons by examining the specific decay channels.
contribution is W ± Z → τ + τ − ± ν with the additional charged lepton ± vetoed if p T ( ) > 7 GeV, |η( )| < 3.5. We use MadGraph5 aMC@NLO [26] to generate signal and backgrounds events, and TAUOLA [27] interfaced with Pythia [28] to simulate tau lepton decay. We follow the search strategy recently carried out by the ATLAS collaboration [29], and adopt the acceptance cuts as The mass of the heavy Higgs resonance can be read from the edge of the total transverse mass as shown in Fig. 2 (a). To enhance the acceptance of our signal, we further require the events pass the following selection cuts, namely • missing energy cut: E T > 40 GeV, • minimal p T cut on the two charged pions: p min T (π) > 65 GeV, • azimuthal angle cut for the back-to-back pions in the transverse plane: The cut efficiencies for the signal and SM backgrounds are collected in Table 1. The dominant backgrounds after E T , p T cuts are the irreducible backgrounds W W, ZZ.
The ZZ background with one Z decaying invisibly and the other decaying to two tau leptons can be further suppressed by the azimuthal angle cut.  5σ discovery, respectively. With 15 ab −1 luminosity, the branching fraction limit of H 0 /A 0 → τ + τ − can be reached as low as 1.5×10 −3 for M H 0 /A 0 350 GeV and H 0 , A 0 with the mass of about 1.85 TeV can be probed for 5σ discovery if BR(H 0 /A 0 → τ + τ − ) = 1. As the decays of H 0 , A 0 into heavy quarks are dominant for small and moderate tan β if kinematically accessible [30,31] and the decay into bb dominates over τ τ mode for large tan β, the realistic branching fraction of H 0 /A 0 → τ + τ − cannot reach the order of unity. We use package 2HDMC [32] to calculate all 2HDM branching fractions below.
The LHC provided the observed 95% CL upper limit on the gluon-gluon fusion production cross section times the branching fraction of a scalar boson decay into τ τ at √ s = 13 TeV, corresponding to an integrated luminosity of about 36 fb −1 [29,33]. We recast the limit in the plane of tan β versus M H 0 /A 0 for the Type-II 2HDM as shown by dashed curves in Fig. 3 the discovery region of 27 TeV LHC in the alignment limit is displayed in Fig. 3 The regions to the left of the curves can be covered by 5σ discovery, corresponding to different luminosities. One can see that the reach at 27 TeV LHC can cover most of the region with small tan β. The wedge region with tan β ∼ 10 loses sensitivity due to the suppression of the production cross section. For tan β = 1 (10) [50], the 27 TeV LHC can probe the neutral Higgs as heavy as 2 TeV (800  L=3 fb We assume tan β = 10 and cos(β − α) = 0. Right: Discovery contour in tan The excluded regions in the Type-II 2HDM are indicated by the dashed curves, based on gg → H 0 /A 0 → τ τ search at the 13 TeV LHC [29,33].

H
By far, the cleanest signals for heavy new physics would be the leptonic final states from the W/Z decays. We now utilize those channels to search for the CP-even Higgs H 0 . The basic requirements for the leptons are and we select the events satisfying for as shown in Fig. 2 for the minimal lepton p T and the invariant mass of the four leptons. The cut efficiencies are given in Tables 2 and 3 for W W and ZZ channels, respectively. One can see that the Z boson veto and the mass window requirement for H 0 resonance significantly suppress the ZZ background for The exclusion contours for H 0 decay to the SM gauge bosons by the 13 TeV LHC [34,35] are added in the right panels of Fig. 4, assuming cos(β − α) = −0.1. For W W (ZZ) decay channel, the LHC has excluded the CP-even Higgs with masses up to 360 (390) GeV and tan β below 1 (3). With realistic branching fractions at tan β = 10 (1), the 27 TeV LHC may discover the CP-even Higgs as heavy as 1.1 TeV (1.5 − 2 TeV) through gg → H 0 → W + W − , ZZ channels as shown in Fig. 4 (b) and (d). The loss of sensitivity at large tan β is mainly due to the reduction of BR(H 0 → W + W − , ZZ).

Single Charged Higgs Production
If the charged Higgs boson is heavier than the top quark mass, the conventional production of heavy charged Higgs is through gg → tbH ± . However, at high energy colliders, an ordinary p T cut (several tens of GeV) on the b-jet in final states is not enough as log( √ŝ /p T ) is still very large. Thus, this exclusive contribution is only meaningful when detecting final state b-jet with sufficiently large p T cut as 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 [36,37] gb → tH ± . (4.1) Its total cross section is more accurately estimated [38][39][40].
The production cross sections versus charged Higgs mass are shown in   Table 4. The cut efficiencies for gb → tH ± → τ ± νbW ∓ → τ ± νbjj and the SM backgrounds after consecutive cuts at the 27 TeV LHC. We take M H ± = 300 or 800 GeV.
We first consider the clean channel of the charged Higgses' leptonic decay, i.e. H ± → τ ± ν with τ ± → π ± ν, and the hadronic decay of the W boson from the top quark. This channel with τ lepton has been studied before and it was argued to be a good production mode for the LHC energy upgrade to search for [41,42]. We adopt the basic acceptance cuts The leading SM backgrounds are given by gb → W ± t with W ± → τ ± ν τ and QCD tt production with one b-jet being vetoed if p T (b) > 30 GeV, |η(b)| < 4.9.
Note that, as the charged Higgs H − only coupled with right-handed charged lepton, the right-handed τ − R decays to a left-handed ν τ and π − . This causes the π − to preferentially move along the τ − momentum direction. In contrast, the τ − coming from W − decay is left-handed, which has the opposite effect on the π − . The similar feature holds for the τ + from H + and W + decays. This is a well-known result of spin correlation in the τ decay [43,44]. Thus, the transverse momentum of π ± from charged Higgs decay to tau lepton yields a harder spectrum than that from W decay in SM backgrounds [45][46][47], as seen in Fig. 6 (a). We thus tighten the missing energy and the p T of pion Furthermore, Fig. 6 (b) indicates that the transverse mass of the pion and missing neutrinos from charged Higgs should be greater than 100 GeV in order to reduce backgrounds. One can see that these cuts help reduce the backgrounds significantly from the cut efficiencies shown in Table 4.
If the exotic decay modes (one neutral Higgs with W boson) are absent, the charged Higgs decay is actually dominated by tb mode once it is kinematically open. The H ± → τ ± ν decay is the secondary significant mode in the decays to the SM particles and becomes more important as tan β increases. Figure 7 (a) displays the reachable limit of BR(H ± → τ ± ν) at the 27 TeV LHC. The HE-LHC with 15 ab −1 luminosity extends the reach of BR(H ± → τ ± ν) to 10 −3 level for tan β = 10. The 13 TeV LHC performed the search for charged Higgs bosons through the production of a heavy charged Higgs boson in association with t and b quarks [48,49]. The results are interpreted in the framework of the hMSSM scenario which is a Type-II 2HDM [50]. As a comparison, the 95% CL exclusion limit on tan β as a function of M H ± is also presented in Fig. 7 (b). The charged Higgs boson mass is excluded up to 1.1 TeV for tan β = 60, with the integrated luminosity of 36 fb −1 [48]. With realistic BR(H ± → τ ± ν), the discovery region in tan β versus M H ± plane is shown in Fig. 7 (b) for gb → tH ± → τ ± νbjj channel at 27 TeV LHC. The region below tan β ∼ 1 can not be covered by 5σ discovery due to the suppression of the decay branching fraction. The 27 TeV pp collider with 3 ab −1 luminosity can discover the charged Higgs mass up to 1 TeV (2 TeV) for tan β = 10 (60).

H ± → tb
Next we consider the signal induced by decay H ± → tb followed by the two top quarks' semi-leptonic decays, i.e. gb → tH ± → btt → bbbjj ± ν. The irreducible SM background is thus gb → btt. The basic cuts are the same as those in Eq. (4.2) for jets and lepton. Any b-jets in the events are assumed to be tagged with an efficiency of 70%.  Left: Reach of BR(H ± → τ ± ν) as a function of M H ± for gb → tH ± → τ ± νbjj channel at the 27 TeV LHC. We assume tan β = 10. Right: Discovery contour in tan β versus M H ± plane for gb → tH ± → τ ± νbjj with realistic BR(H ± → τ ± ν). As a comparison, the 13 TeV LHC exclusion limit on tan β as a function of M H ± is also presented [48].
As the missing neutrino is only from W 's leptonic decay, using W 's mass and the missing transverse momentum ¡ ¡ p T , one can arrive at a solution of the longitudinal momentum of the neutrino and this W boson can thus be reconstructed [45]. The other W can be directly reconstructed by the invariant mass of the two light jets. The three b-jets are then assigned with the two W bosons to fully reconstruct two top quarks and the charged Higgs. The invariant mass of tb for the charged Higgs is displayed in Fig. 8. We apply the kinematic cuts on the missing energy, the p T of b-jet and the invariant mass of charged Higgs as follows The resultant cut efficiencies are listed in Table 5. Due the the complexity of the objects in final states, it turns out that these cuts are not as efficient as those for H ± → τ ± ν signal. The left panel of Fig. 9 shows the reachable limit of BR(H ± → tb) as a function of M H ± with tan β = 10. With 15 ab −1 luminosity, the charged Higgs mass can be probed as heavy as M H ± 950 GeV for 5σ discovery if BR(H ± → tb) = 1. As H ± → tb is the leading decay mode for both small and large tan β in the alignment limit, this discovery potential is also true for realistic values of BR(H ± → tb) calculated by 2HDMC as shown in Fig. 9 (b). In Fig. 9 (b), the regions to the left of the curves are covered by 5σ discovery at 27 TeV LHC. One can see that final states  Table 5. The cut efficiencies for gb → tH ± → btt → bbbjj ± ν and the SM backgrounds after consecutive cuts at the 27 TeV LHC. We take M H ± = 300 or 800 GeV.
with tH ± → btt prove to be a very sensitive channel for regions with both small and large tan β. Although the region with moderate tan β loses sensitivity due to the suppression of the decay branching fraction, the charged Higgs with mass up to 900 GeV can be probed for tan β 10 with 15 ab −1 luminosity.
Early phenomenological studies have performed the analysis of this signature and concluded that the LHC discovery potential might be optimistic for the charged Higgs mass lower than 600 GeV [51][52][53][54][55]. The LHC explored heavy charged Higgs boson decaying into tb(tb) through gb → tH ± at √ s = 8 TeV [56] and gg → tbH ± at √ s = 13 TeV [49,57]. We convert the observed limit on the production cross section σ(gb → tH ± ) times branching fraction for H ± → tb to the constraint on tan β versus M H ± in Type-II 2HDM, as shown by black dashed curve in Fig. 9 Figure 9. Left: Reach of BR(H ± → tb) as a function of M H ± for gb → tH ± → btt → bbbjj ± ν channel at the 27 TeV LHC. We assume tan β = 10. Right: Discovery contour in tan β versus M H ± plane for gb → tH ± → btt → bbbjj ± ν with realistic BR(H ± → tb). The observed exclusion limits at 8 TeV [56] and 13 TeV [57] LHC are indicated by dashed curves.

Pair Production of Higgs Bosons
Besides the above leading production channels of 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 Higgs masses as they are via pure electroweak gauge interactions. The pair productions of Higgs bosons through pure gauge interactions are [45,46,[58][59][60] qq The relevant Higgs couplings to gauge bosons scale as where g is the weak coupling and θ W is the weak-mixing angle with c W = cos θ W . Figure 10 shows their total cross sections at 14 TeV LHC, 27 TeV LHC and 100 TeV pp collider. The total cross section of H ± A 0 production at 27 TeV LHC ranges from 2.3 × 10 −2 pb at M A 0 = M H ± = 250 GeV to 1.5 × 10 −4 pb with 1 TeV Higgs mass. It is larger than that of H + H − production by about twice. We explore their observability based on the leading decay modes.

H
The first signal channel we consider is the associated production of the CP-odd Higgs A 0 and the charged Higgs H ± , followed by A 0 and H ± decay to bb and τ ± ν τ respectively, i.e. pp → H ± A 0 → τ ± ν τ bb. We again adopt the τ 's leading 2-body decay channel, i.e. τ ± → π ± ν τ , with the branching fraction being BR(τ ± → π ± ν τ ) = 0.11. The b-jets and the charged pions π ± 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: qq → gW ± → bbW ± → bbτ ± ν , • the single top production: qq → W ± * → bt(bt) → bbW ± → bbτ ± ν , and the reducible ones • the W ± -gluon fusion process with a forward jet: gq → gq W ± * → q bt(bt) → q bbW ± → q bbτ ± ν , • the QCD tt production: tt → bbW + W − → bbτ ± ∓ ν s ( = e, µ).
We display the distributions of signal and backgrounds after the basic cuts at the 27 TeV LHC in Fig. 11, for (a) missing transverse energy E T and (b) transverse pion momentum p T (π). The signal exhibits a harder E T spectrum than the SM backgrounds from the Jacobian peak around p T ν ∼ M H ± /2. The mass peak of the resonance A 0 also leads to an enhanced distribution near p T b ∼ M A 0 /2. Furthermore, as discussed for single H ± production with H ± → τ ± ν in Sec. 4.1, the signal has a harder p T distribution of π ± compared to the SM backgrounds. The charged Higgs mass M H ± and the CP-odd Higgs mass M A 0 can be read from the edge of transverse mass and the invariant mass of two b-jets M bb , respectively, as shown in Figs. 11 (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 6. One can see that all the SM backgrounds could be suppressed sufficiently and we expect to achieve good signal significance although our signal is induced by a pure electroweak process.
As the H ± A 0 production is independent of any model parameters, except for the Higgs masses, the only unknown in our signal process can be extracted as the decay branching fractions of H ± and A 0 . In Fig. 12 (a) we show the reach of the product of branching fractions, i.e. BR(H ± → τ ± ν τ ) × BR(A 0 → bb), with degenerate spectrum M A 0 = M H ± and different luminosity assumptions. For M A 0 = M H ± 300 GeV, with 15 ab −1 luminosity, the discovery limit of the branching fraction product can be as small as 3 × 10 −2 . With BR(H ± → τ ± ν τ ) × BR(A 0 → bb) = 20%, the maximal discovery mass of degenerate heavy Higgs bosons are around 450 GeV and 800 GeV with an integrated luminosity of 3 ab −1 and 15 ab −1 , 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. 12 (b), by fixing the branching fraction product to be 20%. The regions to the left of the curves can be covered by 5σ discovery.
As we require the CP-odd Higgs to decay into bb, this case still has the Jacobian peak around p T b ∼ M A 0 /2. The missing transverse energy here is softer than that in H ± A 0 → τ ± νbb mode as the neutrino is from the subsequent decay of top quark. Thus, we apply the following kinematic cuts in addition to the basic acceptance cuts cut efficiencies basic cuts  Table 6. The cut efficiencies for pp → H ± A 0 → τ ± ν τ bb and the SM backgrounds after consecutive cuts with τ ± → π ± ν τ channel at the 27 TeV LHC. We take M H ± = M A 0 = 300 or 800 GeV.
The leptonic W boson from the top quark can be reconstructed using the method described in Sec. 4.2. Because of the complexity from the four b-jets in our signal, when requiring the correct combination to reconstruct M H ± and M A 0 , we assume and make use of the nearly-equal mass spectrum of H ± and A 0 . The obtained invariant masses of tb and bb are shown in Figs. 13 (a) and (b), respectively. Then, we can take two mass windows near the resonances The cut efficiencies are illustrated in Table 7.  Figure 13. Top: The differential cross section distributions of M tb (a) and M bb (b) for the signal pp → H ± A 0 → tb(tb)bb → bbbb ± ν and backgrounds at the 27 TeV LHC. Bottom: In our signal process, the only dependence is again the product of decay branching fractions which is BR(H ± → tb) × BR(A 0 → bb) here. As shown in Fig. 13 cut efficiencies basic cuts  Table 7. The cut efficiencies for pp → H ± A 0 → tb(tb)bb → bbbb ± ν and the SM backgrounds after consecutive cuts at the 27 TeV LHC. We take M H ± = M A 0 = 300 or 800 GeV.
(c), with degenerate spectrum M A 0 = M H ± 300 GeV and 15 ab −1 luminosity, the reach of the branching fraction product extends low to the level of 10 −2 . With BR(H ± → tb) × BR(A 0 → bb) = 10%, the heavy Higgs bosons with 600 GeV and 900 GeV of mass can be discovered with an integrated luminosity of 3 ab −1 and 15 ab −1 , respectively.

H + H
The first signal of H + H − pair production consists of two tau leptons plus missing energy H + H − → τ + τ − ν τντ , followed by τ ± → π ± ν. The irreducible SM backgrounds are from diboson productions 9) and the reducible contribution is which can also be vetoed by the requirement in Eq. (5.4). The distributions of signal and backgrounds at the 27 TeV LHC after the basic cuts are shown in Fig. 14, for (a) missing transverse energy E T and (b) transverse pion momentum p T (π). One can see that the tau polarization effect mentioned above tends to be more dramatic in this channel (in comparison with the W W background). We thus strengthen the missing energy and p T (π) as follows E T > 100 GeV, p max T (π) > 100 GeV. (5.11) Cut efficiencies are collected in Table 8. Due to the missing neutrinos from both the charged Higgs and the tau lepton in this channel, one is unable to reconstruct the charged Higgs boson or build a transverse mass to estimate the signal observability. The signal-to-background ratio is not expected to be improved as much as the associated production analyzed in Sec. 5.1. Figure 14 (c) shows the reach of BR(H ± → τ ± ν) versus M H ± for pp → H + H − → τ + τ − ν τντ . One can see that this channel can access the decay branching fraction to be 20% for the charged Higgs just above the top quark threshold with 15 ab −1 luminosity.
Finally, we consider semi-leptonic channel H + H − → tbtb → bbbbjj ± ν induced by H ± → tb and the leading SM background bbtt. Using the methods mentioned in Sec. 4.2, the two charged Higgses can be fully reconstructed. The sensitivity of this search is limited by the efficiency of the top quark tagging due to smaller typical transverse momenta. Assuming BR(H ± → tb) = 1, we can accumulate 250 (9) signal events for M H ± = 300 (800) GeV with 15 Table 8. The cut efficiencies for pp → H + H − → τ + τ − ν τντ and the SM backgrounds after consecutive cuts with τ ± → π ± (−) ν τ channel at the 27 TeV LHC. We take M H ± = 300 or 800 GeV.
Higgs with the mass of 300 GeV, one needs 50 ab −1 luminosity. This mode is thus not optimistic for probing the charged Higgs.

Conclusions
New Higgs bosons are present in many of new physics models and their direct searches yield no signal observation in the LHC experiments so far. LHC upgrades with higher energy, such as the HE-LHC and FCC-hh, are thus motivated to carry out the search for heavy non-SM Higgs bosons.
In this paper, we investigate the discovery potential of the HE-LHC with 27 TeV C.M. energy for the heavy Higgses in Type-II 2HDM. To accommodate the theoretical bounds and experimental limits, we assume degenerate Higgs spectrum M H 0 ≈ M A 0 ≈ M H ± and the parameter cos(β − α) near the alignment limit. We analyze the typical production and decay modes of non-SM Higgses and present the implication on the parameter space of Type-II 2HDM.
We explore the observability of the heavy neutral Higgs bosons by examining the leading decay channel H 0 /A 0 → τ + τ − and the clean signals from H 0 → W + W − , ZZ via gluon-gluon fusion production. With realistic decay branching fractions, for tan β ∼ 1, the 27 TeV LHC can probe the neutral Higgs as heavy as 2 TeV with the luminosity of 15 ab −1 . For large values of tan β(∼ 50), the τ τ channel gives the better sensitivity and can reach heavy Higgs mass up to 1.1 TeV. For the charged Higgs bosons, we consider the inclusive process with the charged Higgs produced in association with a top quark that is gb → tH ± . The region below tan β ∼ 1 can not be covered by 5σ discovery of H ± → τ ± ν decay mode due to the suppression of the decay branching fraction. The final states with tH ± → btt prove to be a very sensitive channel for regions with both small and large tan β. For tan β ∼ 1 (50), the btt channel can extend the reach to about M H ± ≈ 2 (1.4) TeV with 300 fb −1 luminosity.
The electroweak productions of non-SM Higgs boson pairs provide complementary signals in the determination of the nature of the Higgs sector. They are benefitted from pure electroweak gauge interactions and independent of additional model parameters except for Higgs masses. We explore the pair productions H ± A 0 and H + H − , followed by H ± → τ ± ν, tb and A 0 → bb decays. With BR(H ± → τ ± ν τ , tb) × BR(A 0 → bb) = (10 − 20)%, the maximal discovery mass of degenerate heavy Higgs bosons is around 800 − 900 GeV with an integrated luminosity of 15 ab −1 . The pp → H + H − production is not optimistic to probe the charged Higgs. The pp → H + H − → τ + τ − νν channel can access the decay branching fraction BR(H ± → τ ± ν τ ) to be 20% for light charged Higgs with 15 ab −1 luminosity.