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Heavy Higgs bosons at the LHC upgrade

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Tong Li. Heavy Higgs bosons at the LHC upgrade[J]. Chinese Physics C. doi: 10.1088/1674-1137/44/9/093103
Tong Li. Heavy Higgs bosons at the LHC upgrade[J]. Chinese Physics C.  doi: 10.1088/1674-1137/44/9/093103 shu
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Heavy Higgs bosons at the LHC upgrade

    Corresponding author: Tong Li, litong@nankai.edu.cn
  • School of Physics, Nankai University, Tianjin 300071, China

Abstract: We evaluate the discovery potential for the heavy Higgs bosons at the LHC energy upgrade with s=27 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 H0W+W,ZZ via gluon-gluon fusion production. The associated production of a top quark and a charged Higgs boson via gbtH± 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. ppWH±A0 and ppZ/γH+H. 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.

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    1.   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) [5-8] 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 ggϕW+W,ZZ and investigate the implication on the parameter space of the Type-II 2HDM model. The ϕτ+τ channel suffers from major SM backgrounds, such as multijet, Z/γττ, and Wτν [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 H±tb is dominant over other decays H±τ±ν,cs once kinematically accessible, but also suffers from large SM backgrounds (tˉt + light-flavor jets, W/Z + jet(s), tˉt + vector boson, tˉt + Higgs, single top + W, etc.) [10]. 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 benefit from large QCD production cross sections and simple kinematics, they all have a substantial dependence on additional 2HDM parameters, such as tanβ and cos(βα). It is worth emphasizing the potential importance of the electroweak production of Higgs boson pairs, e.g. ppWH±A0 and ppZ/γH+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 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.

    2.   Two Higgs Doublet Model
    • 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(2)L scalar doublets

      Hi=(h+i(vi+hi+iPi)/2),  i=1,2.

      (1)

      After the electroweak symmetry breaking (EWSB), there are four more Higgs bosons (H0,A0,H±) besides the SM-like Higgs boson (h0) in the particle spectrum

      (H0h0)=(cosαsinαsinαcosα)(h1h2),A0=sinβP1+cosβP2,  H±=sinβh±1+cosβh±2.

      (2)

      Here, the important parameter is defined as tanβ=v2/v1 with v21+v22=v=246 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 h0 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 H1 only couples to the down-type quarks and leptons and H2 only couples to the up-type quarks. Their couplings to the SM fermions behave as

      gH0uˉu=sinαsinβ=cos(βα)cotβsin(βα),gH0dˉd=gH0lˉl=cosαcosβ=cos(βα)+tanβsin(βα);

      gA0uˉu=icotβγ5,   gA0dˉd=gA0lˉl=itanβγ5;gH+ˉud=i2vVud[mdtanβ(1+γ5)+mucotβ(1γ5)],gHuˉd=i2vVud[mdtanβ(1γ5)+mucotβ(1+γ5)],gH+ˉνl=i2vmltanβ(1+γ5),gHνˉl=i2vmltanβ(1γ5),

      (3)

      with a normalization factor of imu,d,l/v for neutral Higgses. The couplings between neutral Higgses and two gauge bosons are gH0VV=cos(βα) and gA0VV=0. As such, the parameters involved in our analyses include tanβ, cos(βα), and the relevant Higgs masses under consideration.

      As previously intimated, we identify the lighter CP-even scalar h0 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 cos(βα)=0 or assume the value of cos(βα) 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 [17-21].

      In addition, there are strong constraints on the non-SM Higgs sector from the flavor constraints. In particular, the latest analyses on Br(BXsγ) 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: MH±MA or MH±MH0. 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.

    3.   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

      ggH0, A0.

      (4)

      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 cos(βα)=0 or cos(βα)=0.1 (note that the ggA0 production does not depend on cos(βα)). Note that the mixing angle cos(βα) is also constrained through Higgs rate measurements, and cos(βα)=0.1 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 cos(βα) here for H0VV decays. One should note that a positive value of cos(βα)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 MH0(A0)=250 GeV to 1 (3)×104 pb at MH0(A0)=2 TeV for tanβ=10 in the alignment limit. In addtiion, it increases by four times at MH0/A0=500 GeV and by eight times at MH0/A0=1.5 TeV from 14 TeV to 27 TeV C.M. energy. The ggA0 production does not depend on cos(βα) and its production cross section is larger than that of ggH0 for cos(βα)=0 and tanβ=10. From cos(βα)=0 to cos(βα)=0.1, the production cross section of ggH0 increases and becomes larger than that of ggA0.

      Figure 1.  (color online) Top: Total production cross section versus the Higgs boson mass for ggH0,A0 with cos(βα)=0 (a) or cos(βα)=0.1 (b) and tanβ=10 at pp collider with 14 TeV, 27 TeV and 100 TeV. Bottom: The cross section indicated by contour lines in the plane of tanβ versus the Higgs boson mass for ggH0 with cos(βα)=0 (c) and ggA0 (d) at the 27 TeV LHC.

      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]

      ΔEE=aE/GeVb,ahad=100%,bhad=5%,a=5%,b=0.55%.

      (5)

      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, bhad,b remained almost the same, and ahad and a 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 W/Z decays. We now utilize those channels to search for the CP-even Higgs H0. The basic requirements for the leptons are

      pT()30 GeV,   |η()|<2.5,   ΔR0.4,

      (6)

      and we select the events satisfying

      ET>40 GeV,   pminT()>65 GeV,   M>MH0/3,

      (7)

      for H0W+W channel. The mass of the H0 resonance in the WW channel can be reconstructed by the WW transverse mass

      MT(W+W)=(ET+ET)2(pT(1)+pT(2)+pT)2,ET=|pT|2+m2,

      (8)

      as shown in Fig. 2. The SM backgrounds are the same as those for τ+τ channel, but with gauge bosons' leptonic decay to electron/muon. The ZZ 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 |MMZ|<10 GeV. For the H0ZZ channel, we simply require

      Figure 2.  (color online) The differential cross section distributions of the WW transverse mass MT(WW) for the signal ggH0W+W, together with SM backgrounds at the 27 TeV LHC.

      pminT()>50 GeV,   |M4MH0|<MH0/10,

      (9)

      for the minimal lepton pT and the invariant mass of the four leptons. The tˉt production with pure leptonic decays can also be a reducible background after the two b-jets are vetoed if pT(b)>30 GeV,|η(b)|<4.9 [34]. The cut efficiencies are given in Tables 1 and 2 for WW and ZZ channels, respectively. One can see that the Z boson veto and the mass window requirement for H0 resonance significantly suppress the ZZ background for H0W+W and H0ZZ, respectively.

      cut efficienciesbasic cutsETpTMZ vetoM
      H0W+W(300)0.520.350.0820.0820.082
      H0W+W(800)0.790.660.540.540.50
      WW (300)0.230.10.0160.0160.016
      WW (800)0.230.10.0160.0160.0071
      ZZ (300)0.330.180.0150.000990.00072
      ZZ (800)0.330.180.0150.00099negligible
      WZ (300)0.0460.020.00120.000480.00047
      WZ (800)0.0460.020.00120.000480.00021
      tˉt (300)0.00640.00470.00170.00170.0017
      tˉt (800)0.00640.00470.00170.00170.00082

      Table 1.  The cut efficiencies for ggH0W+W and the SM backgrounds after consecutive cuts at the 27 TeV LHC. We take MH0=300 or 800 GeV.

      cut efficienciesbasic cutspTM4
      H0ZZ(300)0.30.0530.053
      H0ZZ(800)0.690.580.58
      ZZ(300)0.120.00970.0014
      ZZ(800)0.120.00970.00081

      Table 2.  The cut efficiencies for ggH0ZZ and the SM backgrounds after consecutive cuts at the 27 TeV LHC. We take MH0=300 or 800 GeV.

      The decays of H0W+W,ZZ are present away from the alignment limit, and can dominate with larger values of |cos(βα)|. Assuming cos(βα)=0.1 and tanβ=5,10 in the top panels of Figs. 3 and 4, we show the reach of BR(H0W+W,ZZ) as a function of MH0 at the 27 TeV LHC. The solid and dashed curves correspond to 3σ significance and 5σ discovery, respectively. The minimal branching fraction that can be reached with 15 ab1 luminosity is around (12)×102 and H0 with the mass of about 1.2/1.3 TeV can be probed for 5σ discovery if BR(H0WW/ZZ)=1 and tanβ=10. For tanβ=5 with a larger production cross section, a lower branching fraction and larger Higgs mass can be reached. The decays into massive gauge bosons are decreased for large tanβas the decay into bˉb dominates; thus, the realistic branching fraction of H0WW/ZZ cannot reach the order of unity. We use package 2HDMC [35] to calculate all 2HDM branching fractions below.

      Figure 3.  (color online) Top panels: Reach of BR(H0W+W) as a function of MH0 at the 27 TeV LHC. We assume tanβ=10 (a), tanβ=5 (b) and cos(βα)=0.1. Bottom panel: Discovery contour in tanβ versus MH0 plane for ggH0W+W, with realistic BR(H0W+W/ZZ) under the assumption of cos(βα)=0.1. The excluded regions in the Type-II 2HDM are indicated by the dashed curves, based on ggH0WW search at the 13 TeV LHC [34].

      Figure 4.  (color online) Top panels: Reach of BR(H0ZZ) as a function of MH0 at the 27 TeV LHC. We assume tanβ=10 (a), tanβ=5 (b) and cos(βα)=0.1. Bottom panel: Discovery contour in tanβ versus MH0 plane for ggH0ZZ, with realistic BR(H0ZZ) under the assumption of cos(βα)=0.1. The excluded regions in the Type-II 2HDM are indicated by the dashed curves, based on ggH0ZZ search at the 13 TeV LHC [36].

      The exclusion contours for the H0 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 cos(βα)=0.1. For the WW (ZZ) decay channel, the LHC has excluded the CP-even Higgs with masses up to 360 (390) GeV and tanβ below 1 (3). With realistic branching fractions at tanβ=10 (1), the 27 TeV LHC may discover the CP-even Higgs as heavy as 1 TeV (1.52 TeV) through ggH0W+W,ZZ channels as shown in Figs. 3(c) and 4(c). The loss of sensitivity at the large tanβ is mainly due to the reduction of BR(H0W+W,ZZ). It is known that the Higgs production in association with a bˉb pair can enhance the sensitivity for tanβ10in the Type-II 2HDM [37, 38], which is beyond the scope of this article.

    4.   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 ggtbH±. However, in high energy colliders, an ordinary pT cut (several tens of GeV) on the b-jet in final states is not sufficient as log(ˆs/pT) is still very large. Thus, this exclusive contribution is only meaningful when detecting final state b-jet with a sufficiently large pT 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]

      gbtH±.

      (10)

      Its total cross section is more accurately estimated in [41-43].

      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 mb=4.6 GeV. The total production cross section at 27 TeV LHC ranges from 0.5 pb at MH±=250 GeV to 4×104 pb at MH±=2 TeV for tanβ=10. We quantify the signal observability according to the leading decay channels.

      Figure 5.  (color online) Left: Total production cross section versus the Higgs boson mass for gbtH± with tanβ=10 at pp collider with 14 TeV, 27 TeV and 100 TeV. Right: The cross section indicated by contour lines in the plane of tanβ versus the Higgs boson mass for gbtH± at the 27 TeV LHC.

      We consider the clean channel of the charged Higgs boson's leptonic decay, i.e. H±τ±ν with τ±π±ν, with the branching fraction being BR(τ±π±ντ)=0.11, and the hadronic decay of the W boson from the top quark. This channel with the τ 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 τ 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 e/μ 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

      pT(b,π,j)25 GeV;   |η(b,π,j)|<2.5;   ΔR0.4.

      (11)

      The leading SM backgrounds are given by gbW±t with W±τ±ντ. There are more reducible QCD backgrounds, such as the tˉt production with one b-jet vetoed if pT(b)>30 GeV,|η(b)|<4.9 and multijet production with the τ-fake rate being approximately 103102 [46].

      Note that, as the charged Higgs H only coupled with the right-handed charged lepton, the right-handed τR decays to a left-handed ντ and π. This causes the π to move preferentially along the τ momentum direction. In contrast, the τ coming from the W decay is left-handed, which has the opposite effect on the π. A similar feature holds for the τ+ from the H+ and W+ decays. This is a well-known result of spin correlation in the τ decay [47, 48]. Thus, the transverse momentum of π± from the charged Higgs decay to the tau lepton yields a harder spectrum than that from the W decay in the SM backgrounds [49-51], as seen in Fig. 6(a). We thus tighten the missing energy and the pT of pion

      Figure 6.  (color online) The differential cross section distributions of pT(π) (a) and MT(τν) (b) for the signal gbtH±τ±νbWτ±νbjj and backgrounds at the 27 TeV LHC.

      ET>100 GeV,   pT(π)>65 GeV.

      (12)

      Furthermore, Fig. 6(b) indicates that the transverse mass of the pion and missing neutrinos from the charged Higgs

      MT(τν)=(pT(π)+ET)2(pT(π)+pT)2

      (13)

      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.

      cut efficienciesbasic cutsETpπTMT
      tH±(300)0.360.220.160.14
      tH±(800)0.400.360.340.33
      Wt0.10.0340.0087negligible
      tˉt0.0260.0120.00265×106

      Table 3.  The cut efficiencies for gbtH±τ±νbWτ±νbjj and the SM backgrounds after consecutive cuts at the 27 TeV LHC. We take MH±=300 or 800 GeV.

      If the exotic decay modes (one neutral Higgs with W boson) are absent, the charged Higgs decay is actually dominated by the 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 tanβ increases. Figure 7(a) and (b) display the reachable limit of BR(H±τ±ν) at the 27 TeV LHC. The HE-LHC with 15 ab1 luminosity extends the reach of BR(H±τ±ν) to the 103102 level for tanβ=10 and 4.

      Figure 7.  (color online) Top: Reach of BR(H±τ±ν) as a function of MH± for gbtH±τ±νbjj channel at the 27 TeV LHC. We assume tanβ=10 (a) and tanβ=4 (b). Bottom: Discovery contour in tanβ versus MH± plane for gbtH±τ±νbjj with realistic BR(H±τ±ν). As a comparison, the 13 TeV LHC exclusion limit on tanβ as a function of MH± is also presented [52].

      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 tanβ as a function of MH± is also presented in Fig. 7(c). The charged Higgs boson mass is excluded up to 1.1 TeV for tanβ=60, with the integrated luminosity of 36 fb1 [52]. With realistic BR(H±τ±ν), the discovery region in the tanβ versus MH± planes is shown in Fig. 7(c) for the gbtH±τ±νbjj channel at the 27 TeV LHC. The region below tanβ1 can not be covered by 5σdiscovery due to the suppression of the decay branching fraction. The 27 TeV pp collider with 3 ab1 luminosity can discover the charged Higgs mass up to 1 TeV (2 TeV) for tanβ=10 (60).

    5.   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, 55-57]

      qˉqW±H±A0,   qˉqZ/γH+H.

      (14)

      The relevant Higgs couplings to gauge bosons scale is

        WH±A0g/2, ZH+Hgcos2θW/(2cW),γH+Hie,

      (15)

      where g is the weak coupling and θW is the weak-mixing angle with cW=cosθW. Figure 8 shows their total cross sections at 14 TeV LHC, 27 TeV LHC and 100 TeV pp collider. The total cross section of the H±A0 production at 27 TeV LHC ranges from 2.3×102 pb at MA0=MH±=250 GeV to 1.5×104 pb with 1 TeV Higgs mass. It is approximately twice as large as that of the H+H production. We explore their observability based on the leading decay modes.

      Figure 8.  (color online) Left: Total production cross section versus the Higgs boson mass for qˉqH±A0, H+H with MA0=MH± at pp collider with 14 TeV, 27 TeV and 100 TeV. Right: The cross section indicated by contour lines in the plane of MA0 versus MH± for qˉqH±A0 at the 27 TeV LHC.

    • 5.1.   H±A0τ±νbˉb

    • The first signal channel we consider is the associated production of the CP-odd Higgs A0 and the charged Higgs H±, followed by A0 and H± decay to bˉb and τ±ντ respectively; i.e., ppH±A0τ±ντbˉb. We again adopt the τ leading 2-body decay channel, i.e. τ±π±ντ, with the branching fraction being BR(τ±π±ντ)=0.11. The b-jets and the charged pions π± in final states satisfy the following basic cuts

      pT(b,π)25 GeV;   |η(b,π)|<2.5;   ΔRbb,ΔRbπ0.4,

      (16)

      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: qˉqgW±bˉbW±bˉbτ±ν,

      ● the single top production: qˉqW±bˉt(ˉbt)bˉbW±bˉbτ±ν,

      and the reducible ones

      ● the W±-gluon fusion process with a forward jet: gqgqW±qbˉt(ˉbt)qbˉbW±qbˉbτ±ν,

      ● the QCD tˉt production: tˉtbˉbW+Wbˉbτ±νs (=e,μ).

      The last two processes having additional jets or leptons can be vetoed by requiring the extra objects with

      pT(j)>30 GeV,|η(j)|<4.9;   pT()>7 GeV,|η()|<3.5.

      (17)

      We display the distributions of signal and backgrounds after the basic cuts at the 27 TeV LHC in Fig. 9 (a) missing transverse energy ET and (b) transverse pion momentum pT(π). The signal exhibits a harder ET spectrum than the SM backgrounds from the Jacobian peak around pTνMH±/2. The mass peak of the resonance A0 also leads to an enhanced distribution near pTbMA0/2. Furthermore, as discussed for the single H± production with H±τ±ν in Sec. 4, the signal has a harder pT distribution of π± compared to the SM backgrounds. The charged Higgs mass MH± and the CP-odd Higgs mass MA0 can be read from the edge of the transverse mass

      Figure 9.  (color online) The differential cross section distributions of ET (a), pT(π) (b), MT(H±) (c) and Mbb (d) for the signal ppH±A0τ±ντbˉb and SM backgrounds versus at the 27 TeV LHC.

      MT(H±)=(ET(π)+ET)2(pT(π)+pT)2,

      (18)

      and the invariant mass of two b-jets Mbb, as shown in Figs. 9(c) and (d). We thus apply the following kinematic cuts

      ET>MH±/3, pmaxT(b)>MA0/2,pT(π)>MH±/10+40 GeV, |MbbMA0|<MA0/10.

      (19)

      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.

      cut efficienciesbasic cutspbTETpπTMbb
      H±A0(300)0.670.640.550.410.38
      H±A0(800)0.860.810.680.570.55
      bbW (300)0.00640.000930.000570.000171.5×105
      bbW (800)0.00644.0×1052.5×1055.2×106negligible
      bt (300)0.0720.0210.0110.00171.8×104
      bt (800)0.0720.00240.0010.00012.4×105
      Wg (300)0.0110.00210.00120.000223.2×105
      Wg (800)0.0110.000125.6×1058.5×1067.5×107
      tˉt (300)0.0040.00060.000294.3×1059.5×106
      tˉt (800)0.0045.5×1061.8×1062.5×107negligible

      Table 4.  The cut efficiencies for ppH±A0τ±ντbˉb and the SM backgrounds after consecutive cuts with τ±π±ντ channel at the 27 TeV LHC. We take MH±=MA0=300 or 800 GeV.

      As the H±A0 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 A0. In Fig. 10(a) we show the reach of the product of branching fractions, i.e. BR(H±τ±ντ)×BR(A0bˉb), with the degenerate spectrum MA0=MH± and different luminosity assumptions. For MA0=MH±300 GeV with 15 ab1 luminosity, the discovery limit of the branching fraction product can be as small as 3×102. With BR(H±τ±ντ)×BR(A0bˉb) = 20%, the maximal discovery masses of the degenerate heavy Higgs bosons are approximately 450 GeV and 800 GeV with an integrated luminosity of 3 ab1 and 15 ab1, 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 5σdiscovery.

      Figure 10.  (color online) Left: Reach of BR(H±τ±ντ)×BR(A0bˉb) versus MH± for ppH±A0τ±ντbˉb. We assume MA0=MH±. Right: Discovery contour in the plane of MA0 versus MH±. We assume BR(H±τ±ντ)×BR(A0bˉb)=20%.

    • 5.2.   H±A0tˉb(ˉtb)bˉb

    • Next, we study the signal induced by H±tb with the top quark's leptonic decay, i.e. H±A0tˉb(ˉtb)bˉbbbbb±ν, and the leading SM backgrounds including

      ● the virtual W process: qˉqgW±tˉb(ˉtb)bˉb,

      tb production: qˉqW±gtˉb(ˉtb)tˉb(ˉtb)bˉb.

      As we require the CP-odd Higgs to decay into bˉb, this case still has the Jacobian peak at approximately pTbMA0/2. The missing transverse energy here is softer than that in H±A0τ±νbˉb mode as the neutrino is from the subsequent decay of the top quark. Thus, we apply the following kinematic cuts in addition to the basic acceptance cuts described in Sec. 3 and 4.

      ET>40 GeV, pmaxT(b)>MA0/2.

      (20)

      As the missing neutrino is only from W’s leptonic decay, using W’s mass and the missing transverse momentum pT, one can arrive at a solution of the longitudinal momentum of the neutrino and this W boson can thus be reconstructed [49]. Because of the complexity from the four b-jets in our signal, when requiring the correct combination to reconstruct MH± and MA0, we assume and make use of the nearly-equal mass spectra of H± and A0. The obtained invariant masses of tb and bˉb are shown in Figs. 11(a) and (b), respectively. Next, we can take two mass windows near the resonances

      Figure 11.  (color online) Top: The differential cross section distributions of Mtb (a) and Mbb (b) for the signal ppH±A0tˉb(ˉtb)bˉbbbbb±ν and backgrounds at the 27 TeV LHC. Bottom: Reach of BR(H±tb)×BR(A0bˉb) versus MH± for ppH±A0tˉb(ˉtb)bˉbbbbb±ν, assuming MA0=MH±.

      |MtbMH±|<MH±/10,  |MbbMA0|<MA0/10.

      (21)

      The cut efficiencies are illustrated in Table 5.

      cut efficienciesbasic cutspbTETMtbMbb
      H±A0(300)0.340.330.250.160.14
      H±A0(800)0.450.430.390.270.26
      bbbt (300)0.0320.0160.0120.00250.00048
      bbbt (800)0.0320.00240.00210.000111.9×105

      Table 5.  The cut efficiencies for ppH±A0tˉb(ˉtb)bˉbbbbb±ν and the SM backgrounds after consecutive cuts at the 27 TeV LHC. We take MH±=MA0=300 or 800 GeV.

      In our signal process, the only dependence is again the product of the decay branching fractions, which is BR(H±tb)×BR(A0bˉb) here. As shown in Fig. 11(c), with the degenerate spectrum MA0=MH±300 GeV and 15 ab1 luminosity, the reach of the branching fraction product extends low to the level of 102. With BR(H±tb)×BR(A0bˉb) = 10%, the heavy Higgs bosons with masses of 600 GeV and 900 GeV can be discovered with integrated luminosities of 3 ab1and 15 ab1, respectively.

    • 5.3.   H+Hτ+τνˉν,tˉbˉtb

    • The first signal of H+H pair production consists of two tau leptons plus the missing energy H+Hτ+τντˉντ, followed by τ±π±ν. The irreducible SM backgrounds are from diboson productions

      W+Wτ+νττˉντ, ZZτ+τνˉν,

      (22)

      and the reducible contribution is

      W±Zτ+τ±ν,

      (23)

      which can also be vetoed by the requirement in Eq. (17).

      The distributions of the signal and backgrounds at the 27 TeV LHC after the basic cuts are shown in Fig. 12 (a) missing transverse energy ET and (b) transverse pion momentum pT(π). One can see that the tau polarization effect mentioned above tends to be more dramatic in this channel (in comparison with the WW background). Thus, we strengthen the missing energy and pT(π) as follows:

      Figure 12.  (color online) Top: The differential cross section distributions of ET (a) and pT(π) (b) for the signal ppH+Hτ+τντˉντ and backgrounds at the 27 TeV LHC. Bottom: Reach of BR(H±τ±ν) versus MH± for ppH+Hτ+τντˉντ.

      ET>100 GeV,   pmaxT(π)>100 GeV.

      (24)

      The cut efficiencies are presented in Table 6. 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 12(c) shows the reach of BR(H±τ±ν) versus MH± for ppH+Hτ+τντˉντ. One can see that this channel can access the decay branching fraction at 20% for the charged Higgs just above the top quark threshold with 15 ab1luminosity.

      cut efficienciesbasic cutsETpπT
      H+H(300)0.70.490.46
      H+H(800)0.890.840.84
      WW0.0240.000560.00056
      ZZ0.0840.0110.0052
      WZ0.00940.000620.00026

      Table 6.  The cut efficiencies for ppH+Hτ+τντˉντ and the SM backgrounds after consecutive cuts with τ±π±()ντ channel at the 27 TeV LHC. We take MH±=300 or 800 GeV.

      Finally, we consider semi-leptonic channel H+Htˉbˉtbbbbbjj±ν induced by H±tb and the leading SM background bˉbtˉt. Using the methods mentioned in Sec. 5.2, 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 MH±=300 (800) GeV with 15 ab1 luminosity. To discover the charged Higgs with the mass of 300 GeV, one needs 50 ab1 luminosity. This mode is thus not promising for probing the charged Higgs.

      The existing searches for neutral Higgs pair productions h0h0,H0h0,H0H0 at the LHC are performed using gluon fusion with a top quark circulating in the loops and governed by Higgs trilinear couplings [58-65]. As there is no search for electroweak Higgs pair production at the LHC, we do not expect our study can be compared at this stage. We look forward to seeing dedicated searches in the near future.

    6.   Conclusions
    • New Higgs bosons are present in many new physics models and their direct searches have yielded no signal observation in the LHC experiments so far. Thus, LHC upgrades with higher energy, such as the HE-LHC and FCC-hh, are 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 the degenerate Higgs spectrum MH0MA0MH± and the parameter cos(βα) near the alignment limit. We analyze the typical production and decay modes of non-SM Higgses and present the implications on the parameter space of Type-II 2HDM.

      We explore the observability of the heavy neutral Higgs bosons by examining the clean signals from H0W+W,ZZ via gluon-gluon fusion production. With realistic decay branching fractions of H0WW,ZZ channels for tanβ1, the 27 TeV LHC can probe the neutral Higgs up to 1.5-2 TeV with the luminosity of 15 ab1. For the charged Higgs bosons, we consider the inclusive process with the charged Higgs produced in association with a top quark that is gbtH±. The final states with tH±tτ±ν prove to be a very sensitive channel for regions with large tanβ. For tanβ50, the tτ±ν channel can extend to reach MH±>2 TeV with 15 ab1 luminosity. The region below tanβ1 can not be covered by 5σ discovery of H±τ±ν decay mode due to the suppression of the decay branching fraction.

      The electroweak productions of non-SM Higgs boson pairs provide complementary signals in the determination of the nature of the Higgs sector. They benefit from pure electroweak gauge interactions and are independent of additional model parameters except for Higgs masses. We explore the pair productions H±A0 and H+H, followed by H±τ±ν,tb and A0bˉb decays. With BR(H±τ±ντ,tb)×BR(A0bˉb)=(1020)%, the maximal discovery mass of degenerate heavy Higgs bosons is approximately 800900 GeV with an integrated luminosity of 15 ab1. The ppH+H production is not promising for probing the charged Higgs. The ppH+Hτ+τνˉν channel can access the decay branching fraction BR(H±τ±ντ) to be 20% for the light charged Higgs with 15 ab1 luminosity.

      The discovery of heavy non-SM Higgs bosons would certainly be unambiguous evidence for new physics beyond the SM. Once those non-SM Higgses are discovered, kinematic reconstruction would provide important information about their mass spectrum. A cross check with the indirect flavor and precision constraints would be complementary and lead to new clues regarding new physics beyond the SM.

      We would like to thank Tao Han for collaboration at the early stage of this project and valuable discussions.

Reference (65)

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