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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
gg→ϕ→W+W−,ZZ and investigate the implication on the parameter space of the Type-II 2HDM model. Theϕ→τ+τ− channel suffers from major SM backgrounds, such as multijet,Z/γ∗→ττ , andW→τν [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 modeH±→tb is dominant over other decaysH±→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 decayH±→τ±ν , the relevant SM backgrounds involve processes withW±→τ±ν . The difference between the Yukawa coupling forH± and the gauge interaction forW± , 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 andcos(β−α) . It is worth emphasizing the potential importance of the electroweak production of Higgs boson pairs, e.g.pp→W∗→H±A0 andpp→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 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.
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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 doubletsHi=(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)=(cosαsinα−sinαcosα)(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 thanh0 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 andH2 only couples to the up-type quarks. Their couplings to the SM fermions behave asgH0uˉu=sinαsinβ=cos(β−α)−cotβsin(β−α),gH0dˉd=gH0lˉl=cosαcosβ=cos(β−α)+tanβsin(β−α);
gA0uˉu=−icotβγ5, gA0dˉd=gA0lˉl=−itanβγ5;gH+ˉud=−i√2vV∗ud[mdtanβ(1+γ5)+mucotβ(1−γ5)],gH−uˉd=−i√2vVud[mdtanβ(1−γ5)+mucotβ(1+γ5)],gH+ˉνl=−i√2vmltanβ(1+γ5),gH−νˉl=−i√2vmltanβ(1−γ5),
(3) with a normalization factor of
imu,d,l/v for neutral Higgses. The couplings between neutral Higgses and two gauge bosons aregH0VV=cos(β−α) andgA0VV=0 . As such, the parameters involved in our analyses includetanβ ,cos(β−α) , 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 limitcos(β−α)=0 or assume the value ofcos(β−α) 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
(B→Xsγ) 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 orMH±∼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. -
Just like the Higgs boson discovery, the leading production channel for a heavy neutral Higgs boson is through the gluon fusion
gg→H0, 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(β−α)=0 orcos(β−α)=−0.1 (note that thegg→A0 production does not depend oncos(β−α) ). Note that the mixing anglecos(β−α) is also constrained through Higgs rate measurements, andcos(β−α)=−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 ofcos(β−α) here forH0→VV decays. One should note that a positive value ofcos(β−α) 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 atMH0(A0)=250 GeV to1 (3)×10−4 pb atMH0(A0)=2 TeV fortanβ=10 in the alignment limit. In addtiion, it increases by four times atMH0/A0=500 GeV and by eight times atMH0/A0=1.5 TeV from 14 TeV to 27 TeV C.M. energy. Thegg→A0 production does not depend oncos(β−α) and its production cross section is larger than that ofgg→H0 forcos(β−α)=0 andtanβ=10 . Fromcos(β−α)=0 tocos(β−α)=−0.1 , the production cross section ofgg→H0 increases and becomes larger than that ofgg→A0 .Figure 1. (color online) Top: Total production cross section versus the Higgs boson mass for
gg→H0,A0 withcos(β−α)=0 (a) orcos(β−α)=−0.1 (b) andtanβ=10 atpp collider with 14 TeV, 27 TeV and 100 TeV. Bottom: The cross section indicated by contour lines in the plane oftanβ versus the Higgs boson mass forgg→H0 withcos(β−α)=0 (c) andgg→A0 (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=a√E/GeV⊕b,ahad=100%,bhad=5%,aℓ=5%,bℓ=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,bℓ remained almost the same, andahad andaℓ 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 HiggsH0 . The basic requirements for the leptons arepT(ℓ)⩾30 GeV, |η(ℓ)|<2.5, ΔRℓℓ⩾0.4,
(6) and we select the events satisfying
⧸ET>40 GeV, pminT(ℓ)>65 GeV, Mℓℓ>MH0/3,
(7) for
H0→W+W− channel. The mass of theH0 resonance in theWW channel can be reconstructed by theWW transverse massMT(W+W−)=√(EℓℓT+⧸ET)2−(→pT(ℓ1)+→pT(ℓ2)+→⧸pT)2,EℓℓT=√|→pℓℓT|2+m2ℓℓ,
(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. TheZZ background has the opposite-sign lepton pairsℓ+ℓ− from Z boson decay and can be further reduced by vetoing the invariant mass of opposite sign leptons if|Mℓℓ−MZ|<10 GeV. For theH0→ZZ channel, we simply requireFigure 2. (color online) The differential cross section distributions of the
WW transverse massMT(WW) for the signalgg→H0→W+W− , together with SM backgrounds at the 27 TeV LHC.pminT(ℓ)>50 GeV, |M4ℓ−MH0|<MH0/10,
(9) for the minimal lepton
pT and the invariant mass of the four leptons. Thetˉt production with pure leptonic decays can also be a reducible background after the two b-jets are vetoed ifpT(b)>30 GeV,|η(b)|<4.9 [34]. The cut efficiencies are given in Tables 1 and 2 forWW andZZ channels, respectively. One can see that the Z boson veto and the mass window requirement forH0 resonance significantly suppress theZZ background forH0→W+W− andH0→ZZ , respectively.cut efficiencies basic cuts ⧸ET pℓT MZ vetoMℓℓ H0→W+W−(300) 0.52 0.35 0.082 0.082 0.082 H0→W+W−(800) 0.79 0.66 0.54 0.54 0.50 WW (300)0.23 0.1 0.016 0.016 0.016 WW (800)0.23 0.1 0.016 0.016 0.0071 ZZ (300)0.33 0.18 0.015 0.00099 0.00072 ZZ (800)0.33 0.18 0.015 0.00099 negligible WZ (300)0.046 0.02 0.0012 0.00048 0.00047 WZ (800)0.046 0.02 0.0012 0.00048 0.00021 tˉt (300)0.0064 0.0047 0.0017 0.0017 0.0017 tˉt (800)0.0064 0.0047 0.0017 0.0017 0.00082 Table 1. The cut efficiencies for
gg→H0→W+W− and the SM backgrounds after consecutive cuts at the 27 TeV LHC. We takeMH0=300 or 800 GeV.cut efficiencies basic cuts pℓT M4ℓ H0→ZZ(300) 0.3 0.053 0.053 H0→ZZ(800) 0.69 0.58 0.58 ZZ(300) 0.12 0.0097 0.0014 ZZ(800) 0.12 0.0097 0.00081 Table 2. The cut efficiencies for
gg→H0→ZZ and the SM backgrounds after consecutive cuts at the 27 TeV LHC. We takeMH0=300 or 800 GeV.The decays of
H0→W+W−,ZZ are present away from the alignment limit, and can dominate with larger values of|cos(β−α)| . Assumingcos(β−α)=−0.1 andtanβ=5,10 in the top panels of Figs. 3 and 4, we show the reach of BR(H0→W+W−,ZZ) as a function ofMH0 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 ab−1 luminosity is around(1−2)×10−2 andH0 with the mass of about1.2/1.3 TeV can be probed for 5σ discovery if BR(H0→WW/ZZ)=1 andtanβ=10 . Fortanβ=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 largetanβ as the decay intobˉb dominates; thus, the realistic branching fraction ofH0→WW/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
(H0→W+W−) as a function ofMH0 at the 27 TeV LHC. We assumetanβ=10 (a),tanβ=5 (b) andcos(β−α)=−0.1 . Bottom panel: Discovery contour intanβ versusMH0 plane forgg→H0→W+W− , with realistic BR(H0→W+W−/ZZ) under the assumption ofcos(β−α)=−0.1 . The excluded regions in the Type-II 2HDM are indicated by the dashed curves, based ongg→H0→WW search at the 13 TeV LHC [34].Figure 4. (color online) Top panels: Reach of BR
(H0→ZZ) as a function ofMH0 at the 27 TeV LHC. We assumetanβ=10 (a),tanβ=5 (b) andcos(β−α)=−0.1 . Bottom panel: Discovery contour intanβ versusMH0 plane forgg→H0→ZZ , with realistic BR(H0→ZZ) under the assumption ofcos(β−α)=−0.1 . The excluded regions in the Type-II 2HDM are indicated by the dashed curves, based ongg→H0→ZZ 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, assumingcos(β−α)=−0.1 . For theWW (ZZ) decay channel, the LHC has excluded the CP-even Higgs with masses up to 360 (390) GeV andtanβ below 1 (3). With realistic branching fractions attanβ=10 (1) , the 27 TeV LHC may discover the CP-even Higgs as heavy as 1 TeV (1.5−2 TeV) throughgg→H0→W+W−,ZZ channels as shown in Figs. 3(c) and 4(c). The loss of sensitivity at the largetanβ is mainly due to the reduction of BR(H0→W+W−,ZZ) . It is known that the Higgs production in association with abˉb pair can enhance the sensitivity fortanβ≳10 in the Type-II 2HDM [37, 38], which is beyond the scope of this article. -
If the charged Higgs boson is heavier than the top quark mass, the conventional production of heavy charged Higgs occurs through
gg→tbH± . However, in high energy colliders, an ordinarypT cut (several tens of GeV) on the b-jet in final states is not sufficient aslog(√ˆs/pT) is still very large. Thus, this exclusive contribution is only meaningful when detecting final state b-jet with a sufficiently largepT 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 ofH± with a top quark [39, 40]gb→tH±.
(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 atMH±=250 GeV to4×10−4 pb atMH±=2 TeV fortanβ=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
gb→tH± withtanβ=10 atpp collider with 14 TeV, 27 TeV and 100 TeV. Right: The cross section indicated by contour lines in the plane oftanβ versus the Higgs boson mass forgb→tH± at the 27 TeV LHC.We consider the clean channel of the charged Higgs boson's leptonic decay, i.e.
H±→τ±ν withτ±→π±ν , with the branching fraction beingBR(τ±→π±ντ)=0.11 , and the hadronic decay of the W boson from the top quark. This channel with theτ 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 theτ 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 thee/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 cutspT(b,π,j)⩾25 GeV; |η(b,π,j)|<2.5; ΔR⩾0.4.
(11) The leading SM backgrounds are given by
gb→W±t withW±→τ±ντ . There are more reducible QCD backgrounds, such as thetˉt production with one b-jet vetoed ifpT(b)>30 GeV,|η(b)|<4.9 and multijet production with theτ -fake rate being approximately10−3−10−2 [46].Note that, as the charged Higgs
H− only coupled with the right-handed charged lepton, the right-handedτ−R decays to a left-handedντ andπ− . This causes theπ− to move preferentially along theτ− momentum direction. In contrast, theτ− coming from theW− decay is left-handed, which has the opposite effect on theπ− . A similar feature holds for theτ+ from theH+ andW+ decays. This is a well-known result of spin correlation in theτ decay [47, 48]. Thus, the transverse momentum ofπ± 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 thepT of pionFigure 6. (color online) The differential cross section distributions of
pT(π) (a) andMT(τν) (b) for the signalgb→tH±→τ±νbW∓→τ±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 efficiencies basic cuts ⧸ET pπT MT tH±(300) 0.36 0.22 0.16 0.14 tH±(800) 0.40 0.36 0.34 0.33 Wt 0.1 0.034 0.0087 negligible tˉt 0.026 0.012 0.0026 5×10−6 Table 3. The cut efficiencies for
gb→tH±→τ±νbW∓→τ±νbjj and the SM backgrounds after consecutive cuts at the 27 TeV LHC. We takeMH±=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. TheH±→τ±ν decay is the secondary significant mode in the decays to the SM particles and becomes more important astanβ 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 ab−1 luminosity extends the reach of BR(H±→τ±ν) to the10−3−10−2 level fortanβ=10 and 4.Figure 7. (color online) Top: Reach of BR
(H±→τ±ν) as a function ofMH± forgb→tH±→τ±νbjj channel at the 27 TeV LHC. We assumetanβ=10 (a) andtanβ=4 (b). Bottom: Discovery contour intanβ versusMH± plane forgb→tH±→τ±νbjj with realistic BR(H±→τ±ν) . As a comparison, the 13 TeV LHC exclusion limit ontanβ as a function ofMH± 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 ofMH± is also presented in Fig. 7(c). The charged Higgs boson mass is excluded up to 1.1 TeV fortanβ=60 , with the integrated luminosity of 36 fb−1 [52]. With realistic BR(H±→τ±ν) , the discovery region in thetanβ versusMH± planes is shown in Fig. 7(c) for thegb→tH±→τ±νbjj channel at the 27 TeV LHC. The region belowtanβ∼1 can not be covered by5σ 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) fortanβ=10 (60) . -
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]
qˉq′→W±∗→H±A0, qˉq→Z∗/γ∗→H+H−.
(14) The relevant Higgs couplings to gauge bosons scale is
WH±A0∝g/2, ZH+H−∝−gcos2θW/(2cW),γH+H−∝−ie,
(15) where g is the weak coupling and
θW is the weak-mixing angle withcW=cosθW . Figure 8 shows their total cross sections at 14 TeV LHC, 27 TeV LHC and 100 TeVpp collider. The total cross section of theH±A0 production at 27 TeV LHC ranges from2.3×10−2 pb atMA0=MH±=250 GeV to1.5×10−4 pb with 1 TeV Higgs mass. It is approximately twice as large as that of theH+H− production. We explore their observability based on the leading decay modes. -
The first signal channel we consider is the associated production of the CP-odd Higgs
A0 and the charged HiggsH± , followed byA0 andH± decay tobˉb andτ±ντ respectively; i.e.,pp→H±A0→τ±ντbˉb . We again adopt theτ leading 2-body decay channel, i.e.τ±→π±ντ , with the branching fraction beingBR(τ±→π±ντ)=0.11 . The b-jets and the charged pionsπ± in final states satisfy the following basic cutspT(b,π)⩾25 GeV; |η(b,π)|<2.5; ΔRbb,ΔRbπ⩾0.4,
(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:
qˉq′→gW±→bˉbW±→bˉbτ±ν ,● the single top production:
qˉq′→W±∗→bˉt(ˉbt)→bˉbW±→bˉbτ±ν ,and the reducible ones
● the
W± -gluon fusion process with a forward jet:gq→gq′W±∗→q′bˉt(ˉbt)→q′bˉbW±→q′bˉbτ±ν ,● the QCD
tˉt production:tˉt→bˉbW+W−→bˉbτ±ℓ∓ν′s (ℓ=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(ℓ)>7 GeV,|η(ℓ)|<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 momentumpT(π) . The signal exhibits a harder⧸ET spectrum than the SM backgrounds from the Jacobian peak aroundpTν∼MH±/2 . The mass peak of the resonanceA0 also leads to an enhanced distribution nearpTb∼MA0/2 . Furthermore, as discussed for the singleH± production withH±→τ±ν in Sec. 4, the signal has a harderpT distribution ofπ± compared to the SM backgrounds. The charged Higgs massMH± and the CP-odd Higgs massMA0 can be read from the edge of the transverse massFigure 9. (color online) The differential cross section distributions of
⧸ET (a),pT(π) (b),MT(H±) (c) andMbb (d) for the signalpp→H±A0→τ±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, |Mbb−MA0|<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 efficiencies basic cuts pbT ⧸ET pπT Mbb H±A0(300) 0.67 0.64 0.55 0.41 0.38 H±A0(800) 0.86 0.81 0.68 0.57 0.55 bbW (300)0.0064 0.00093 0.00057 0.00017 1.5×10−5 bbW (800)0.0064 4.0×10−5 2.5×10−5 5.2×10−6 negligible bt (300)0.072 0.021 0.011 0.0017 1.8×10−4 bt (800)0.072 0.0024 0.001 0.0001 2.4×10−5 Wg (300)0.011 0.0021 0.0012 0.00022 3.2×10−5 Wg (800)0.011 0.00012 5.6×10−5 8.5×10−6 7.5×10−7 tˉt (300)0.004 0.0006 0.00029 4.3×10−5 9.5×10−6 tˉt (800)0.004 5.5×10−6 1.8×10−6 2.5×10−7 negligible Table 4. The cut efficiencies for
pp→H±A0→τ±ντbˉb and the SM backgrounds after consecutive cuts withτ±→π±ντ channel at the 27 TeV LHC. We takeMH±=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 ofH± andA0 . In Fig. 10(a) we show the reach of the product of branching fractions, i.e.BR(H±→τ±ντ)×BR(A0→bˉb) , with the degenerate spectrumMA0=MH± and different luminosity assumptions. ForMA0=MH±≃300 GeV with 15 ab−1 luminosity, the discovery limit of the branching fraction product can be as small as3×10−2 . WithBR(H±→τ±ντ)×BR(A0→bˉb) = 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−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. 10(b) by fixing the branching fraction product to be 20%. The regions to the left of the curves can be covered by 5σ discovery. -
Next, we study the signal induced by
H±→tb with the top quark's leptonic decay, i.e.H±A0→tˉb(ˉtb)bˉb→bbbbℓ±ν , and the leading SM backgrounds including● the virtual W process:
qˉq′→gW±∗→tˉb(ˉtb)bˉb ,●
tb production:qˉq′→W±∗→gtˉb(ˉtb)→tˉb(ˉtb)bˉb .As we require the CP-odd Higgs to decay into
bˉb , this case still has the Jacobian peak at approximatelypTb∼MA0/2 . The missing transverse energy here is softer than that inH±A0→τ±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 reconstructMH± andMA0 , we assume and make use of the nearly-equal mass spectra ofH± andA0 . The obtained invariant masses oftb andbˉb are shown in Figs. 11(a) and (b), respectively. Next, we can take two mass windows near the resonancesFigure 11. (color online) Top: The differential cross section distributions of
Mtb (a) andMbb (b) for the signalpp→H±A0→tˉb(ˉtb)bˉb→bbbbℓ±ν and backgrounds at the 27 TeV LHC. Bottom: Reach ofBR(H±→tb)×BR(A0→bˉb) versusMH± forpp→H±A0→tˉb(ˉtb)bˉb→bbbbℓ±ν , assumingMA0=MH± .|Mtb−MH±|<MH±/10, |Mbb−MA0|<MA0/10.
(21) The cut efficiencies are illustrated in Table 5.
cut efficiencies basic cuts pbT ⧸ET Mtb Mbb H±A0(300) 0.34 0.33 0.25 0.16 0.14 H±A0(800) 0.45 0.43 0.39 0.27 0.26 bbbt (300)0.032 0.016 0.012 0.0025 0.00048 bbbt (800)0.032 0.0024 0.0021 0.00011 1.9×10−5 Table 5. The cut efficiencies for
pp→H±A0→tˉb(ˉtb)bˉb→bbbbℓ±ν and the SM backgrounds after consecutive cuts at the 27 TeV LHC. We takeMH±=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(A0→bˉb) here. As shown in Fig. 11(c), with the degenerate spectrumMA0=MH±≃300 GeV and 15 ab−1 luminosity, the reach of the branching fraction product extends low to the level of10−2 . WithBR(H±→tb)×BR(A0→bˉb) = 10%, the heavy Higgs bosons with masses of 600 GeV and 900 GeV can be discovered with integrated luminosities of 3 ab−1 and 15 ab−1 , respectively. -
The first signal of
H+H− pair production consists of two tau leptons plus the missing energyH+H−→τ+τ−ντˉντ , followed byτ±→π±ν . The irreducible SM backgrounds are from diboson productionsW+W−→τ+νττ−ˉντ, ZZ→τ+τ−νˉν,
(22) and the reducible contribution is
W±Z→τ+τ−ℓ±νℓ,
(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 momentumpT(π) . One can see that the tau polarization effect mentioned above tends to be more dramatic in this channel (in comparison with theWW background). Thus, we strengthen the missing energy andpT(π) as follows:Figure 12. (color online) Top: The differential cross section distributions of
⧸ET (a) andpT(π) (b) for the signalpp→H+H−→τ+τ−ντˉντ and backgrounds at the 27 TeV LHC. Bottom: Reach ofBR(H±→τ±ν) versusMH± forpp→H+H−→τ+τ−ντˉντ .⧸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) versusMH± forpp→H+H−→τ+τ−ντˉντ . 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 ab−1 luminosity.cut efficiencies basic cuts ⧸ET pπT H+H−(300) 0.7 0.49 0.46 H+H−(800) 0.89 0.84 0.84 WW 0.024 0.00056 0.00056 ZZ 0.084 0.011 0.0052 WZ 0.0094 0.00062 0.00026 Table 6. The cut efficiencies for
pp→H+H−→τ+τ−ντˉντ and the SM backgrounds after consecutive cuts withτ±→π±(−)ντ channel at the 27 TeV LHC. We takeMH±=300 or 800 GeV.Finally, we consider semi-leptonic channel
H+H−→tˉbˉtb→bbbbjjℓ±ν induced byH±→tb and the leading SM backgroundbˉbtˉt . 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 forMH±=300 (800) GeV with 15 ab−1 luminosity. To discover the charged Higgs with the mass of 300 GeV, one needs 50 ab−1 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. -
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
MH0≈MA0≈MH± and the parametercos(β−α) 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
H0→W+W−,ZZ via gluon-gluon fusion production. With realistic decay branching fractions ofH0→WW,ZZ channels fortanβ∼1 , the 27 TeV LHC can probe the neutral Higgs up to 1.5-2 TeV with the luminosity of 15 ab−1 . For the charged Higgs bosons, we consider the inclusive process with the charged Higgs produced in association with a top quark that isgb→tH± . The final states withtH±→tτ±ν prove to be a very sensitive channel for regions with largetanβ . Fortanβ∼50 , thetτ±ν channel can extend to reachMH±>2 TeV with 15 ab−1 luminosity. The region belowtanβ∼1 can not be covered by5σ discovery ofH±→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 andH+H− , followed byH±→τ±ν,tb andA0→bˉb decays. WithBR(H±→τ±ντ,tb)×BR(A0→bˉb)=(10−20) %, the maximal discovery mass of degenerate heavy Higgs bosons is approximately800−900 GeV with an integrated luminosity of 15 ab−1 . Thepp→H+H− production is not promising for probing the charged Higgs. Thepp→H+H−→τ+τ−νˉν channel can access the decay branching fractionBR(H±→τ±ντ) to be 20% for the light charged Higgs with 15 ab−1 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.
Heavy Higgs bosons at the LHC upgrade
- Received Date: 2020-01-16
- Accepted Date: 2020-05-15
- Available Online: 2020-09-01
Abstract: We evaluate the discovery potential for the heavy Higgs bosons at the LHC energy upgrade with