Probing Exotic Charged Higgs Decays in the Type-II 2HDM through Top Rich Signal at a Future 100 TeV pp Collider

The exotic decay modes of non-Standard Model Higgs bosons are efficient in probing the hierarchical Two Higgs Doublet Models (2HDM). In particular, the decay mode $H^\pm\to HW^\pm$ serves as a powerful channel in searching for charged Higgses. In this paper, we analyzed the reach for $H^\pm\to HW^\pm \to t\bar{t}W$ at a 100 TeV $pp$ collider, and showed that it extends the reach of the previously studied $\tau\tau W$ final states. Top tagging technique is used, in combination with the boosted decision tree classifier. Almost the entire hierarchical Type-II 2HDM parameter space can be probed via the combination of all channels at low $\tan\beta$ region.

the type-II 2HDM, the current LHC exclusion limit is weak [21]: only regions of tan β > 40 and < 2 at m H ± ∼ 300 GeV are excluded. The reach will be further reduced once the exotic decay mode of H ± → AW ± /HW ± opens up.
The exotic decay mode of H ± → AW ± /HW ± provides an alternative channel for charged Higgs search. The reach of this channel via A/H → τ τ mode has been studied in literature [12,17]. In the m H ± − tan β plane, the exclusion region extends to m H ± = 600 GeV in both small and large tan β regimes at the 14 TeV LHC with 300 fb −1 luminosity [12]. At a future 100 TeV pp collider, the reach is further extended to 2.5 TeV for tan β 10 [17]. While τ τ channel is effective due to it's clean signature, its sensitivity is reduced once the Higgs mass is above the top pair threshold or at small tan β. The A/H → tt channel has been studied in literature [13] focusing on the signal events with trilepton and same-sign dilepton (SSDL) signature at the 14 TeV LHC with 30 fb −1 luminosity. It shows great sensitivity in the m H/A − m H ± plane at m H ± > 500 GeV. In particular, for low tan β ∼ 1, tt channel extends the reach of charged Higgs to about 1 TeV, well beyond the reach of τ τ mode.
In recent years, there have been worldwide efforts of proposing a 100 TeV pp collider, including the Future Circular Collider (FCC) at CERN [22] and the Super proton-proton Collider (SppC) in China [23]. Given the high energy environment of such machine, highly boosted object such as top quark can be identified using top-tagging technique [24][25][26][27][28][29], which offers additional handle for new physics discovery by suppressing SM hadronic backgrounds. This technique has been implemented in searching the exotic decay of A → HZ, with H → tt at the future 100 TeV pp-collier, which extends the reach of H → τ τ mode above the di-top threshold [17]. It's also widely used in conventional search modes such as A/H → tt [30][31][32].
In this study, we propose to search the charged Higgs via exotic decay H ± → HW ± with H → tt channel at a future 100 TeV pp collider, using top tagging technique. We focus on the hierarchical scenario of m A = m H ± > m H , which is motivated by theoretical constraints and electroweak precision measurement [17]. The Boosted Decision Tree (BDT) classifier [2] is used to distinguish the signal and background events.
The rest of the paper is organized as follows. In Sec. 2 we briefly introduce Type-II 2HDM, as well as the charged Higgs interactions. We also discuss benchmark plane for collider study and the current experimental search bounds. In Sec. 3, we describe the detailed collider analyses and the reach for the charged Higgs. We concluded in Sec. 4.

Type-II 2HDM and Charged Higgses
Two SU(2) L doublets Φ i , i = 1, 2 are introduced in the 2HDM: where v 1 and v 2 are the vacuum expectation values (VEVs) of the neutral components which satisfy the relation v = v 2 1 + v 2 2 = 246 GeV after EWSB. In scenarios with only a soft breaking of a discrete Z 2 symmetry allowed, the most general Higgs potential has eight parameters, which can be chosen as four physical Higgs masses (m h , m H , m A , m H ± ), the electroweak VEV v, the CP-even Higgs mixing angle α, the ratio of the two VEVs, tan β = v 2 /v 1 , and the Z 2 soft breaking parameter m 2 12 . In our study of the heavy non-SM Higgses, we assume the light netural CP even Higgs h to be the observed SM-like 125 GeV Higgs. Current measurements on the properties of the 125 GeV Higgs have already imposed strong constraints on the 2HDM parameter space [7,33], pushing towards the alignment limit of cos(β − α) 0. Note that under such limit, the charged Higgses H ± preferably couple to the non-SM-like Higgses A or H: where g is the SU(2) L coupling and p µ is the incoming momentum for the corresponding particle. Once m H ± − m A/H > m W , H ± → AW ± /HW ± opens up with sizable decay branching fractions. We refer the readers to our previous papers (Ref. [17,34]) for more detailed discussion on the constraints on the 2HDM parameter space from theoretical considerations and electroweak precision measurements. For TeV-scale masses, two benchmark planes are proposed for collider studies [17]: In this paper, we focus on the benchmark plane BP-B, which permits the decay of H ± → HW ± → ttW ± .
Searches for charged Higgses have been performed both at the ATLAS and CMS experiments. A search with clean τ ν final state by ATLAS using 36 fb −1 integrated luminosity at 13 TeV [35] excludes H ± mass range up to 1100 GeV (400 GeV) at tan β = 60 (30) in the hMSSM scenario of the Minimal Supersymmetric Standard Model (MSSM). The reach is reduced greatly at low tan β region though. For 0.5 < tan β < 10, there is only a very weak lower bound for charged Higgs mass (m H ± 160 GeV). The CMS results [36] are similar.
Both ATLAS and CMS have also searched for a heavy charged Higgs boson produced in association with a top quark with H ± → tb [37][38][39], which is sensitive to both the small and large tan β region. The null search results at ATLAS using multi-jet final states with one or two electrons or muons [37] impose an upper limit for σ(pp → H ± tb) Br(H ± → tb) of 0.07 pb at m H ± = 2000 GeV and 2.9 pb at m H ± = 200 GeV. When interpreted in the hMSSM scenario, the charged Higgs with m H ± up to 200 (965) GeV for tan β ∼ 1.95(0.5) has already been ruled out. The CMS results [38] using events with a single isolated electron or muon or an opposite-sign electron or muon pair are slightly better, while the limits with all-jet final states are weaker [39].
Various flavor measurements [40,41], mostly from B-system, also provide indirect constraints on the charged Higgs mass m H ± . The most stringent of these comes from the measurement of the branching fraction of the decays b → sγ and B + → τ ν, which conservatively disfavor m H ± < 580 GeV in the Type-II 2HDM [42]. Flavor constraints, however, can be relaxed with contributions from other sectors of new physics models [43]. In the following study, we focus on the direct collider reach of charged Higgses.
Note that direct searches for non-SM neutral Higgs also provide constraints on the 2HDM parameter space. We refer the interested readers to Ref. [17,34] for details. A recent paper [44] summarises the status of neutral Higgs searches at the LHC, with both direct and indirect measurements.

Signal Analysis
In this section we perform the collider analyses of charged Higgs with tbH ± associated production and the consequent decay of H ± → HW ± → ttW ± at a 100 TeV pp collider in the m A = m H ± > m H parameter region. We require the final state containing two hadronically decaying top, and a pair of charged leptons.

Charged Higgs Production Cross Section and Decay
The dominant production channel for heavy charged Higgses at a pp collider is gg → H ± tb. The production cross section calculated at next to leading order (NLO) using Prospino [45,46] is plotted in the left panel of Fig. 1. The suppression at tan β ∼ 7 is due to the suppression of the H ± tb coupling at intermediate value of The decay branching fractions of H ± are shown in the right panel of Fig. 1 for m H = 600 GeV and tan β = 1.5. For m H ± < m H + m W , H ± → tb dominates, with H ± → τ ν, cs being almost negligible. However, once m H ± > m H +m W , H ± → HW ± quickly dominates, as shown by the black curve. All branching fractions are calculated using 2HDMC [47].

Search Strategy
The exotic decay of H ± → HW ± has been studied via H → τ τ channel [17], with same-sign dilepton events by requiring one τ and one W of the same sign decaying leptonically while the other τ and W decaying hadronically. The main background comes from t h t (Z/h/γ * → τ h τ ). While this search mode has a good reach at large tan β, the reach is limited at low tan β, especially for m H > 2m t when H → tt dominates.
For these reasons, in this study, we explore the reach of H → tt channel for charged Higgs discovery. In particular, top tagging technique can be used to identify the highly boosted top produced from heavy Higgs decay. The production and decay chain is Within four W s in the final states, we require two of them decay hadronically, which are needed for top-tagging or top reconstruction, and the other two decay leptonically. The event signature for detection is Note that for 2 t h , we mean at least one t h being top-tagged, while the other being either top-tagged or reconstructed, as explained in details below. Extra b-jet is required here to suppress the SM ttZ background.
The dominant irreducible SM background arises from four-top process with two tops decaying leptonically and the other two decaying hadronically. The total cross section of the four-top production at 100 TeV pp collider calculated using MadGraph 5 [48] at leading order (LO) is σ(gg → tttt) = 2.97 pb. We use a K-factor of 1.66 to take into account the NLO effect [49]. The subdominant background is the tttbW ± process with bW ± in the final state not coming from a resonant top. The corresponding LO cross section is σ(gg → tttbW ) = 0.623 pb.
As mentioned earlier, the top quarks originating from the neutral Higgs H are highly boosted for a heavy Higgs H, with top decay products grouping into a cone of size 1.5. The top tagging techniques [24][25][26][27][28][29] developed in recent years could be used to identify the top quark in the signal process, while suppress both the SM hadronic backgrounds and the SM background with softer top quarks. However, due to the complexity of the signal signature, the hadronic W boson out of H ± along with the associated bottom quark have non-negligible probability to be identified as a hadronic top as well. Furthermore, at a 100 TeV pp collider, a considerable portion of tops produced associated with the charged Higgses are energetic enough to be captured by the top tagger. Therefore, we need to consider all possible combinations of dilepton decay in Eq. (3.1), including same-sign dilepton (SSDL) as well as opposite-sign dilepton (OSDL) signals.
To identify different combinations of top decays that lead to the dilepton signals, we list the sub-processes for SSDL and OSDL events in Table 1. For OSDL, there are four sub-processes with OS1 being both hadronic decaying top from H decay, OS2 and OS3 being one hadronic top from H decay and one hadronic top from either the associated produced top, or the hadronic W from H ± decay, and OS4 being the case when both tops from H decay leptonically. There are two sub-processes for SSDL, both of them having one hadronic top from H decay, and the other one from either the associated top or the W .
To perform a detail collider simulation, all signal and background events are generated using MadGraph5 aMC@NLO v2.6.6 [48], then interfaced with Pythia8 [50] to simulate showering and hadronization. The events are then passed into Delphes 3 [51] for detector Channel Divisions
For the purpose of triggering, we require the leading and sub-leading leptons to have the transverse momentum: p T, 1 > 20 GeV and p T, 2 > 10 GeV. Other than the OSDL/SSDL signature, a b-tagged jet with P T,b > 30 GeV is also required. In addition, we demand at least one hadronic top to be identified by top-tagging algorithm and a second hadronic top being either top-tagged or reconstructed for each event. Specifically, for event with one tagged top, we further require it contains at least two bottom jets and at least two untagged jets. We then reconstruct another hadronic top following Ref. [53] by iterating over all pairs of untagged jets and find the one that has invariant mass |m jj − m W | ≤ 20 GeV. We further combine the jet pair with b-jet that satisfies |m bjj − m t | ≤ 50 GeV. We also require the reconstructed top to have P T,t > 100 GeV. Note that requiring two top tagging reduces the cut efficiency of the signal significantly due to the complexity of the final states. Therefore we only require one tagged top in the signal events.
Next, we pass the selected events to a BDT classifier [28] implemented in the Toolkit for Multivariate Data Analysis (TMVA) [54] to help distinguish the signal and backgrounds.

The observables used in BDT include
• the transverse momenta of the two hadronic tops: p T,t 1 and p T,t 2 ; • the transverse momenta of the leading and sub-leading lepton: p T, 1 and p T, 2 ; • invariant mass of the two hadronic tops m t 1 ,t 2 ; • the number of jets N j ; • difference of pseudo-rapidity between the two leptons ∆η 1 2 ; • scalar sum of all transverse energy H T and miss transverse energy / E T .
We generate 100K events in each signal division (600K total) as listed in Table. 1 for a given benchmark point, 3M (1M) tttt events for OSDL (SSDL) backgrounds, and 1M tttbW events each for OSDL and SSDL backgrounds. We use half of the events to train the BDT and compute the BDT response of the other half. An optimal cut on the BDT output is used to perform the hypothesis test at each benchmark point. A minimum requirement of three events are imposed after the BDT cuts. The projected statistical significance is obtained at an integrated luminosity L = 3000 fb −1 . Assuming 10% systematic error in the background cross sections, the expected exclusion and discovery significance Z excl and Z disc are estimated following Ref. [17]. Note that two separate BDT cuts are chosen to maximize the discovery and exclusion significance separately. We claim the search region has the potential to be discovered at 5 σ significance if Z disc ≥ 5 and excluded at 95% C.L. if Z excl ≥ 1.645.

Opposite-Sign Dilepton Search
To illustrate the cut efficiency and compare the significance between different OSDL signal divisions and different benchmark points, in Table 2, we show the cross sections after each step of cuts for two benchmark points at tan β = 1.5: m H ± = 1200 GeV, m H = 900 GeV representing a heavy neutral Higgs and m H ± = 800 GeV, m H = 600 GeV representing a light neutral Higgs. The combined background cross section for the dominant nonirreducible backgrounds of tttt and tttbW is given as well. The other reducible background such as tt(Z), ttjj and jjjj will be sufficiently suppressed after all levels of cuts, comparing to the irreducible backgrounds of tttt and tttbW . The final Z disc and Z exc shown in the last column already include the 10% systematic error. For benchmark point m H ± = m A = 1200 GeV, m H = 900 GeV, the signal events in OS1 contribute the most to the signal cross section, consistent with the fact that the hadronic tops out of H are energetic and relatively easier to be top tagged. Note, however, that even in OS4 when the tagged top is the associated top, it still contribute to about 10% of the total signal cross sections.
As the transverse momenta of tops from H decay reduce, the contribution from the hadronic associated top become more prominent, as shown in benchmark m H ± = m A = 800 GeV, m H = 600 GeV. Signal events in OS2 contributes the most, while the contribution from OS4 is comparable to that of OS3. This could be explained by the long tail in the p T distribution of the associated top towards high p T region, as comparing to that of the top from H decay, as shown in the blue and red solid curves in Fig. 2, respectively. Hadronic tops of higher p T are preferred by top tagger due to the higher tagging efficiency. The dashed curves in Fig. 2 shows the hadronic top p T distribution for benchmark m H ± = m A = 1200 GeV, m H = 900 GeV as a comparison. The p T distribution of hadronic tops in OS3 is harder than that of OS4. However, OS4 still permits a considerable amount of energetic tops, which explain the 10% contribution of OS4 to the final signal cross section.

Same-Sign Dilepton Search
Given that considerable amount of tagged top coming from the associated top, decays leading to SSDL would also contribute to the signal process. The results are presented in Table 3. Comparing divisions SS1 and SS2 with divisions OS2 and OS3 in Table 2, we find that the event rates are almost equal. The change of significance between OSDL and SSDL is primarily due to the difference in the total cross sections. The combined OSDL and SSDL results are given in Table 4.

Reach of Charged Higgs
In Fig. 3, we present the discovery (dashed lines) and exclusion (solid lines) reach in the m H ± vs. tan β plane for BP-B with m H ± = m A > m H at a 100 TeV pp collider with 3000 fb −1 integrated luminosity for a fixed mass splitting of ∆m = m H ± − m H = 200 GeV. Also shown are the production cross sections of the dilepton signal, which are indicated by the gray contour lines.   Table 4. The combined signal and background cross sections with cuts at two benchmark points.
The sensitivity at large tan β is primarily limited by the branching fraction of H → tt, which is reduced due to the competing processes H → bb and τ τ . For low tan β around 1, this channel shows great sensitivity once it passes the H → tt threshold. The advantage of top tagging is evident at large mass region, which extends the exclusion region beyond 1.6 TeV.
In the left panel of Fig. 4, we present the reach of the charged Higgs via H ± → HW ± → ttW ± channel in m H ± vs. m H ± − m H plane, for tan β = 1.5. The left boundary of the enclosed region is given by the top pair mass threshold of H, above which the branching fraction of H → tt vanishes. Consistent with Fig. 3, this channel shows great sensitivity once m H passes the top pair mass threshold. Above the top pair mass threshold, almost all mass splitting with m H ± − m H 100 GeV at m H ± 500 GeV could be excluded at 95% C.L. There is no loss of sensitivity for m H near the top pair mass threshold when tops from H decay are almost at rest in the rest frame of the neutral Higgs H. In this parameter region, the top tagging rate for the associated hadronic tops from OS2 and SS1 signal divisions remains to be high. Meanwhile, the hadronic tops from neutral Higgs H decay, despite being relatively soft,   Color coding is the same as in Fig. 3. The right panel shows the reaches of H ± → HW ± → ttW ± as well as other exotic channels [17]. See text for more detail.
are energetic enough to be reconstructed with p T > 100 GeV. In the right panel of Fig. 4, we present the reach of the search channel in our study along with other exotic decay channels explored in Ref. [17]. The solid and dash lines represent the 95% exclusion and 5 σ discovery reaches. The hatched region is disfavored by unitarity consideration. Except for the blue region, which shows the reach of A → HZ → τ τ at the LHC with 300 fb −1 integrated luminosity, reaches of all other channels are for a 100 TeV pp collider with 3000 fb −1 integrated luminosity. Comparing with the gold region, which is the reach for H ± → HW ± → τ τ W ± , H → tt channel enhance the reach above the top pair threshold with the help of top tagging technique. This is similar to the neutral Higgs exotic decay A → HZ case, when the combination of H → tt (magenta) above the top threshold and H → τ τ (light blue) also covers the entire interesting parameter space. Combing all the exotic decay channels, almost all the parameter space of BP-B (m A = m H ± > m H ) that permits the exotic decay can be explored in both the neutral and charged Higgs channels.

Conclusion
While the conventional channels for the non-SM Higgses decay into a pair of SM fermions or gauge bosons play an important role in searching for non-SM Higgses, the exotic decays of non-SM Higgses into two light non-SM Higgses or one non-SM Higgs plus one SM gauge boson dominate once they are kinematically open. The reaches from conventional channels are relaxed under such scenario. Exotic decays, however, provide new opportunities for the discovery of non-SM Higgses, which are complementary to the conventional channels. In particular, in the subsequent decay of daughter Higgs, channels with top quarks in the final states can be studied with top tagging at 100 TeV pp collider given the boosted top quark from heavy Higgs decays.
In this paper, we analyzed the sensitivity of charged Higgs via the H ± → HW → ttW exotic decay mode at a 100 TeV pp collider in a benchmark plane, BP-B (m A = m H ± > m H ), which is viable under the alignment limit after considering theoretical constraints and experimental limits. Given the tbH ± associated production of charged Higgses, multi-top quarks are present in the final state. A BDT classifier is trained to distinguish between the signal events and the SM background events by requiring at least one top quark being top tagged, with a second hadronic top being either top tagged or reconstructed. Two additional leptons are required to reduce the SM hadronic backgrounds. We find that a charged Higgs with masses up to m H ± ≈ 1 TeV at small tan β (≈ 1) for a mass splitting of m A − m H = 200 GeV can be discovered at 5 σ with 3000 fb −1 data collected at a 100 TeV pp collider. The 95% exclusion reach extends beyond 1.6 TeV.
We also present the combined reach in the benchmark plane BP-B for tan β = 1.5 in Fig. 4. Decay channel A → HZ → tt has already shown to be powerful to search for heavy neutral Higgs, well beyond the reach of τ τ once the daughter particle H is above the di-top threshold. H ± → HW → ttW discussed in this paper also complements the previous study of H ± → HW → τ τ W . Combining all exotic Higgs decay channels, almost the entire parameter space in hierarchical 2HDMs can be probed at a future 100 TeV pp collider.
At future energy frontier colliders, exotic decay channels provide new discovery avenues for heavy BSM Higgses. The discovery of an extended Higgs sector beyond the SM could shed light on the underlying mechanism of electroweak symmetry breaking.