Exotic Higgs Decays in Type-II 2HDMs at the LHC and Future 100 TeV Hadron Colliders

The exotic decay modes of non-Standard Model (SM) Higgses in models with extended Higgs sectors have the potential to serve as powerful search channels to explore the space of Two-Higgs Doublet Models (2HDMs) that cannot be studied effectively using conventional decay channels. Once kinematically allowed, heavy Higgses could decay into pairs of light non-SM Higgses, or a non-SM Higgs and a SM gauge boson, with branching fractions that dominate those of the conventional decay modes to SM particles. In this study, we focus on the prospects of probing exotic decay channels at the LHC and a future 100 TeV \emph{pp} collider in the context of Type-II 2HDMs. We study the three prominent exotic decay channels, A ->HZ, A ->H^+ W and H^+ ->HW, and find that a 100-TeV pp collider can probe the entire region of the Type-II 2HDM parameter space that survives current theoretical and experimental constraints with exotic decay branching fraction>20%.


Introduction
With the discovery of a light Standard Model (SM)-like Higgs boson at the LHC [1,2], the search for new physics beyond the SM has become even more pressing, given the need to stabilize the the mass of the Higgs boson against large radiative corrections. Many of the new physics models constructed to augment the SM contain an extended Higgs sector that is responsible for electroweak symmetry breaking. One of the most straightforward and well-motivated class of extensions to the SM is the category of models collectively known as Two-Higgs-Doublet Models (2HDMs) [3]. After electroweak symmetry breaking, the spectra of 2HDMs contain five mass eigenstates (h, H, A, H ± ), with the CP-even Higgs h being the observed SM-like Higgs. These new Higgs bosons can be constrained through either indirect searches via precision measurements of Higgs properties at future Higgs factories [4,5] or direct searches at particle colliders at the energy frontier. In this paper, we focus on the potential for direct discovery of these heavy states at the Large Hadron Collider (LHC) as well as a proposed 100 TeV pp collider [6,7]. The conventional searches for neutral heavy Higgses (A and H ) in 2HDMs mainly focus on modes in which they decay into pairs of SM particles. While these modes have been proven to be effective in the search for the SM Higgs, they suffer from certain limitations when it comes to searches for non-SM heavy Higgses. In particular, current data indicates that the observed 125 GeV Higgs is very SM-like, which implies that the couplings of A and H to the SM gauge bosons (W, Z ) are suppressed, which in turn implies the suppression of both their production via weak-boson fusion and weak-boson associated processes, as well as their decays to SM gauge boson pairs (WW/ZZ ). The decay channel to a pair of top quarks, which becomes kinematically accessible for large Higgs masses, suffers from both the large top-quark pair production background in the SM as well as non-trivial interference effects [8], significantly reducing its sensitivity.
If the BSM Higgs sector is hierarchical -that is, its states are sufficiently well-separated in mass -additional decay channels open up, for example, the decay of a heavy Higgs to two lighter Higgses, or to a lighter Higgs and an SM gauge boson. Given the corresponding unsuppressed couplings and the large amount of available phase space, these decay modes can be dominant in large regions of parameter space. In this scenario, the branching fractions of the conventional decay modes are reduced and the experimental search limits obtained using them are relaxed correspondingly.
The exotic decay modes of heavy neutral Higgses to lighter Higgses, namely H/A → AZ/HZ/H ± W ∓ and H → AA/hh/H + H − , offer alternative avenues for discovering heavy Higgses that complement the conventional ones. The reach of individual channels at the LHC have been studied in the literature [9,10] and searches for the most promising channel, H/A → AZ/HZ, have been carried out at both ATLAS [11] and CMS [12]. The current experimental data excludes heavy neutral Higgses with masses up to about 700 -800 GeV, depending on the BSM Higgs spectrum and values of tan β. Additionally, the A → hZ, H → hh channels have also been studied at the LHC [13][14][15]. However, no constraints on the 2HDM parameter space can be imposed using these channels, the observed Higgs boson is SM-like, corresponding to the alignment limit in 2HDMs, in which such channels are highly suppressed.
Charged Higgs bosons pose a special challenge for experimental searches [16][17][18]. They are dominantly produced in association with top quarks (tbH ± ), with a cross section much smaller than that of the dominant production channels for the neutral Higgses(gluon fusion and bbH/A associated production at large tan β). The branching fractions of the conventional search channels, H ± → τ ν, cs are suppressed once the decay mode H ± → tb opens up. Despite its large branching fraction, the H ± → tb decay mode holds little promise for discovering charged Higgses at the LHC due the large SM backgrounds to this process. The exotic decay modes H ± → AW ± /HW ± could potentially be useful in charged Higgs searches [19,20]. However, the complicated decay final states and relatively large SM backgrounds limit their reaches at the LHC.
The study in Ref. [21] constructs benchmark planes for these exotic decay channels at the LHC, taking into account both theoretical constraints such as perturbativity, unitarity, and vacuum stability, as well as current experimental limits from direct and indirect searches on the parameter space of Type-II 2HDMs. Sizable mass splittings between Higgses, required for the exotic decay modes, can be achieved for heavy Higgs masses up to about 2 TeV. Thus, in this paper, we focus on a subset of the benchmark scenarios in Ref. [21] that permit TeV-scale masses, and construct two benchmark planes: BP- In recent years, a possible 100 TeV pp collider has been discussed worldwide, with the two leading proposals being the Future Circular Collider (FCC) at CERN [7] and the Super proton-proton Collider (SppC) in China [6]. It is important to explore the discovery potential for new physics models at such a machine to establish the physics case for building it. One advantage of such a high energy machine is that top quarks produced in heavy particle decays will be highly boosted, resulting in fat jets that can be effectively identified using top-tagging techniques [22][23][24][25][26][27]. This will allow us to distinguish new physics signals with top quarks in the final states from the large SM backgrounds involving top quarks, which typically pose a formidable challenge at the LHC.
In this paper, we study the discovery potential of non-SM heavy Higgses in Type-II 2HDMs at the LHC, the High Luminosity LHC (HL-LHC), as well as a 100 TeV pp collider: LHC: L = 300 fb −1 , HL-LHC: L = 3 ab −1 , 100 TeV: L = 3 ab −1 , combining all the viable exotic decay channels. We perform a detailed collider analysis to obtain the 95% C.L. exclusion limits as well as 5σ discovery reach for benchmark planes BP-A and BP-B. In recent years, multivariate analysis techniques such as neural networks [1], boosted decision trees (BDT) [2], the Matrix Element Method [28,29] and Information Geometry [30,31] have begun to be more widely used in experimental particle physics searches. In our study, we construct a set of physics-motivated variables that we use as input features for gradient BDT classifiers. The rest of the paper is organized as follows. In Sec. 2, we present a brief review of hierarchical 2HDMs and introduce the benchmark planes BP-A and BP-B. In Sec. 3, we study the 'golden' channels A/H → HZ/AZ and explore their reach at the LHC, HL-LHC, as well as a 100 TeV pp collider. In particular, we studied both the bb and τ τ states as well as the tt final state using top tagging techniques to identify boosted top quarks in the final state. In Sec. 4, we present the H → H ± W ∓ channel. In Sec. 5, we explore the discovery potential for charged Higgses via the H ± → HW ± channel. In Sec. 6, we present the combined reach in 2HDM parameter space obtained with these channels at the LHC and a future 100 TeV pp collider. In Sec. 7, we conclude. Appendix A and Appendix B describe the methodology used for our collider analysis and how we simulate top tagging, respectively.

Properties of 2HDMs
In this section, we provide a brief review of the aspects of 2HDMs that are most relevant to this study. For a pedagogical introduction to this topic, see [32,33]. The scalar sector of 2HDMs consists of two SU(2) doublets Φ i , with i = 1, 2, which can be explicitly parameterized in terms of their real and complex components as shown below.
Here, v i are the vacuum expectation values (VEVs) for the neutral components of the doublets, satisfying the condition v 2 GeV. This allows us to introduce the mixing angle β such that tan β = v 2 /v 1 1 . Assuming CP conservation and a softly-broken Z 2 symmetry 2 , the scalar portion of the 2HDM Lagrangian can be written down as

(2.2)
After the mechanism of electroweak symmetry breaking (EWSB), the scalar sector of a 2HDM consists of five mass eigenstates: a pair of neutral CP-even Higgses, h and H, a CP-odd Higgs, A, and a pair of charged Higgses H ± . For these states we can write In the following, we will identify h with the discovered SM-like 125 GeV Higgs 3 and study the collider reach of heavy non-SM Higgses. 1 In this paper we often employ the shorthand notation s θ , c θ , t θ = sin θ, cos θ, tan θ. 2 The most general scalar potential also contains the term λ6 c. and potentially leads to flavor-changing neutral currents (FCNC). In the following we will neglect this term by imposing a Z2 symmetry under which the scalar fields transform as Φ1 → −Φ1 and Φ2 → Φ2.
3 This is slightly different from the usual convention that the mass eigenstates h 0 and H 0 are ordered by their masses. In this study, h can either be the light one or the heavy one. In our discussion of the collider study below, which focusses on heavy BSM Higgs boson, H is typically taken to be the heavy CP-even Higgs, although H being the light CP-even Higgs is still a viable possibility given the current experimental search results [34].
The potential in Eq. (2.2) contains eight independent parameters: three mass parameters m 2 11,22,12 and five quartic couplings λ 1,2,3,4,5 . For our purposes, it is convenient to parameterize 2HDMs by the physical Higgs masses, m h , m H , m A and m H ± , the mixing angle between the two CP-even Higgses α, tan β, the electroweak VEV v, and the soft Z 2 symmetry breaking parameter m 2 12 . Two of these parameters, namely the vacuum expectation value v and the mass of the SM-like Higgs, m h are known to be 246 GeV and 125 GeV respectively, leaving the remaining six independent parameters. Note that in a generic 2HDM, there are no mass relations between the Higgs states, and therefore exotic Higgs decays such as A → HZ are possible.
As mentioned earlier, we have introduced a Z 2 symmetry to avoid tree-level FCNCs, which implies that each fermion type is only allowed to couple to one Higgs doublet. In this work we will focus on Type-II 2HDM, in which the up-type quarks only couple to Φ 2 , and the down-type quarks and leptons only couple to Φ 1 .

Couplings in the Alignment Limit
The most recent data from the LHC indicate that the coupling strength of the recently discovered 125 GeV Higgs boson is consistent with the SM [35]. In the context of a 2HDM, this can naturally be achieved in the alignment limit, where c β−α = 0, with h being identified with the SM Higgs in our convention. Its couplings to fermions and gauge bosons are precisely those predicted by the SM.
Any deviation of the signal strength of the SM-like Higgs h from its SM prediction will constitute clear evidence for new physics and provide strong motivation for additional experimental searches to understand its nature. In the absence of such deviations at the LHC, or possibly a future lepton collider, future limits will further push us towards the alignment limit [4,5,9]. For this reason, the following discussion will assume c β−α = 0. A discussion of the more general case can be found in [21].
Near the alignment limit, the coupling of the SM-like Higgs h to pairs of gauge bosons V = Z, W ± is SM-like, while the coupling of the heavier CP-even neutral Higgs H to gauge boson pairs is suppressed, g HV V ∼ c β−α . Furthermore, the couplings of h to a heavier scalar and a gauge boson g hAZ ∼ g hH ± W ∓ ∼ c β−α are also suppressed. The unsuppressed 4 couplings of the additional scalars to vector bosons in the alignment limit are given by where p µ X represents the outgoing momentum for particle X. We can see that the non-SM like Higgses have unsuppressed couplings only to the other non-SM like Higgses, but suppressed couplings to the SM-like Higgs and pairs of gauge bosons. Therefore, only the heavier non-SM Higgs will decay into a lighter non-SM like Higgs and a gauge boson via an exotic decay mode. The lightest non-SM like Higgs will then decay into fermion pairs.
In the Type-II 2HDM, the couplings of the non-SM Higgses to SM fermion pairs in the alignment limit can be written as where y f are the SM fermion Yukawa couplings. Note that the fermion coupling for both heavy neutral scalars, A and H, have the same scaling with the mixing angle β under the alignment limit. The couplings of the charged Higgs boson to the fermions are

Constraints on Hierarchical 2HDMs
To understand the theoretical constraints on 2HDMs, it is useful to consider the relations between the quartic couplings and the physical masses. In the alignment limit, we can express the quartic couplings of the scalar potential as follows [21].
We can see that the soft Z 2 breaking term m 2 12 plays a crucial role, as it affects the size of the trilinear and quartic scalar self-couplings. As discussed in [21], its possible allowed values are dictated by requiring vacuum stability and tree-level unitarity of the theory. The latter roughly requires the quartic couplings to be perturbative, λ i 4π. Thus, perturbativity of λ 1,2 requires |m 2 12 − m 2 H s β c β | v 2 , which naturally leads us to fix the coefficient of the soft Z 2 breaking term in the Lagrangian to be It is possible to deviate from this relation for values of t β close to unity and for low scalar masses m H ∼ v. However, in this study we focus on the high scalar mass region that can be probed at a future high energy collider and we therefore require Eq. (2.8) to hold for the rest of the paper. In the following, we summarize the theoretical and experimental constraints on the 2HDM parameter space, and their implications for exotic Higgs decays. We only consider the alignment limit c β−α = 0 and require m 2 12 = m 2 H s β c β . A more detailed discussion is presented in [21].
Vacuum Stability In order to have a stable electroweak vacuum [36], the following scalar mass conditions need to be fulfilled: This implies that for m H > m A,H ± , the mass splittings between the heavy CP-even Higgs H and the other heavy scalars A and H ± have to be small, such that the decays of H into the AZ, AA, H + H − and H ± W ∓ final states are not kinematically allowed.
Tree-Level Unitarity Requiring tree-level unitarity of the scattering matrix in the 2HDM scalar sector [37] imposes the following additional mass constraints: (2.10) Here we have ignored sub-leading terms proportional to m 2 h . Note that these constraints are independent of the value of t β .
Electroweak Precision Measurements Measurements of electroweak precision observables impose strong constraints on the 2HDM mass spectrum [38]. In particular, these constraints require the charged scalar mass to be close to the mass of one of the heavy neutral scalars.
Flavour Constraints Various flavor measurements [38,39] provide indirect constraints on the 2HDM parameter space, in particular on the mass of the charged scalar. The most stringent of these comes from the measurement of the branching fraction for the decays b → sγ and B + → τ ν, which disfavor m H ± < 580 GeV [40] and large values of t β respectively. Flavor constraints, however, can be alleviated with contributions from other sectors of new physics models [41]. In this paper, we focus on the direct collider reach of heavy Higgses without imposing the flavor constraints.
Direct Searches at LEP and LHC While the search for pair-produced charged Higgs bosons at the Large Electron-Positron Collider (LEP) imposes a lower bound of 80 GeV on the mass of the charged Higgs boson [42], LEP searches for AH production constrain the sum of the masses m H + m A > 209 GeV [43]. LEP bounds on single neutral Higgs production do not apply in the alignment limit, due to their vanishing coupling to the gauge bosons.
The leading LHC bounds on neutral scalars come from searches for their conventional decays into pairs of τ -leptons [44], and mainly constrain the low mass and high t β region. The low t β region for high scalar masses, in which the scalar predominantly decays into pairs of top quarks, is basically unconstrained. This channel remains an experimental challenge due to the complicated final state, large backgrounds and nontrivial interference patterns [8]. Note that limits from searches for conventional decays are significantly weakened once exotic Higgs decay channels are kinematically allowed. The ATLAS [11] and CMS [12] searches for the exotic decay mode A/H → HZ/AZ constrain hierarchical 2HDMs with low scalar masses.
Additional constraints for charged Higgs bosons are derived from experimental searches at the LHC via the H ± → τ ν decay mode. A light charged scalar with m H ± < m t is mostly excluded by the non-observation of the decay t → H + b, although these limits can be weakened at low t β by the existence of exotic decay modes [20]. A heavy charged scalar is only weakly constrained at very large t β [16-18]. For a detailed discussion of constraints on the charged Higgs, see [45].

Exotic Higgs decays in Hierarchical 2HDMs
We have seen that in a 2HDM with heavy scalar masses close to the aligment limit, the requirements of unitarity and vacuum stability fix the soft Z 2 breaking term m 2 12 = m 2 H s β c β and demand the mass hierarchy m H ≤ m A , m H ± . Additionally, electroweak precision constraints require the mass of the charged scalar to be close to that of one of the neutral scalars, m H ± ≈ m H or m H ± ≈ m A . Hierarchical 2HDMs are therefore restricted to be close to the following two benchmark scenarios: If the charged Higgs H ± is mass-degenerate with the heavy CP-even Higgs H, only the exotic decays of the pseudoscalar A are allowed (A → H ± W ∓ /HZ). Requiring unitarity additionally imposes an upper bound on the mass splitting: If the charged Higgs H ± is mass-degenerate with the pseudoscalar A, only the exotic decays into the CP-even Higgs H are allowed: H ± → HW ± and A → HZ. In this case, unitarity imposes an upper bound on the mass splitting: While these benchmark scenarios are representative, small deviations from them are permitted. This is illustrated in Fig. 1, where we show the accessible regions of the Type-II 2HDM parameter space in the alignment limit when all the theoretical considerations and precision constraints are taken into account. Note that these results are independent of the value of t β .
While the requirement of vacuum stability imposes a lower bound of m H on m A and m H ± , electroweak precision constraints force the charged scalar to be almost mass degenerate with one of the neutral scalars. The additional unitarity constraints restrict the mass splittings, in particular for large scalar masses, to be small. This imposes an upper limit on the scalar masses in hierarchical 2HDMs that permit exotic Higgs decays. The exotic decay channel A → HZ becomes kinematically disallowed at m A ≈ 1.7 TeV for BP-A and m A ≈ 2.8 TeV for BP-B. Scalar particles in this mass range will be copiously produced at a future 100 TeV pp collider. Such a machine will therefore allow us to probe the entire hierarchical 2HDM parameter space, in which the heavy scalar predominantly decays via exotic modes. For even higher masses, the mass spectrum is forced to be near degenerate and can be effectively probed by conventional decay channels. Note that close to the alignment limit, exotic decays of the heavy Higgses into the light SM-like Higgs h, such as A → hZ, H → hh and H ± → hW ± , are suppressed by c β−α .

Production Cross Sections
In Fig. 2, we show the production cross sections of the CP-even (left panel), CP-odd (center panel), and charged (right panel) Higgs bosons at a 100 TeV pp collider as functions of their masses and t β in the alignment limit. The dominant production processes for the neutral Higgses are gluon fusion (gg → A/H) and bottom quark fusion (bb → A/H), shown as solid red and dashed blue lines, respectively. The NNLO cross sections for both processes have been calculated using SusHi [46][47][48]. The gluon fusion process will be dominant in the small t β region, where the production cross section can be greater than 10 5 fb for Higgs masses below 600 GeV. In contrast, the bottom-quark fusion process is dominant in the large t β region. The charged Higgs is predominantly produced via the process gg → tbH ± , and its production cross section has been adopted from Ref. [49] (which used Prospino [50,51] to calculate it).
Compared to the 14 TeV LHC [21], a 100 TeV pp collider enhances the production rates of 500 GeV neutral Higgses by roughly a factor of 30-50. For charged Higgses with the same mass, the rate is enhanced by a factor of 90. For heavier Higgses, the enhancement is even greater.
In Fig. 3, we show the exotic branching fractions of heavy Higgs bosons as functions of their masses and t β for the two benchmark scenarios defined in Sec. 2.4. The exotic decay channels have sizable branching fractions ( 20 %) over the entire parameter space and even dominate in the so-called wedge region, corresponding to moderate values of t β (2 t β 20). This phenomenon reduces the reach of the conventional search channels, but also opens up promising avenues for heavy Higgs searches in the form of the exotic decay channels. In particular, with the cleanness of the leptonic decay modes of the vector bosons, the exotic decays of heavy Higgses provide an opportunity to study the wedge region in 2HDMs.    3 The Golden Channel: A → HZ

Signal Processes
As discussed in Sec. 2.3, the requirements of unitarity and vacuum stability constrain the CP-odd state A to be heavier than the CP-even state, thereby opening up the exotic decay mode A → HZ. A further leptonic decay of the Z-boson leads to a experimental signature that is both clean and covered by the conventional trigger menu of the LHC experiments. This makes the decay A → HZ the most promising exotic decay channel, or the golden channel.
Below the top threshold, H will predominantly decay to either a pair of b-quarks or a pair of τ leptons. Although the branching fraction of the former (≈ 90%) is significantly higher than that of the latter (≈ 10%), it suffers from large SM backgrounds, making it experimentally challenging to detect. In contrast, the latter channel is much cleaner, making it particularly interesting at high luminosities at which sufficient statistics will be available to make up for its lower branching fraction.
If m H is above the top threshold, that is, greater than twice the mass of the top quark, H will predominantly decay into top quark pairs except at large values of t β 30, where the coupling of H to top quarks is suppressed. If m H is relatively small, leptonic top decays will provide the most sensitive signal. On the other hand, if it is large, on the order of a TeV or greater, the top quarks in the final state can be highly boosted and top-tagging techniques can be profitably applied. The latter approach will work particularly well at a future 100 TeV pp collider, at which TeV-scale heavy Higgses will be produced in sufficient numbers. In this section we therefore consider the three dominant channels While we focus on the pp → A → HZ channel, we note that the same search can also be performed for the pp → H → AZ channel.

bb -channel
We first consider the A → HZ → bb channel, which is the dominant decay channel for low mass scalars and has been subject to searches at both ATLAS [11] and CMS [12]. As discussed in [9], the dominant SM background to this channel is fully-leptonic top pair production (tt → bb + / E T ), followed by bottom-associated Z -boson production (bbZ → bb ) for = e, µ. Decays to τ s are included in the tt background as well. Additional backgrounds from multi-boson production or mis-tagged jets play a sub-dominant role. The fully-leptonic top pair production background process is simulated with up to one additional jet and its cross-section normalized to 102 pb and 3714 pb at 14 TeV [52] and 100 TeV [53], respectively. The sub-leading bbZ → bb background is simulated at leading order taking into account a next-to-leading order (NLO) K -factor of 1.45 [54]. For a transverse momentum threshold of p b > 15 GeV, this implies a background rate of 9.7 pb and 350 pb at 14 TeV and 100 TeV, respectively.
Both the signal and the background process are simulated using MadGraph 5 [55], interfaced with Pythia [56,57] and Delphes 3 [58] for detector simulation. Each signal benchmark is simulated with the correct width and branching fractions as obtained from 2hdmc [59]. We then select events with at least two same-flavor leptons passing the trigger requirements p T, 1 > 20 GeV and p T, 2 > 10 GeV and two b-tagged jets with p T,b > 25 GeV 5 . For these events, we construct a set of observables which is then used to train and test a boosted decision tree classifier. For the bb channel, the set of observables includes: • the transverse momenta of the leading b-tagged jet (p T,b 1 ), the sub-leading b-tagged jet (p T,b 2 ), the leading lepton (p T, 1 ) and the sub-leading lepton (p T, 2 ) • the invariant mass of the leptons (m ), the jets (m bb ) and the lepton-jet system (m bb ) • the scalar sum of all the transverse energy (H T ) and the missing transverse energy (/ E T ).
Finally, a hypothesis test is performed for each benchmark point to obtain the projected statistical significance of the BSM hypothesis versus the SM. We assume a 10% systematic error in the background cross section 6 . More details of our analysis can be found in Appendix A.

τ τ -channel
With increasing luminosities, the reach of the A → HZ → bb channel will be limited by systematic uncertainties in estimating the background rates. Such limitations do not apply to the A → HZ → τ τ channel due to its clean final state with significantly smaller background rates. Thus, despite having a cross section roughly ten times lower than that of the bb channel, the sub-leading τ τ channel is expected to have a superior reach. This channel has been considered by CMS [12] and has already been found to provide a reach comparable to the bb channel with the 8 TeV data set. In this work we focus on the case in which both τ s decay hadronically, since this allows for a more precise reconstruction of the Higgs mass than the case in which one or both τ s decay leptonically, with missing energy arising from neutrinos in the final state. Note that the reach can be further enhanced by combining the hadronic and leptonic decays, which is beyond the scope of this work. The main SM background to the A → HZ → τ τ signal comes from boson pair production with the subsequent decay into leptons, (Z/h/γ * )Z → τ τ . The corresponding cross sections at NLO for the τ τ final state are 6.8 fb at 14 TeV [60] and 67 fb at 100 TeV [53] for invariant masses m τ τ > 100 GeV. Note that this includes both resonant production via ZZ and hZ dominating at small masses m τ τ as well as off-shell contributions dominating at large m τ τ . Sub-dominant backgrounds, for example from ZWW production, were found to be negligible.
For this analysis, we select events with two same-flavor leptons with p T, 1 > 20 GeV and p T, 2 > 10 GeV and two τ -tagged jets with p T,τ > 25 GeV and consider the following list of observables: • the transverse momenta of leading τ -tagged jet (p T,τ 1 ), the sub-leading τ -tagged jet (p T,τ 2 ), the leading lepton (p T, 1 ) and the sub leading lepton (p T, 2 ) • the invariant mass of the leptons (m ), the jets (m τ τ ) and the lepton-jet system (m τ τ ) • the scalar sum of all the transverse energy (H T ) and the missing transverse energy (/ E T ).

tt -channel
With increasing collision energy, the daughter particle CP-even scalar H with mass above the top threshold can be produced efficiently. In this case, the reaches of both the A → HZ → bb and the A → HZ → τ τ channel are limited by statistics due to the suppressed branching fractions, especially in the small t β region, while the A → HZ → tt channel is expected to improve the reach for H above the top quark threshold. The decay products of H can have fairly large p T for TeV-scale Higgses, leading to collimated top decay products. Therefore, the standard top reconstruction method for the leptonic decay mode will lose its efficiency. However, top-tagging techniques [61] developed in recent years could retain up to 30% of hadronic tops while rejecting most of the QCD events (see Appendix B). For simplicity, in this work we focus on the case in which both tops decay hadronically, which allows for a more precise reconstruction of the Higgs mass. Note that mixed hadronic and leptonic top decays lead to another potentially interesting channel, A → HZ → t h t , which is beyond the scope of this work.
The dominant SM background to this channel is the process ttZ → tt . The corresponding cross section at NLO is 1.91 pb at 100 TeV [53]. We select events with two same-flavor leptons passing the trigger requirements p T, 1 > 20 GeV and p T, 2 > 10 GeV and two top-tagged jets with p T,t > 200 GeV. The following list of observables is used to train and test a BDT classifier: • the transverse momenta of the leading top-tagged jet (p T,t 1 ), the sub-leading toptagged jet (p T,t 2 ), the leading lepton (p T, 1 ) and the sub-leading lepton (p T, 2 ) • the invariant mass of the leptons (m ), the jets (m tt ) and the lepton-jet system (m tt ) • the scalar sum of all the transverse energy (H T ) and the missing transverse energy (/ E T ).

Reach
As discussed in Sec. 2.5, the production of A occurs primarily via gluon fusion in the small tan β region and bottom quark fusion in the large tan β region. We perform a separate analysis for each of these production modes and combine their significances when presenting the reach. In Fig. 4 At low values of tan β, both the H → bb and H → τ τ channels are particularly sensitive at masses below the top threshold, m A = 2m t + ∆m ≈ 550 GeV, while the branching fractions for these decays are strongly suppressed at larger masses due to the opening up of the H → tt channel. Increasing the luminosity to 3 ab −1 at HL-LHC or a 100 TeV collider does not enhance the reach significantly. At large values of tan β, the  decay H → tt is strongly suppressed and so the H → bb and H → τ τ channels retain sensitivity for large masses.
The bb channel is limited by systematic uncertainties and hence the reach does not increase much with increasing luminosities or center-of-mass energies. In contrast, the τ τ channel has a much cleaner signature and therefore is mainly limited by statistical uncertainty and hence superior in sensitivity to the bb channel. At tan β = 50 the exclusion reach of the τ τ channel extends up to ∼ 1 TeV at the LHC, ∼ 1.5 TeV at the HL-LHC and ∼ 3 TeV at a 100 TeV pp collider. The maximal discovery regions are around 0.5 TeV, 1 TeV and 2.5 TeV for LHC, HL-LHC and 100 TeV pp collider, respectively.
The H → t h t h channel is able to probe scenarios with larger Higgs masses in the range 700 GeV m A 2 TeV for small values of tan β 3. For smaller masses, the sensitivity of this search is limited by the efficiency of the hadronic top-tagging due to smaller typical transverse momenta. At larger values of tan β, this search loses sensitivity due to both the smaller Higgs production rates and the smaller Higgs branching fraction into top pairs.
While the heavy pseudoscalar A can decay either into HZ or H ± W ∓ in BP-A, only the A → HZ channel is available in BP-B. Thus, the discovery and exclusion reach attainable in BP-B is greater than in BP-A. 4 The Charged Higgs Channel: A → H ± W ∓

Signal Processes
If the mass splitting between the pseudoscalar and charged Higgs is large enough (m A > m H ± + m W ), the additional decay channel A → H ± W ∓ opens up. This happens in scenarios such as BP-A, where m H = m H ± < m A . In this case the branching fraction for the exotic decay mode A → H ± W ∓ is typically twice as large as that of the A → HZ decay mode which can be understood from the Goldstone equivalence theorem. The leptonic decay of the W -boson provides a clean experimental signature and permits the use of a lepton trigger, which makes the decay mode A → H ± W ∓ a promising exotic decay channel to explore.
If the charged Higgs is light (m H ± m t ), it will dominantly decay into either τ ν at high t β or cs at low values of t β . However, such a light charged Higgs boson is excluded by the non-observation of the top decay t → H + b [17]. If the charged Higgs is heavier (m H ± > m t ), the H ± → tb decay mode opens up and becomes dominant over the entire phase space. In this case the exotic decay channel A → H ± W → tbW will have the same event topology as top-quark pair production, making background suppression the main challenge for this channel.
If the charged Higgs mass is relatively small (m H ± ∼ a few 100 GeV), the top quark decay products will be both soft as well as spread out over the detector area. In this case leptonic top decays are expected to provide the most sensitive channel. However, at larger masses (m H ± 1 TeV), the top quark from a heavy charged Higgs decay will be boosted and top-tagging techniques can be used to identify the top quark candidate. In contrast to leptonic top decays, which suffer from additional missing energy due to the neutrino in the final state, hadronic top decays also allow for a more precise reconstruction of the masses of the top quark and the charged Higgs. In this study, we therefore focus on the following production and decay chain: (4.1)

Analysis
After requiring a hadronic top-tagged jet in the final state, the leading irreducible background is semi-leptonic top pair production, tt → t h b ν, where = e, µ, τ . The corresponding cross section at a 100 TeV collider is 15.1 nb at NNLO [53], which is reduced by a factor of roughly 0.2 once we require p T,t > 250 GeV. Additional backgrounds arising from the production of a leptonically decaying W -boson in association with a boosted jet with p T,j > 250 GeV, which could be misidentified as a top quark, were found to be small, σ(W ± + j → ± ν + j) = 0.43 nb [53] and are further reduced upon including the mis-tagging rate for QCD jets j ∼ 10 −3 (see Appendix B). Similarly, backgrounds from single top production were found to be negligible. We select events containing one lepton with p T, 1 > 20 GeV, at least one top-tagged jet with p T,t 1 > 200 GeV, at least one b-tagged jet with p T,b > 50 GeV and a small amount of missing transverse energy, / E T > 20 GeV. The following set of observables is then used to train and test a BDT classifier: • the transverse momenta of the leading top-tagged jet (p T,t 1 ), the leading b-tagged jet (p T,b 1 ) and the leading lepton (p T, 1 ).
• the invariant masses of the jets (m tb ) and the lepton-jet system (m tb ν ), and the angular separation of the jets (∆R tb ).
• the scalar sum of the transverse energy (H T ) and the missing transverse energy (/ E T ).
To reconstruct the mass of the heavy neutral Higgs (m tb ν ), we reconstruct the neutrino momentum from / E T following the method shown in Ref. [62].

Reach
In Fig. 5 we present the reach for the exotic decay channel A → H ± W ± for BP-A. Note that this channel is not open in BP-B, where m H ± = m A . We find that the LHC is insensitive to this channel due to a low heavy Higgs production rate and insufficiently boosted decay products. In contrast, a 100 TeV collider will be able to produce a sufficient number of heavy Higgses with ∼ TeV scale masses that can decay into top quarks with the sizable boosts necessary for the use of top-tagging techniques. The corresponding exclusion and discovery reaches are shown as solid and dashed lines, respectively.
At small values of t β (< 2) where the pseudoscalar A is dominantly produced via gluon fusion, the exclusion reach can be up to m A 1.3 TeV. At large t β ( 20) the bottomquark associated production process dominates and this channel can discover a CP-odd scalar A with mass up to 1.2 TeV or exclude CP-odd scalars with masses up to 1.6 TeV. The low reach in the wedge region (2 t β 20), results from the small production cross section for both the gluon fusion and the bottom quark fusion production of the CP-odd scalar A.
Finally, we note that the reach of this channel is dominated by systematic uncertainties, given the large top pair backgrounds. In particular, when estimating the reach we assumed a 10 % systematic uncertainty on the background rate. A better theoretical understanding of QCD processes, especially top-pair production, will be extremely important for accurate background estimation at future 100 TeV colliders to reduce the systematic uncertainties.

Signal Processes
While in the previous section we considered exotic decays of neutral Higgses to charged Higgses, it is also possible for charged Higgses themselves to undergo exotic decays. As  discussed in Sec. 2.4, the only viable exotic decay mode for heavy charged Higgses in hierarchical 2HDMs in the alignment limit is the decay H ± → HW ± , which appears in BP-B when the mass splitting between the charged and neutral Higgses is sufficiently large (m H ± > m H + m W ). As discussed in Sec. 2.5, the charged Higgs is mainly produced in association with a top and bottom quark (pp → H ± tb), which leads to a busy final state topology (H ± tb → HW + W − bb).

BP-
If the daughter Higgs H is light (m H < 2m t ), it will dominantly decay into pairs of bquarks and τ leptons with branching fractions of ∼ 90% and ∼ 10% respectively. Despite its larger branching fraction, the H → bb decay channel remains experimentally challenging, due to the large hadronic SM backgrounds associated with it 7 . In contrast, the H → τ τ decay channel can lead to a same-sign di-lepton signature where one lepton arises from a leptonic τ -decay and the other from a leptonic W -decay. As shown in [19], this signature allows for the effective suppression of SM backgrounds -in particular, the background from top pair production.
If the daughter Higgs is heavier (m H > 2m t ), it will dominantly decay into pairs of top quarks, leading to a final state equivalent to four top quarks. Searches for this channel therefore will be extremely challenging due to the large hadronic SM backgrounds. However, the authors of [64] have proposed to utilize the possible tri-lepton and same-sign di-lepton signatures and have shown that these can be promising for larger values of m H . In this study we consider the following signal production and decay chain: with a focus on the same-sign di-lepton final state.

Analysis
As mentioned above, we consider the case in which one of the W bosons and one of the τ leptons decay hadronically, and the other W boson and τ lepton decay leptonically. The resulting final state permits the same-sign di-lepton signature ± ± + 2b + 2j + τ h + / E T , which allows the suppression of most SM backgrounds.
The remaining background is dominated by the ttτ τ production process, where at least one of the top quarks decays leptonically (where the definition of leptons includes τ s) [19]. The τ s originate from the decay of a neutral SM boson (Z, h, γ * ). As discussed below, the neutral Higgs candidate H is reconstructed by combining the momentum of the hadronic τ with the momentum of the softer lepton. A large invariant mass of the Higgs candidate in ttτ τ background events typically only arises when combining a hadronic τ from boson decay with a lepton from top quark decay, providing a smooth background spectrum. Using MadGraph 5, we obtain a cross section for t h/ t τ τ production of 886 fb for a 100 TeV collider, with the largest individual contribution corresponding to the resonant backgrounds ttZ and tth. For completeness, we also consider the sub-dominant backgrounds, which can provide a same-sign di-lepton signature, ttW → t τ t ν and ttZ → t τ t with cross sections of 99 fb and 166 fb, respectively.
Following the analysis strategy outlined in [19], we select events with two same-sign leptons, one or two b-tagged jets, one τ -tagged jet with sign opposite that of the leptons, and at least two untagged jets. We loop over all combinations of the untagged jets and choose the combination that has invariant mass closest to the mass of the W boson. We reconstruct the leptonically-decaying W boson by first reconstructing the neutrino momentum using the procedure in [62] and then combining it with the momentum of the hardest lepton. We then combine the momentum of the τ -tagged jet with the momentum of the softer lepton to approximate the momentum of the neutral Higgs boson H. Finally, we combine the H candidate with the W candidate that gives the mass closest to the mass of the charged Higgs. The input features for the BDT classifier are the following: • the transverse momenta of the leading lepton (p T, 1 ), the leading untagged jet (p T,j 1 ), the b-tagged jet (p T,b ), and the τ -tagged jet (p T,τ h ).
• the invariant masses of the neutral and charged Higgs candidates (m τ h 2 and m τ h 2 W ).
• the missing transverse energy (/ E T ).

Reach
In Fig. 6, we show the discovery and exclusion reaches (the dashed and solid lines respectively) for the exotic decay channel H ± → HW for BP-B. The reach at the 14 TeV LHC [19] for this channel is limited by the low production cross section of heavy charged Higgs bosons, and thus we only show the reach for a 100 TeV pp collider, which will be able to produce charged Higgses with TeV-scale masses in large numbers. Below the top-quark threshold, m A < 2m t + ∆m ≈ 550 GeV, the H → τ τ channel can probe the entire range of tan β. Above this threshold, the H → tt decay channel opens  up, eliminating the reach at lower values of tan β. In the interesting wedge region, around t β = 10, this channel can discover scenarios with charged Higgs masses up to 1.7 TeV and exclude charged Higgses with masses up to 2.5 TeV.

Reach in Benchmark Planes
In Fig. 7, we present the exclusion and discovery reaches in the ∆m = m A − m H versus m A plane for BP-A (left panel) and BP-B (right panel) with tan β = 1.5. As discussed in Sec. 2.4, these two benchmark scenarios, corresponding to the mass hierarchies m H = m H ± < m A and m H < m H ± = m A respectively, have been found to be representative of hierarchical 2HDMs. In particular, they are permitted by theoretical considerations of unitarity and vacuum stability as well as electroweak precision measurements. For the purpose of illustration, we consider tan β = 1.5. This choice is representative of the interesting low tan β region, which will be particularly hard to constrain using the conventional searches such as A/H → τ τ and H ± → τ ν which are expected to provide the best sensitivity at higher values of tan β.
For the A → HZ → τ τ channel, the blue, cyan, and green regions show the reaches at the LHC, HL-LHC, and a future 100 TeV collider, respectively. For the A → HZ → tt channel, as well as the channels involving charged Higgs bosons, A → H ± W and H ± → AW , the reaches at a 100 TeV collider are shown in magenta, orange and yellow, respectively. For each of the six colors, we distinguish between discovery and exclusion regions using differing line styles and opacities for the contours and the shading of the regions they enclose. Regions that are more opaque and bounded by dashed contours correspond to discovery, and regions that are more transparent and bounded by solid  contours correspond to exclusion (the discovery regions are always subsets of the exclusion regions).
The highest sensitivity at low values of m H is provided by the A → HZ → τ τ channel. At both the LHC (blue) and HL-LHC (cyan), the reach extends up to m H = 2m t , resulting in almost straight lines for the sensitivity contours. This can be understood from the fact that the H → tt channel quickly becomes dominant once it is kinematically accessible in the low t β regions, with a branching fraction close to 100%. Therefore, in this channel, the HL-LHC will not be able to improve the expected reach for hierarchical 2HDMs compared to the LHC. In contrast, a future 100 TeV collider (green) will be able to provide a sufficient event rate for the A → HZ → τ τ channel to significantly extend the reach towards higher masses m H > 2m t , despite the suppressed branching fraction for H → τ τ . Comparing both benchmark planes, the reach for BP-A is slightly reduced compared to BP-B due to the suppressed branching fraction for the A → HZ in the presence of the additional decay channel A → H ± W . The A → HZ → bb channel is limited by systematic errors, resulting in a significantly weakened sensitivity, and is therefore not shown in Fig. 7. Scenarios with larger Higgs masses m H can be probed with the decay channel A → HZ → tt . We focus on the case of hadronically decaying top quarks, which can be identified using top tagging techniques, and present the reach at a 100 TeV hadron collider (magenta). The sensitivity is weakened in regions with lower Higgs masses m H 600 GeV in which the top quarks will no longer have sufficient transverse momentum (p T,t ∼ (m H − 2m t )/2) to exceed the top tagging threshold (p T,t > 200 GeV). As before, the reach in BP-A is reduced relative to BP-B due to the lower branching fraction for the decay A → HZ.
In addition to the neutral Higgs channel A → HZ, hierarchical 2HDMs can also be probed via exotic Higgs decays involving charged Higgs bosons. BP-A permits the additional exotic Higgs decay channel A → H ± W . Above the top threshold, the charged Higgs decays predominantly into H ± → tb. Again we focus on subsequent hadronic top decays, which permit the use of top tagging techniques, and obtain the projected sensitivity at a 100 TeV collider (orange). For smaller charged Higgs masses (m H ± 400 GeV), the sensitivity of this search channel is limited by the efficiency of the hadronic top-tagging due to smaller typical transverse momenta p T,t ∼ (m H ± − m t )/2. Note that the slightly larger typical p T,t in H ± → tb decays compared to H → tt decays results in a mildly extended reach towards lower masses compared to the A → HZ → tt channel.
The exotic decay of a charged Higgs boson H ± → HW is permitted only in the mass hierarchy of BP-B. While searches for this channel at the LHC suffer from a low charged Higgs production rate, the production cross section increases significantly towards higher energies. We obtain the projected sensitivity at a 100 TeV hadron collider (yellow) considering the neutral Higgs decay H → τ τ . Below the H → tt threshold, this channel provides 5-σ discovery at a future 100 TeV collider, which is comparable with A → HZ → τ τ channel.
As discussed in Sec. 2.4, unitarity disfavors large mass splittings m A −m H at large Higgs masses m A . This constraint is represented by the hatched region in Fig. 7. In particular, unitarity constrains a larger region of parameter space for BP-A than for BP-B, imposing upper bounds on the mass splittings of 5(m 2 A − m 2 H ) < 8πv 2 and 3(m 2 A − m 2 H ) < 8πv 2 , respectively.
To indicate the importance of exotic Higgs decays relative to the conventional Higgs decays, we also show branching fraction for exotic Higgs decays of the heavy pseudoscalar A as black contours in Fig. 7. The dotted, solid, and dashed black contours correspond to branching fractions of 20%, 50%, and 90%, respectively. We can see that a future 100 TeV hadron collider will be able to probe the entire region of the Type-II 2HDM parameter space that survives current theoretical and experimental constraints with exotic branching fraction 20% using the combination of all viable heavy Higgs exotic decay channels.

Conclusion
While most direct searches for an BSM Higgs sector focus on the conventional decays of the corresponding Higgs bosons, additional exotic decays of these states can arise if the BSM Higgs sector is hierarchical. These exotic decays include the decay of a heavy Higgs to two lighter Higgses, or to a lighter Higgs and a SM gauge boson. The presence of those exotic decay channels weaken the bounds of conventional searches, but also open up new complementary search channels.
In this paper, we studied the sensitivity of the LHC, HL-LHC and s 100 TeV pp collider to exotic Higgs decays in Type-II 2HDMs. As discussed in Sec. 2, theoretical considerations such as unitarity and vacuum stability and experimental limits, e.g. from electroweak precision measurements, severely constrain the parameter space of hierarchical 2HDMs. Besides the fully degenerate case m H ≈ m A ≈ m H ± , there are two benchmark planes that are viable under the alignment limit: A 100 TeV pp collider provides the opportunity to probe exotic decays of heavy Higgses with top quarks in the final state. Top quarks originating from the decay of a heavy Higgs are typically boosted, permitting the use of top tagging techniques to identify them. This allows us to take advantage of the large decay rates of heavy Higgses into top quarks while also getting a handle on QCD backgrounds.
To obtain the projected reach of the considered exotic Higgs decay channels, we perform a multivariate analysis using boosted decision tree classifiers which are trained to distinguish between the signal events and the SM background events. We find that the best sensitivity is provided by the exotic decay channel A → HZ due to its clean final state, and hence we term it the golden channel. Regions of parameter space with low values of m H (m H < 2m t ) and large values of tan β can efficiently be probed with the final states bb and τ τ , where the τ τ channel has a better reach compared to bb channel due to the significantly lower backgrounds. For moderate mass splittings (m A − m H = 200 GeV) and large values of tan β (> 10), a 100 TeV pp collider can discover (at 5σ) and exclude (at 95% C.L.) Higgs masses up to m A ≈ 3 TeV and 4 TeV, respectively. In the low tan β region above the top-pair threshold, the tt channel is complementary to τ τ , extending the reach to about m A ≈ 1.2 TeV (2 TeV) for discovery (exclusion).
Hierarchical 2HDMs can further be probed via exotic decay channels involving the charged Higgs boson. In the mass hierarchy corresponding to BP-A, the exotic decay channel A → H ± W is kinematically open. Using the dominant charged Higgs decay mode H ± → tb, a 100 TeV collider can exclude Higgs masses up to m A ≈ 1.6 TeV at large tan β (≈ 50) and about m A ≈ 1.3 TeV at small tan β (≈ 1) for a mass splitting of m A − m H = 200 GeV. In BP-B, exotic decays of the charged Higgs H ± → HW become kinematically permissible. We analyze this decay considering tbH ± associated charged Higgs production and the subsequent decay of the neutral Higgs H → τ τ , which permits for a same-sign di-lepton signature. For moderate mass splittings (m A − m H = 200 GeV) and values of tan β (≈ 10), a 100 TeV pp collider can discover (exclude) Higgs masses up to m H ± ≈ 1.7 TeV and 2.4 TeV, respectively. The channel H → tt could provide additional reach at low values of tan β above the top pair threshold [64].
Combining all the aforementioned exotic decay channels, we present the reach in the benchmark planes BP-A and BP-B for tan β = 1.5 in Fig. 7. All three channels complement each other nicely: final states with τ s prove to be the most sensitive channels for regions with relatively low values of m A , and, as might be expected, final states with tops are useful above the top threshold. We find that these exotic Higgs decay channels can probe the entire parameter space in which the exotic decay branching fraction is more than 20%. Additionally, if a future 100 TeV collider observes the A → HZ channel, it would imply the existence of additional exotic decay channels involving the charged Higgs, which will be observable in many parts of the parameter space.
While most of the recent searches for additional Higgs bosons have focused on conventional decay channels, searches using exotic decay channels have just started [11,12]. At a possible high energy future hadron collider, both the exclusion and the discovery reach for non-SM Higgses will be greatly enhanced compared to that of the LHC. The discovery of a non-SM heavy Higgs would serve as unambiguous evidence for new physics beyond the SM and could also provide valuable insights into mechanism underlying electroweak symmetry breaking.
selection cuts for detector reconstruction from the Delphes cards listed above: LHC/HL-LHC: p T, > 10 GeV, p T,j/b/τ > 20 GeV, ∆R > 0.5, |η | < 2.5, |η j | < 5.0, |η b/τ | < 2.5 100 TeV: p T, > 20 GeV, p T,j/b/τ > 50 GeV, ∆R > 0.3, |η | < 6.0, |η j | < 6.0, |η b/τ | < 6.0 where ∆R is the angular distance between any two objects. The reconstructed-level events from Delphes are filtered through a series of trigger and identification cuts (described in sections 3.2, 4.2, and 5.2), after which a set of features were collected for each simulated collision event to serve as inputs to gradient boosted decision tree (BDT) classifiers [68] implemented in TMVA [69]. The set of input features included both low-level features such as the transverse momenta of individual particles, and physically-motivated high-level features such as the invariant masses of combinations of particle momenta. The events were then divided into training and test sets, and we trained our classifiers on the training sets with the following hyperparameters: • The number of trees was set to 1000.
• The maximum depth of each tree was set to 3.
• Bagging was employed, with the bagged sample fraction set to 0.6.
• The Gini index was used as the separation criterion for node splitting.
The classifiers were then used to compute the BDT response value for signal and background events in the test set. We then scanned across a range of response values to determine the optimal cutoff with corresponding values of the total number of leftover signal (s) and background (b) events that resulted in the greatest discovery and exclusion significance. The values of s and b were obtained by multiplying their respective crosssections by the integrated luminosity, which was taken to be 300 fb −1 for the LHC, and 3000 fb −1 for the HL-LHC and the 100 TeV collider.
Generating a large enough number of Monte Carlo events to estimate the backgrounds at a 100 TeV collider was a technically challenging task. For certain points in parameter space, a series of cuts could reduce the number of expected background events to zero. However, in such cases, we artificially set a minimum three background events, i.e. b = 3, to ensure that our significance estimates are not overly optimistic.
To estimate the median expected discovery and exclusion significances, Z disc and Z excl , we follow [70][71][72] and use the following expressions: Here is the relative systematic uncertainty of the background rate. In the special case of vanishing systematic uncertainty → 0 these expressions simplify to In the limit of a large number of background events, b s, these expressions further simplify to the well known Gaussian approximations Z disc ≈ s/ √ b and Z excl ≈ s/ √ s + b. In this work we choose a systematic uncertainty of = 10% for both the LHC and the 100 TeV collider. We define regions with Z disc ≥ 5 as discoverable regions, and regions with Z excl ≤ 1.645 as regions that can be excluded at 95% CL.

B Simulation of Top-Tagging
When an energetic top quark decays hadronically, its decay products are collimated and form a big jet, often called a fat jet. The size of a top-initiated fat jet is given by R ∼ 2m t /p T,t , which implies that only boosted top quarks with p T > 250 GeV will be able to form a fat jet of size R < 1.5. While top-initiated fat jets show a characteristic substructure with subjets corresponding to the individual top decay products, such features are not present in QCD jets. Top-taggers are tools that analyze the fat jet's substructure to distinguish top-initiated from QCD initiated fat jets. Many ideas and techniques have been developed within the last year: QCD-based taggers like the HEPTopTagger [22][23][24] or the Johns Hopkins Tagger [25], Event-shape based tagger like N-subjettiness [26] or template-overlap method based taggers like the TemplateTagger [73]. A (not so recent) review about top tagging can be found in [74].
While most of the early taggers rely on only one analysis strategy, the more modern top taggers combine different approaches using machine learning tools. Examples include the HEPTopTagger Version-2 [75], the Deep-Top Tagger [27] (focusing on low p T ), and the Deep Neural Network Tagger [76] (same idea, focusing on high p T ). A recent summary comparing modern top tagging approaches has been published by CMS [61].
However, these techniques are usually computationally intensive, making them impractical for exploratory phenomenological studies such as this one. For this reason, we use a parametric approach, implementing a Delphes top-tagging module inspired by the built-in b-tagging module. We first reconstruct all fat jets with the size of R = 1.5 using the Cambridge-Aachen algorithm [77] as implemented in FastJet 3 [78]. We then assert that a fat jet is top quark initiated if a parton-level top quark is found within a cone with a radius R = 0.8 (we find that varying R between 0.8 and 1.5 will not affect the results). Leptonically-decaying top quarks are rejected by vetoing fat jets with leptons in the jet cone. Once a fat jet is determined to be top-initiated, we apply a top-tagging efficiency t for each of these fat jets. For QCD initiated fat jets, a misidentification rate j is applied.
In Fig. 8 we show the top-tagging rate (left) and QCD-jet mis-tagging rate (right) as adapted from Fig. 10 in the CMS study [61]. As representative examples we show the performance of the HEPTopTagger V2 [75] and SoftDrop [79] in combination with groomed N-subjettiness and b-tagging. Both taggers have similar tagging and mis-tagging rates   Figure 8. Top-tagging efficiencies (left) and QCD-jet mis-tagging rate (right) for the HEPTopTagger (red) and SoftDrop (green) as adapted from the CMS study [61]. The analytic parameterization used in this study is shown as a solid black line.
which are roughly independent of number of pile-up vertices. We parameterize their performance using an analytic form for top-tagging efficiency t and QCD-jet mis-identification rate j and obtain [17] ATLAS Collaboration, M. Aaboud et al., Search for charged Higgs bosons decaying via H ± → τ ± ν τ in the τ +jets and τ +lepton final states with 36 fb −1 of pp collision data recorded at √ s = 13 TeV with the ATLAS experiment, arXiv:1807.07915.