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). 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 quickly dominate those
of the conventional decay modes to SM particles. In this study, we focus on the
prospects of probing Type-II 2HDMs at the LHC and a future 100 TeV

Article funded by SCOAP3

m_{H}=m_{H^\pm}$) with $A\rightarrow HZ/H^\pm W^\mp$ and \bpb~($m_{A}=m_{H^\pm}>m_{H}$) with $A\rightarrow HZ$, $H^\pm\rightarrow H W^\pm$. 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~\cite{fccplan,Benedikt-ml-2651300} and the Super proton-proton Collider (SppC) in China~\cite{CEPC-SPPCStudyGroup-ml-2015csa}. 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~\cite{Plehn-ml-2010st,Plehn-ml-2011sj,Kling-ml-2012up,Kaplan-ml-2008ie,Thaler-ml-2011gf,Kasieczka-ml-2017nvn}. 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 \emph{pp} collider: \begin{equation}\begin{aligned} \textbf{LHC:}~\mathcal{L}=300\,\ifb, \quad \textbf{HL-LHC:}~\mathcal{L}=3\,\iab, \quad \textbf{100\,TeV:}~\mathcal{L}=3\,\iab, \quad \end{aligned}\end{equation} combining all the viable exotic decay channels. We perform a detailed collider analysis to obtain the 95\% C.L. exclusion limits as well as 5$\sigma$ discovery reach for benchmark planes \bpa~and \bpb. In recent years, multivariate analysis techniques such as neural networks~\cite{Aad-ml-2012tfa}, boosted decision trees (BDT)~\cite{Chatrchyan-ml-2012xdj}, the Matrix Element Method~\cite{ Kondo-ml-1988yd,Gainer-ml-2013iya} and Information Geometry~\cite{Brehmer-ml-2016nyr,Brehmer-ml-2017lrt} 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 section~\ref{sec:2hdm}, we present a brief review of hierarchical 2HDMs and introduce the benchmark planes \bpa{} and \bpb{}. We also discuss the prospects of the conventional Higgs search channels. In section~\ref{sec:HAZ}, we study the channels $A/H\rightarrow HZ/AZ$ and explore their reach at the LHC, HL-LHC, as well as a 100\,TeV $pp$ collider. In particular, we study both the $bb\ell\ell$ and $\tau\tau\ell\ell$ states as well as the $tt\ell\ell$ final state using top tagging techniques to identify boosted top quarks in the final state. In section~\ref{sec:HCW}, we present the analysis for the $H\rightarrow H^\pm W^\mp$ channel. In section~\ref{sec:CHW}, we explore the discovery potential for charged Higgses via the $H^\pm \rightarrow HW^\pm$ channel. In section~\ref{sec:reach}, we present the combined reach in 2HDM parameter space obtained with these channels at the LHC and a future 100\,TeV $pp$ collider. In section~\ref{sec:conclusion}, we conclude. Appendix~\ref{sec:method} and appendix~\ref{sec:toptagging} describe the methodology used for our collider analysis and top tagging simulation, respectively. ]]>

0 , \quad \text{and}\quad \mh^2+\mA^2-\mH^2 >0 \, . \label{eq:stability} \end{aligned}\end{equation} This implies that for $m_H > m_{A, H^\pm}$, the mass splittings between the heavy CP-even Higgs \emph{H} and the other heavy scalars \emph{A} and $H^{\pm}$ have to be small, such that the decays of $H$ into the \emph{AZ, AA,} $H^+ H^{-}$ and $H^\pm W^{\mp}$ final states are not kinematically allowed. \item[Tree-level unitarity.] Requiring tree-level unitarity of the scattering matrix in the 2HDM scalar sector~\cite{Ginzburg-ml-2005dt} imposes the following additional mass constraints: {\rdmathspace \begin{align} \hspace{-20pt}| \mH^2 - \mA^2 | &< 8\pi v^2 ,& |3\mH^2 + \mA^2 - 4\mC^2| &< 8\pi v^2 , & | \mH^2 + \mA^2 - 2\mC^2| &< 8\pi v^2 , \nonumber\\ \hspace{-20pt}|3\mH^2 - \mA^2 - 2\mC^2| &< 8\pi v^2 , & |3\mH^2 - 5\mA^2 + 2\mC^2| &< 8\pi v^2 . \end{align}}\relax Here we have ignored sub-leading terms proportional to $\mh^2$. Note that these constraints are independent of the value of $\tbeta$. \item[Electroweak precision measurements.] Measurements of electroweak precision observables impose strong constraints on the 2HDM mass spectrum~\cite{Haller-ml-2018nnx}. In particular, these constraints require the charged scalar mass to be close to the mass of one of the heavy neutral scalars. \begin{equation}\begin{aligned} \mC \approx \mH \quad \text{or} \quad \mC\approx \mA. \end{aligned}\end{equation} \item[Flavour constraints.] Various flavor measurements~\cite{Amhis-ml-2016xyh, Haller-ml-2018nnx} 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 $b \to s \gamma$ and $B^+ \to\tau \nu$, which disfavor $\mC < 580\,\gev$~\cite{Misiak-ml-2017bgg} and large values of $\tbeta$ respectively. Flavor constraints, however, can be alleviated with contributions from other sectors of new physics models~\cite{Han-ml-2013mga}. In this paper, we focus on the direct collider reach of heavy Higgses without imposing the flavor constraints. \item[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~\cite{Abbiendi-ml-2013hk}, LEP searches for $AH$ production constrain the sum of the masses $m_H + m_A > 209\,\gev$~\cite{Schael-ml-2006cr}. LEP bounds on single neutral Higgs production do not apply in the alignment limit, due to their vanishing coupling to the gauge bosons. Note that limits from searches for conventional decays are significantly weakened once exotic Higgs decay channels are kinematically allowed. The ATLAS~\cite{Aaboud-ml-2018eoy} and CMS~\cite{Khachatryan-ml-2016are} searches for the exotic decay mode $A/H \to HZ/AZ$ constrain hierarchical 2HDMs with low scalar masses. \sloppy Additional constraints for charged Higgs bosons are derived from experimental searches at the LHC via the $H^\pm \to \tau\nu$ decay mode. A light charged scalar with $\mC< m_t$ is mostly excluded by the non-observation of the decay $t\to H^+ b$, although these limits can be weakened at low $t_\beta$ by the existence of exotic decay modes~\cite{Kling-ml-2015uba}. A heavy charged scalar is only weakly constrained at very large $\tbeta$~\cite{Aaboud-ml-2018cwk,Aaboud-ml-2018gjj,CMS-PAS-HIG-16-031}. For a detailed discussion of constraints on the charged Higgs, see~\cite{Akeroyd-ml-2016ymd}. \fussy \end{description} ]]>

\mH=\mC$ \looseness=-1 If the charged Higgs $H^\pm$ is mass-degenerate with the heavy CP-even Higgs \emph{H}, only the exotic decays of the pseudoscalar \emph{A} are allowed $\left(A\to H^\pm W^\mp/HZ\right)$. Requiring unitarity additionally imposes an upper bound on the mass splitting: $5(\mA^2-\mH^2)\!<\!8\pi v^2$. \item[BP-B:] $\mA=\mC>\mH$ If the charged Higgs $H^\pm$ is mass-degenerate with the pseudoscalar \emph{A}, only the exotic decays into the CP-even Higgs \emph{H} are allowed: $H^\pm \to HW^\pm$ and $A\to HZ$. In this case, unitarity imposes an upper bound on the mass splitting: $3(\mA^2-\mH^2)<8\pi v^2$. \end{description} \begin{figure} \centering \includegraphics[width=0.48\textwidth]{Figs/Constraints_1.pdf}\hfill \includegraphics[width=0.48\textwidth]{Figs/Constraints_2.pdf} ]]>

15\,\gev$, this implies a background rate of 9.7 pb and 350 pb at 14\,TeV and 100\,TeV, respectively. \looseness=-1 Both the signal and the background process are simulated using \textsc{MadGraph~5}~\cite{Alwall-ml-2014hca}, interfaced with \textsc{Pythia}~\cite{Sjostrand-ml-2006za,Sjostrand-ml-2014zea} and \textsc{Delphes 3}~\cite{deFavereau-ml-2013fsa} for detector simulation. Each signal benchmark is simulated with the correct width and branching fractions as obtained from \textsc{2hdmc}~\cite{Eriksson-ml-2009ws}. We then select events with at least two same-flavor leptons passing the trigger requirements $p_{T,\ell_1} > 20\,\gev$ and $p_{T,\ell_2}>10\,\gev$ and two $b$-tagged jets with $p_{T,b}>25\,\gev$.\footnote{Stronger selections cuts are applied at a 100\,TeV collider for all the search channels (see appendix~\ref{sec:method}).} For these events, we construct a set of observables which is then used to train and test a boosted decision tree classifier. For the $bb\ell\ell$ channel, the set of observables includes: \begin{itemize} \tightlist \item the transverse momenta of the leading \emph{b}-tagged jet ($p_{T,b_1}$), the sub-leading \emph{b}-tagged jet ($p_{T,b_2}$), the leading lepton ($p_{T,\ell_1}$) and the sub-leading lepton ($p_{T,\ell_2}$) \item the invariant mass of the leptons ($m_{\ell\ell}$), the jets ($m_{bb}$) and the lepton-jet system ($m_{bb\ell\ell}$) \item the scalar sum of all the transverse energy ($H_T$) and the missing transverse energy ($\met$). \end{itemize} 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.\footnote{The typical systematic error at the LHC is between 20\% and 50\%~\cite{Aaboud-ml-2018eoy}. However, the largest contributions arise from simulation statistics and background modeling which could be improved greatly at the future colliders, while theory uncertainties are below 10\%. We adopted a value of 10\% for the systematic uncertainty to take into account the theory uncertainties.} More details of our analysis can be found in appendix~\ref{sec:method}. \boldmath ]]>

100\,\gev$. Note that this includes both resonant production via \emph{ZZ} and \emph{hZ} dominating at small masses $m_{\tau\tau}$ as well as off-shell contributions dominating at large $m_{\tau\tau}$. Sub-dominant backgrounds, for example from \emph{ZWW} production, were found to be negligible. For this analysis, we select events with two same-flavor leptons with $p_{T,\ell_1} > 20\,\gev$ and $p_{T,\ell_2}>10\,\gev$ and two $\tau$-tagged jets with $p_{T,\tau}>25\,\gev$ and consider the following list of observables: \begin{itemize} \tightlist \item the transverse momenta of leading $\tau$-tagged jet ($p_{T,\tau_1}$), the sub-leading $\tau$-tagged jet ($p_{T,\tau_2}$), the leading lepton ($p_{T,\ell_1}$) and the sub leading lepton ($p_{T,\ell_2}$) \item the invariant mass of the leptons ($m_{\ell\ell}$), the jets $(m_{\tau\tau})$ and the lepton-jet system ($m_{\tau\tau\ell\ell}$) \item the scalar sum of all the transverse energy ($H_T$) and the missing transverse energy ($\met$). \end{itemize} \boldmath ]]>

20\,\gev$ and $p_{T,\ell_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: \begin{itemize} \tightlist \item the transverse momenta of the leading top-tagged jet ($p_{T,t_1}$), the sub-leading top-tagged jet ($p_{T,t_2}$), the leading lepton ($p_{T,\ell_1}$) and the sub-leading lepton ($p_{T,\ell_2}$) \item the invariant mass of the leptons ($m_{\ell\ell}$), the jets $(m_{tt})$ and the lepton-jet system ($m_{tt\ell\ell}$) \item the scalar sum of all the transverse energy ($H_T$) and the missing transverse energy ($\met$). \end{itemize} ]]>

m_H$ (left panels) and \bpb~$m_A>m_{H^\pm} = m_H$ (right panels) at the LHC, HL-LHC and a 100\,TeV hadron collider for a fixed mass splitting between the heavy neutral Higgses of $\Delta m = m_A-m_H=200\,\gev$. The top panels show the reach for the $bb\ell\ell$ and $t_ht_h\ell\ell$ final states while the bottom panels show the reach for the $\tau_h\tau_h\ell\ell$ final state. At low values of $\tan\beta$, both the $H \to bb$ and $H \to \tau\tau$ channels are particularly sensitive at masses below the top threshold, $m_A = 2m_t+\Delta m\approx 550\,\gev$, while the branching fractions for these decays are strongly suppressed at larger masses due to the opening up of the $H \to tt$ channel. Increasing the luminosity to $3\,\iab$ at HL-LHC or a 100\,TeV collider does not enhance the reach significantly. At large values of $\tan\beta$, the decay $H\to tt$ is strongly suppressed and so the $H \to bb$ and $H \to \tau\tau$ channels retain sensitivity for large masses. The $bb\ell\ell$ 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 $\tau\tau\ell\ell$ channel has a much cleaner signature and therefore is mainly limited by statistical uncertainty and hence superior in sensitivity to the $bb\ell\ell$ channel. At $\tan\beta=50$ the exclusion reach of the $\tau\tau\ell\ell$ channel extends up to $\sim 1\,\tev$ at the LHC, $\sim 1.5\,\tev$ at the HL-LHC and $\sim 3\,\tev$ 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 $H \to t_h t_h$ channel is able to probe scenarios with larger Higgs masses in the range $700\,\gev \lesssim m_A \lesssim 2\,\tev$ for small values of $\tan\beta \lesssim 3$. For smaller masses, the sensitivity of this search is limited by the efficiency of the hadronic top-tagging due to smaller typical transverse momenta. In comparison, the conventional search channel, $ttH/A \to tttt$~\cite{Craig-ml-2016ygr}, is more sensitive to heavy Higgs mass regions at small $\tan\beta$ due to its larger production cross sections, smaller dominant irreducible SM backgrounds, and certain discriminative kinematic features of $ttH/A \to tttt$ signal. At larger values of $\tan\beta$, 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 \emph{HZ} or $H^{\pm} W^{\mp}$ in \bpa, only the $A\to HZ$ channel is available in \bpb. Thus, the discovery and exclusion reach attainable in \bpb~is greater than in \bpa. ]]>

\mC + m_W$}), the additional decay channel $A \to H^\pm W^\mp$ opens up. This happens in scenarios such as \bpa, where $\mH=\mC<\mA$. In this case the branching fraction for the exotic decay mode $A\to H^\pm W^\mp$ is typically twice as large as that of the $A \to HZ$ decay mode which can be understood from the Goldstone equivalence theorem. The leptonic decay of the \emph{W}-boson provides a clean experimental signature and permits the use of a lepton trigger, which makes the decay mode $A \to H^\pm W^\mp$ a promising exotic decay channel to explore. \fussy If the charged Higgs is light ($\mC \lesssim m_t$), it will dominantly decay into either $\tau\nu$ at high $t_\beta$ or $cs$ at low values of $t_\beta$. However, such a light charged Higgs boson is excluded by the non-observation of the top decay $t \to H^+ b$~\cite{Aaboud-ml-2018gjj}. If the charged Higgs is heavier ($\mC > m_t$), the $H^\pm \to tb$ decay mode opens up and becomes dominant over the entire phase space. In this case the exotic decay channel $A \to H^\pm W \to tbW$ 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 ($\mC \sim \text{a few}~100\,\gev$), 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 ($\mC \gtrsim 1\,\tev$), 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: \begin{equation}\begin{aligned} pp \to A \to H^\pm W^\mp \to t_h b\ \ell\nu. \end{aligned}\end{equation} ]]>

250\,\gev$. Additional backgrounds arising from the production of a leptonically decaying \emph{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, $\sigma(W^\pm+j\to\ell^\pm\nu+j) = 0.43\,\nb$~\cite{Mangano-ml-2016jyj} and are further reduced upon including the mis-tagging rate for QCD jets $\epsilon_j \sim 10^{-3}$ (see appendix~\ref{sec:toptagging}). Similarly, backgrounds from single top production were found to be negligible. We select events containing one lepton with $p_{T,\ell_1} > 20\,\gev$, at least one top-tagged jet with $p_{T, t_1} > 200\,\gev$, at least one \emph{b}-tagged jet with $p_{T, b} > 50\,\gev$ and a small amount of missing transverse energy, $\met > 20\,\gev$. The following set of observables is then used to train and test a BDT classifier: \begin{itemize} \tightlist \item the transverse momenta of the leading top-tagged jet ($p_{T, t_1}$), the leading \emph{b}-tagged jet ($p_{T,b_1}$) and the leading lepton ($p_{T, \ell_1}$). \item the invariant masses of the jets ($m_{tb}$) and the lepton-jet system ($m_{tb\ell\nu}$), and the angular separation of the jets ($\Delta R_{tb}$). \item the scalar sum of the transverse energy ($H_T$) and the missing transverse energy ($\met$). \end{itemize} To reconstruct the mass of the heavy neutral Higgs ($m_{tb\ell\nu}$), we reconstruct the neutrino momentum from $\met$ following the method shown in ref.~\cite{Aad-ml-2015eia}. ]]>

\mH + m_W\right)$. As discussed in section~\ref{sec:2hdm-xs}, the charged Higgs is mainly produced in association with a top and bottom quark $\left(pp \to H^\pm tb\right)$, which leads to a busy final state topology $\left(H^\pm tb \to HW^+W^-bb\right)$. If the daughter Higgs \emph{H} is light $\left(\mH<2m_t\right)$, it will dominantly decay into pairs of \emph{b}-quarks and $\tau$ leptons with branching fractions of $\sim 90\%$ and $\sim 10\%$ respectively. Despite its larger branching fraction, the $H \to bb$ decay channel remains experimentally challenging, due to the large hadronic SM backgrounds associated with it.\footnote{The authors of~\cite{Li-ml-2016umm} have shown that a jet substructure analysis of the pseudoscalar and \emph{W} jets can be used to significantly reduce hadronic backgrounds and provide some reach for low values of $m_H$ and $\tan\beta$.} In contrast, the $H\to\tau \tau$ decay channel can lead to a same-sign di-lepton signature where one lepton arises from a leptonic $\tau$-decay and the other from a leptonic \emph{W}-decay. As shown in~\cite{Coleppa-ml-2014cca}, this signature allows for the effective suppression of SM backgrounds --- in particular, the background from top pair production. If the daughter Higgs is heavier $\left(\mH > 2 m_t\right)$, 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~\cite{Patrick-ml-2017ele} 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: \begin{equation}\begin{aligned} gg \to H^\pm tb \to H~W^+W^-~bb \to \tau\tau~W^+W^-~bb. \end{aligned}\end{equation} with a focus on the same-sign di-lepton final state. ]]>

2 m_t$, despite the suppressed branching fraction for $H\to\tau\tau$. Comparing both benchmark planes, the reach for \bpa{} is slightly reduced compared to \bpb{} due to the suppressed branching fraction for the $A \to HZ$ in the presence of the additional decay channel $A \to H^\pm W$. The $A \to HZ \to bb\ell\ell$ channel is limited by systematic errors, resulting in a significantly weakened sensitivity, and is therefore not shown in figure~\ref{fig:BPA-B-tb1.5}. Scenarios with larger Higgs masses $\mH$ can be probed with the decay channel $A \to HZ \to tt\ell\ell$. 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 $\mH\lesssim 600\,\gev$ in which the top quarks will no longer have sufficient transverse momentum $\left(p_{T,t} \sim (m_H-2m_t)/2\right)$ to exceed the top tagging threshold $\left(p_{T,t}>200\,\gev\right)$. As before, the reach in \bpa{} is reduced relative to \bpb{} due to the lower branching fraction for the decay $A \to HZ$. In addition to the neutral Higgs channel $A \to HZ$, hierarchical 2HDMs can also be probed via exotic Higgs decays involving charged Higgs bosons. \bpa~ permits the additional exotic Higgs decay channel $A \to H^\pm W$. Above the top threshold, the charged Higgs decays predominantly into $H^\pm \to tb$. 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 $\left(\mC \lesssim 400\,\gev\right)$, the sensitivity of this search channel is limited by the efficiency of the hadronic top-tagging due to smaller typical transverse momenta $p_{T,t}\sim (\mC-m_t)/2$. Note that the slightly larger typical $p_{T,t}$ in $H^\pm \to tb$ decays compared to $H \to tt$ decays results in a mildly extended reach towards lower masses compared to the $A \to HZ \to tt\ell\ell$ channel. \looseness=-1 The exotic decay of a charged Higgs boson $H^\pm \to H W$ is permitted only in the mass hierarchy of \bpb. 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 $H \to \tau\tau$. Below the $H\rightarrow tt$ threshold, this channel provides 5-$\sigma$ discovery at a future 100\,TeV collider, which is comparable with \mbox{$A\to HZ\to\tau\tau\ell\ell$} channel. As discussed in section~\ref{sec:2hdm-bmp}, unitarity disfavors large mass splittings $\mA-\mH$ at large Higgs masses $\mA$. This constraint is represented by the hatched region in figure~\ref{fig:BPA-B-tb1.5}. In particular, unitarity constrains a larger region of parameter space for \bpa{} than for \bpb{}, imposing upper bounds on the mass splittings of $5(\mA^2-\mH^2)<8\pi v^2$ and \mbox{$3(\mA^2-\mH^2)<8\pi v^2$}, 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 \emph{A} as black contours in figure~\ref{fig:BPA-B-tb1.5}. 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 most regions of the Type-II 2HDM parameter space that survive current theoretical and experimental constraints with sizable exotic branching fractions using the combination of all the viable heavy Higgs exotic decay channels. ]]>

m_H=m_{H^\pm}$) with $A\rightarrow HZ/H^\pm W^\mp$ and \bpb~($m_{A}=m_{H^\pm}>m_{H}$) with $A\rightarrow HZ$, $H^\pm\rightarrow H W^\pm$. 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 $A \to HZ$ due to its clean final state. Regions of parameter space with low values of $\mH$ $\left(\mH<2m_t\right)$ and large values of $\tan\beta$ can efficiently be probed with the final states $ bb\ell\ell$ and $\tau\tau\ell\ell$, where the $\tau\tau\ell\ell$ channel has a better reach compared to $bb\ell\ell$ channel due to the significantly lower backgrounds. For moderate mass splittings $\left(\mA-\mH=200\,\gev\right)$ and large values of $\tan\beta$ $\left(>10\right)$, a 100\,TeV \emph{pp} collider can discover (at $5\sigma$) and exclude (at 95\% C.L.) Higgs masses up to $\mA \approx 3\,\tev$ and $4\,\tev$, respectively. In the low $\tan\beta$ region above the top-pair threshold, the $tt\ell\ell$ channel is complementary to $\tau\tau\ell\ell$, extending the reach to about $\mA \approx 1.2\,\tev$ ($2\,\tev$) for discovery (exclusion). Hierarchical 2HDMs can further be probed via exotic decay channels involving the charged Higgs boson. In the mass hierarchy corresponding to \bpa{}, the exotic decay channel $A \to H^\pm W$ is kinematically open. Using the dominant charged Higgs decay mode $H^\pm \to tb$, a 100\,TeV collider can exclude Higgs masses up to $\mA \approx 1.6\,\tev$ at large $\tan\beta$ $\left(\approx 50\right)$ and about $\mA \approx 1.3\,\tev$ at small $\tan\beta$ $\left(\approx 1\right)$ for a mass splitting of $\mA-\mH=200\,\gev$. In \bpb{}, exotic decays of the charged Higgs $H^\pm \rightarrow H W$ become kinematically permissible. We analyze this decay considering $tbH^\pm$ associated charged Higgs production and the subsequent decay of the neutral Higgs $H \to \tau\tau$, which permits for a same-sign di-lepton signature. For moderate mass splittings $\left(m_A - m_H=200\,\gev\right)$ and values of $\tan\beta$ $\left(\approx 10\right)$, a 100\,TeV $pp$ collider can discover (exclude) Higgs masses up to $\mC \approx 1.7\,\tev$ and $2.4\,\tev$, respectively. The channel $H\rightarrow tt$ could provide additional reach at low values of $\tan\beta$ above the top pair threshold~\cite{Patrick-ml-2017ele}. Combining all the aforementioned exotic decay channels, we present the reach in the benchmark planes \bpa{} and \bpb{} for $\tan\beta=1.5$ in figure~\ref{fig:BPA-B-tb1.5}. All three channels complement each other nicely: final states with $\tau$s prove to be the most sensitive channels for regions with relatively low values of $\mA$, and, as might be expected, final states with tops are useful above the top threshold. We find that these exotic decay channels can probe most of the parameter space in which their branching fraction is sizable, and are thus complementary to the conventional decay channels for heavy non-SM Higgses. Additionally, if a future 100\,TeV collider observes the $A \to HZ$ 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~\cite{Aaboud-ml-2018eoy, Khachatryan-ml-2016are}. 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. ]]>

&~10\,\gev, &p_{T,j/b/\tau}>&~20\,\gev, &\Delta R>&~0.5, \\ & &|\eta_{\ell}|<&~2.5, &|\eta_{j}|<&~5.0, &|\eta_{b/\tau}|<&~2.5 \\ \textbf{100\,TeV:} & &p_{T,\ell}>&~20\,\gev, &p_{T,j/b/\tau}>&~50\,\gev, &\Delta R>&~0.3, \\ & &|\eta_{\ell}|<&~6.0, &|\eta_{j}|<&~6.0, &|\eta_{b/\tau}|<&~6.0 \ \end{aligned}\end{equation} where $\Delta R$ is the angular distance between any two objects. The reconstructed-level events from \textsc{Delphes} are filtered through a series of trigger and identification cuts (described in sections~\ref{sec:golden_channel_analysis},~\ref{sec:charged_higgs_channel_analysis}, and~\ref{sec:exotic_charged_higgs_analysis}), after which a set of features were collected for each simulated collision event to serve as inputs to gradient boosted decision tree (BDT) classifiers~\cite{Yang-ml-2005nz} implemented in \textsc{TMVA}~\cite{Hocker-ml-2007ht}. 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: \begin{itemize} \tightlist \item The number of trees was set to 1000. \item The maximum depth of each tree was set to 3. \item Bagging was employed, with the bagged sample fraction set to 0.6. \item The Gini index was used as the separation criterion for node splitting. \end{itemize} 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 (\emph{s}) and background (\emph{b}) events that resulted in the greatest discovery and exclusion significance. The values of \emph{s} and \emph{b} were obtained by multiplying their respective cross-sections by the integrated luminosity, which was taken to be $300\,\ifb$ for the LHC, and $3000\,\ifb$ 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, $Z_\text{disc}$ and $Z_\text{excl}$, we follow~\cite{Kumar-ml-2015tna,Cowan-ml-2010af, Cowan-ml-2010js} and use the following expressions: {\rdmathspace \begin{equation}\begin{aligned} Z_\text{disc} &= \sqrt{2\left[(s+b)\ln\left(\frac{(s+b)(1+\epsilon^2 b)}{b+\epsilon^2 b(s+b)}\right) - \frac{1}{\epsilon^2 }\ln\left(1+\epsilon^2\frac{s}{1+\epsilon^2 b}\right)\right]} \\ Z_\text{excl} &=\sqrt{2\left[s-b\ln\left(\frac{b+s+x}{2b}\right) - \frac{1}{\epsilon^2 }\ln\left(\frac{b-s+x}{2b}\right) - \left(b+s-x\right)\left(1+\frac{1}{\epsilon^2 b}\right)\right]} \\ \text{with} \quad x&=\sqrt{(s+b)^2- 4 \epsilon^2 s b^2/(1+\epsilon^2 b)}. \end{aligned}\end{equation}}\relax Here $\epsilon$ is the relative systematic uncertainty of the background rate. In the special case of vanishing systematic uncertainty $\epsilon \to 0$ these expressions simplify to \begin{align} Z_\text{disc}^{\epsilon=0} = \sqrt{2[(s+b)\ln(1+s/b)-s]}, && Z_\text{excl}^{\epsilon=0} = \sqrt{2[s-b\ln(1+s/b)]} \end{align} In the limit of a large number of background events, $b \gg s$, these expressions further simplify to the well known Gaussian approximations $Z_\text{disc} \approx s/\sqrt{b}$ and $Z_\text{excl} \approx s/\sqrt{s+b}$. In this work we choose a systematic uncertainty of $\epsilon=10\%$ for both the LHC and the 100\,TeV collider. We define regions with $Z_\text{disc} \geq 5$ as discoverable regions, and regions with $Z_\text{excl} \leq 1.645$ as regions that can be excluded at 95\% CL. \pagebreak ]]>

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~\cite{Plehn-ml-2010st,Plehn-ml-2011sj,Kling-ml-2012up} or the Johns Hopkins Tagger~\cite{Kaplan-ml-2008ie}, Event-shape based tagger like N-subjettiness~\cite{Thaler-ml-2011gf} or template-overlap method based taggers like the TemplateTagger~\cite{Backovic-ml-2012jk}. A (not so recent) review about top tagging can be found in~\cite{Plehn-ml-2011tg}. \relax 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~\cite{Kasieczka-ml-2015jma}, the Deep-Top Tagger~\cite{Kasieczka-ml-2017nvn} (focusing on low $p_T$), and the Deep Neural Network Tagger~\cite{Pearkes-ml-2017hku} (same idea, focusing on high $p_T$). A recent summary comparing modern top tagging approaches has been published by CMS~\cite{CMS-ml-2016tvk}. However, these techniques are usually computationally intensive, making them impractical for exploratory phenomenological studies such as this one. For this reason, we use a \emph{parametric} approach, implementing a \textsc{Delphes} top-tagging module inspired by the built-in \emph{b}-tagging module. We first reconstruct all fat jets with the size of $R=1.5$ using the Cambridge-Aachen algorithm~\cite{Dokshitzer-ml-1997in} as implemented in \textsc{FastJet 3}~\cite{ Cacciari-ml-2011ma}. 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 $\epsilon_t$ for each of these fat jets. For QCD initiated fat jets, a misidentification rate $\epsilon_j$ is applied. \begin{figure}[t] \centering \includegraphics[width=0.48\textwidth]{Figs/TopTagging_Top.pdf}\hfill \includegraphics[width=0.48\textwidth]{Figs/TopTagging_BG.pdf} ]]>