Investigation of Charged Higgs Boson in the Bottom and Top Quark Decay Channel at the FCC-hh

After the recent discovery of a neutral Higgs boson with a mass about 125 GeV, we assess the extend of discovery potential of future circular hadron collider (FCC-hh) for a charged Higgs boson in the bottom and top quark decay channel. The charged Higgs boson can be produced through the pp → h−t + X process with a subsequent decay h− → bt̄ channel. This decay channel is particularly important for studying the charged Higgs boson heavier than the top quark. We consider an extension of the standard model Higgs sector, namely two Higgs doublet model (2HDM), and perform a dedicated signal significance analysis to test this channel for the FCC-hh running at the center of mass energy of 100 TeV and the integrated luminosity of 1 ab−1 (initial) and 30 ab−1 (ultimate). We find that an important part of the parameter spaces of two Higgs doublet model are examinable at the FCC-hh.


I. INTRODUCTION
The Higgs boson have been discovered by the ATLAS [9] and CMS [2] experiments at the CERN LHC in 2012. This discovery has motivated a lot of measurements to identify the nature of the discovered particle. We have elementary fermions (quarks and leptons) and bosons (vectors and scalar) within the standard model (SM) of particle physics. However, multiple scalars are predicted by some extensions of the standard model, such as two Higgs doublet model (2HDM) [3,4], and supersymmetry (SUSY) [5] (and references therein), to deal with some issues such as dark matter, hierarchy, etc.
At a center of mass energy of 13 TeV in proton proton collisions, the ATLAS and CMS Collaborations have performed several searches for charged Higgs bosons [6,7], where low values of tan β < 1 are excluded for a charged Higgs boson mass up to 160 GeV. The most stringent upper limit from ATLAS on σ(pp → h + t + X) × B(h + → τ + ν) and σ(pp → h + t + X) × B(h + → tb) at 95% CL is in the range 4.2-0.0025 pb and 9.6-0.01 pb for a charged Higgs boson mass in the range 90 − 2000 GeV [6] and 200-3000 GeV [8], respectively.

II. SIGNAL AND BACKGROUND
For the signal, we use the scalar potential and the Yukawa sector of the general 2HDM [5], in which the complex (pseudo) scalar doublets Φ j (j = 1, 2) can be parametrized as where v 1,2 are vacuum expectation values of two Higgs doublets satisfying v = v 2 1 + v 2 2 with v 246 GeV. The ratio of the vacuum expectation values is defined arXiv:2011.11105v1 [hep-ph] 22 Nov 2020 v 1 /v 2 = tan β as a free parameter. Two CP-even physical field can be written in terms of two neutral scalar fields and the CP-odd neutral field A 0 = −G 1 sin β + G 2 cos β and charged field h ± = −φ ± 1 sin β + φ ± 2 cos β. After electroweak symmetry breaking, five degrees of freedom become physical Higgs bosons (three neutral h 0 , H 0 , A 0 and two charged h + , h − ), while three degrees of freedom kept by Goldstone bosons (neutral G 0 and charged G + , G − ) to attribute massive longitudinal component of gauge fields (corresponding to neutral Z 0 and charged W + , W − bosons). The other independent parameters are the masses (m h 0 , m H 0 , m A , m h ± ) of the physical Higgs bosons in the alignment limit.
The cross section for signal process pp → h − t + X can be calculated at leading order integrating over parton distribution functions through the subprocess gb → h − t partonic cross section.
The limits of the integrals are defined as x imax = 1 and (x 1 x 2 ) min = s min /S (where √ S is the process center of mass energy of FCChh taken as 100 TeV). The partonic cross section for the subprocess σ(gb → h − t) can be calculated from the process kinematics and the matrix elements. The matrix element squared expressions (M 2→2 ) averaged over initial state (spins, colors) and summed over final state (spins, colors) for (2 → 2) subprocess g( (1) and the expression (M 1→2 ) for decay process (h − → bt) is given by where g e and g s are the electromagnetic coupling and strong coupling corresponding to U (1) Q and SU (3) C gauge groups, the s W is the sinus of Weinberg weak mixing angle, and V tb is the relevant CKM matrix element. The Mandelstam variables s = (p 1 + p 2 ) 2 , t = (p 1 − p 3 ) 2 and u = (p 1 − p 4 ) 2 are used to shorten the amplitude of the signal subprocess in Lorentz invariant form.
We generate the signal samples of the process pp → h − t + X followed by the decay mode h − → bt leading to an intermediate state of a pair of top quarks and a b-quark. We use Pythia 8 package [11] for the signal event generation, where the subprocess gb → h − t already exists in this publicly available software. The respective Feynman diagrams for the signal process are prsented in Fig. 1.
The decay chain, in general, ends with three possible channels depending on the decay channels of a pair of W bosons: (i) all hadronic mode (7 jets: 4 light jets and 3 b-jets), (ii) single lepton mode (1 charged lepton and missing transverse energy, 2 light jets and 3 b-jets), (iii) dilepton mode (2 oppositly charged leptons and missing transverse energy, 3 b-jets). We may generalize the final state by including different type of fermion particles (f i ) and b-jets Here, we focus on the final state including single lepton mode of the signal: 1 lepton + MET + 3 b-jet + 2 jets.
Signal events are generated with Pythia 8 within the FCC software (FCCSW) [10] for different model parameters: mass (m h − ≡ m H 0 ) in the range of (500 − 2000) GeV, ratio of the vacuum expectation values (tan β) in the range of (1 − 30), and a parameter cos(β − α) = 0 (alignment limit) which is relevant for H 0 V V , h 0 AZ and h 0 h ± W ∓ couplings. However, the background Les Houches events (LHE) are generated with MadGraph 5 [12]. For further hadronization and showering for signal and background events are performed through Pythia 8 within this software. A fast detector simulation is performed with Delphes 3 [13] for parametric card (FC-Chh.tcl) of an FCC-hh detector. Event selection is applied on those samples with Heppy [15]. Flat ntuples are produced with observables of interest and analyzed with Heppy. It reads events in FCC EDM format, and creates lists of objects adapted to an analysis in python. The gen-level and reco-level plots are produced with python scripts where Heppy writes a Root program [15] tree.
Background samples for the processes pp → tt, pp → ttb and pp → ttj are simulated using Delphes 3 with FCC-hh detector card. The main background is tt+jets, in particular tt+bjet in the most signal-sensitive regions.

III. ANALYSIS AND RESULTS
For the signal cross section calculation we have performed benchmarking of the parameter space of the model considered here, requiring the mass m h − to lie in the 500 GeV-2000 GeV range. We find signal cross sections (from Pythia 8 with generator level defaults) as shown in Table I, by taking tan β variable and setting cos(β − α) = 0. The bottom rows of Table I show the cross sections for relevant SM backgrounds obtained using MadGraph 5.
Both the signal and background samples are analysed with python scripts by reading Root trees. Events are selected as the presence of required number of objects in the final state. We deal with events including at least 5 jets (n jet ≥ 5) where there is at least two b-jets. In addition, we require one lepton (electron or muon) and a significant MET (focusing on 1l + M ET + 5jets). At the end of the analysis histograms are printed as figure files. The distributions of kinematical variables (p T of jets and leptons, η of jets and leptons) for the final state objects are presented in Fig. 2 and 3 for the signal events with mass m h − = 1000 GeV and m h − = 2000 GeV, respectively. In Fig. 4 and 5, the hadronic transverse energy (H T ) for jets, missing transverse energy (MET) and lepton (both electron (e) and electron+muon (e+mu)) kinematical distributions (p T and η) for signal with mass m h − = 1000 GeV and m h − = 2000 GeV, respectively.
The charged Higgs boson mass is reconstructed from one top (reconstructed from the hadronically decaying W boson and subleading b-jet) and the leading b-jet candidate. Further steps are followed as the isolation criteria for one electron or muon (initiated from the leptonically decaying W boson), rejection of events with additional muon or electron candidates, removal of electrons or muons if the are separated from the nearest jet by ∆R < 0.4. The cut flow for the analysis is shown in Table II.
Invariant mass distribution of four jets initiated from bottom (leading b-jet) and top quark are presented in Fig.  6 for charged Higgs boson signal with masses m h − = 500 GeV, m h − = 1000 GeV and m h − = 2000 GeV.
We calculate statistical significance (SS) from signal (N S ) and background (N B ) events within the interval Number of signal and background events and statistical significance for the integrated luminosity of L = 1 ab −1 (initial) and L = 30 ab −1 (ultimate) at FCC-hh are given in Table III.

IV. CONCLUSION
We have studied the charged Higgs boson (predicted by the 2HDM type-II or MSSM) and top quark associ-  ated production in proton-proton collisions at the FCChh collider. The single production of charged Higgs boson through pp → h − t + X process have been investigated in the mass range 500 GeV to 2000 GeV using multi-jets (at least 5 jets) final states with one electron or muon and missing transverse momentum. Using the relevant SM backgrounds from the lepton+jets final states, we obtain a significant coverage of the signal parameter space and distinguish the charged Higgs boson-top-bottom interaction for a mass up to 2 TeV for parameter tan β = 1 and tan β = 30 at an integrated luminosity of 30 ab −1 .
Other possible extensions of the Higgs sector can also be searched for a wide range of parameter space in high energy proton-proton collisions at the FCC-hh.