Searches for additional Higgs bosons in multi-top-quarks events at the LHC and the International Linear Collider

We study direct searches of additional Higgs bosons in multi-top-quarks events at the LHC Run-II, its luminosity upgraded version with 3000 fb$^{-1}$, and the International Linear Collider (ILC) with the collision energy of 1 TeV. Additional Higgs bosons are predicted in all kinds of extended Higgs sectors, and their detection at collider experiments is a clear signature of the physics beyond the standard model. We consider two Higgs doublet models with the discrete symmetry as benchmark models. If these additional Higgs bosons are heavy enough, the decay modes including top quarks can be dominant, and the searches in multi-top-quarks events become an important probe of the Higgs sector. We evaluate the discovery reach in the parameter space of the model, and find that there are parameter regions where the searches at the LHC with 3000 fb$^{-1}$ cannot survey, but the searches at the ILC 1 TeV run can. The combination of direct searches at the LHC and the ILC is useful to explore extended Higgs sectors.

the mass reach for additional Higgs bosons is relatively limited. Thus, the searches at the LHC Run-II or its luminosity upgraded version with 3000 fb −1 (LHC 3000 fb −1 ) and the ILC can be complementary to servey the wide parameter regions in extended Higgs sectors [17].
In this paper, we study multi-top-quarks events as distinct signals of production of additional Higgs bosons. As benchmark models of extended Higgs sectors, we consider two Higgs doublet models (2HDMs). 1  be an attractive signal of the heavy Higgs bosons. Such multi-top-quarks events have been studied at the LHC as a signal of new particle in various models [20][21][22][23][24][25][26][27][28][29][30][31][32][33][34]. A large production rate of multi-top-quarks events is predicted at the LHC for the models with colored new particles such as gluinos, color-octet scalars, etc., but that for non-colored particles such as heavy additional Higgs bosons is limited. At the ILC, four top-quarks production can be considered as a signal of H and A, through e + e − → HA and e + e − → ff H/A [17,35,36].
To produce a pair of H and A which decay into top-quark pairs, both the masses of H and A are required to be larger than about 350 GeV, and the collision energy should be higher than about 700 GeV. Such an experiment can be realized at the ILC with √ s = 1 TeV.
Up to our knowledge, there has been no dedicated study on this process at lepton colliders.
Therefore, in this paper, we aim to present a detailed analysis on this process including the hadron-level simulation with jet clustering, flavor tagging, detector acceptance and momentum resolution effects. We find that the four top-quarks events can be detected by simple kinematical cuts, and thus be useful to survey the parameter regions in the 2HDM. We note that the signal of heavy charged Higgs boson can be H ± → tb(tb), and its observability has been studied in gb → tH ± process at hadron colliders [37,38], and also at lepton colliders in e + e − → H + H − and e + e − → H ± ff ′ [39][40][41].
The paper is organized as follows. In Sec. II, we briefly introduce the 2HDM with Z 2 symmetry considering the four types of Yukawa interactions. In Sec. III, we present an analysis for the search prospect of additional Higgs bosons in multi-top-quarks events at the LHC. In Sec. IV, we study the four top-quarks events at the ILC by performing the  Monte-Carlo simulation for the signal and background processes at the hadron level with detector effects. By using the simulation analysis, we evaluate the discovery potential of the neutral Higgs bosons at the ILC in the four top-quarks events in the parameter space in the 2HDM with four types of Yukawa interactions. The obtained discovery reaches at the LHC and at the ILC are compared. Sec. V is devoted to discussions for further investigation and future prospects. Finally, we draw a conclusion in Sec. VI.

II. TWO HIGGS DOUBLET MODEL
In this section, we briefly introduce the model we consider, namely the 2HDM with the softly-broken Z 2 symmetry. We introduce two isospin doublet scalar fields, Φ 1 and Φ 2 , which transform as Φ 1 → +Φ 1 and Φ 2 → −Φ 2 under the Z 2 transformation. For the SM fermions, there are four kinds of Z 2 parity assignment [42][43][44], as listed in Table I. We denote the four types of Yukawa interactions as Type-I, Type-II, Type-X and Type-Y [44]. The Yukawa interaction to the SM fermions in each flavor is allowed for only one Higgs field, Φ 1 or Φ 2 , to make each interaction term Z 2 invariant. It forbids the flavor changing neutral currents at the tree-level [45], which are severely constrained by experimental observations.
in terms of these physical scalars as where the scaling factor ξ f φ with φ = h, H, A and f = u, d, ℓ can be found in Table II. The scaling factor is a function of α and β, the mixing angles in the neutral CP -even component The gauge coupling of h is given by g 2HDM hV V = g SM hV V sin(β − α) and that of H is given by g 2HDM Theoretically, a deviation of sin(β − α) from unity is constrained by the arguments of perturbative unitarity [46][47][48] and vacuum stability [49][50][51]. If a softbreaking scale of the Z 2 symmetry M is larger than the electroweak scale, M ≫ v, only small value of 1 − sin(β − α) is allowed by these constraints [52]. found, e.g., in Refs. [14,17]. For larger tan β, the dominant branching ratio is replaced by the other fermionic mode, bb for Type-II and Type-Y, τ + τ − for Type-X Yukawa interactions.
For Type-I, since the tan β dependence is common for all fermions, the dominance of tt decay mode is true for any value of tan β.

III. MULTI-TOP-QUARKS PRODUCTION AT THE LHC
In this section, we study the four top-quarks production through the production of additional Higgs boson(s) at the LHC. The largest contribution comes from the top-quark pair associated production process, since it emerges via the strong interaction. At the tree level, there are two subprocesses in this process. One is gg → ttH(ttA) and the other is qq → ttH(ttA). Because H(A) is radiated off from the top quarks, the cross section is proportional to the square of y H t (y A t ) which is proportional to cot β in the SM-like limit. Therefore, the cross section is large for smaller tan β.
The four top-quarks production through the pair production of H and A, is described by the quark anti-quark annihilation process, qq → Z * → HA at the tree level.
Since the HA production cross section does not depend on tan β, the cross section of the final four top-quarks production depends on tan β through the branching ratios of H and A into the top-quark pair, B H/A (tt).
There are also three top-quarks production processes via the associated production of H ± and H(A), which subsequently decay into tb(tb) and tt, respectively, At the tree level, this production process is described by the W boson mediated diagram [53,54], example, we take the 2HDM with Type-II Yukawa interactions. For simplicity, we take a common mass for all the additional Higgs bosons. Our calculation is performed with the use of analytic equations in Ref. [55] and the numerical codes generated by MadGraph5 [56].
To calculate the branching fractions of H → tt and A → tt, the off-shell effect of top quarks is included. To estimate the hadronic cross section, the CTEQ6L parton distribution functions (PDFs) [57] are used with setting the scale of PDFs to µ F = m Φ 1 + m Φ 2 for HA and H ± H + H ± A production processes, and to µ F = m t + m Φ /2 for the ttH(A) production process [55]. In Fig. 1, the results are plotted as a function of the mass for the LHC 8 TeV For each process, the largest cross section is realized for the mass of additional Higgs bosons at around 350 GeV. Below this value, the branching ratio into tt is suppressed because one of the top quarks is forced to be off-shell, while above that value the production cross sections of additional Higgs bosons get decreased. For tan β = 1, the cross section of the four top-quarks production can be at most 6 fb (50 fb) for the LHC 8 TeV (14 TeV).
We note that there has been already an experimental upper limit for the cross section of four top-quarks production at the LHC 8 TeV [58,59]. The CMS Collaboration has set the limit to σ 4t ≤ 32 fb at the 95% CL (confidence level) [59], by observing the lepton plus multi-jets events. However, the limit is not tight enough to constrain the parameter regions in the 2HDM. We also note that the SM prediction to the four top-quarks production at the LHC 8 TeV is about 1 fb [24]. For the three top-quarks production, since the expected cross section is smaller than that of four top-quarks production while the signatures mix up with that of four top-quarks production, the detection may be more challenging.
We now study the prospect of measuring four top-quarks production as a signal of the production of additional Higgs bosons at the future LHC run. For the four top-quarks production within the SM contribution, the total cross section and its uncertainty are estimated to be σ SM = 15 fb and δσ SM = 4 fb, respectively [60]. To deal with the background for the Type-II 2HDM. four top-quarks production from ttH + ttA production, HA production and three top-quarks production from HH ± + AH ± production are shown with tan β = 1 (solid lines) and 3 (dashed lines).
processes, we follow the analysis in Ref. [22] where the selection cuts to extract the four top-quarks events out of the background events are demonstrated by simulation analysis.
In their analysis, the background rate of B = 7.2 fb after selection cuts is obtained with the signal efficiency of ǫ = 0.03. By taking into account the statistical and systematical uncertainties for the signal, SM and background processes, the accuracy of measuring the signal cross section σ S can be estimated as where δB denotes the systematic uncertainty of the background rate. We take δB = 0.05B, which may be achieved at the later stage of the LHC experiment. By solving Eq. (6), we obtain that σ S has to be larger than 25 fb (63 fb) to achieve δσ S /σ S < 0.5 (0.2) with the integrated luminosity of L = 300 fb −1 . In our setup, the total uncertainty is dominated by the systematic uncertainty from the background. To reduce the statistical uncertainty smaller than the systematical one, one needs only more than 10 fb −1 of the data. Thus, the accuracy will not be improved by accumulating the integrated luminosity up to 3000 fb

IV. MULTI-TOP-QUARKS PRODUCTION AT THE ILC
In this section, we consider the four top-quarks production at the ILC. In the 2HDM, the four top-quarks final state is generated via the pair and single production of H and/or A.
For √ s > m H + m A , pair production of H and A, e + e − → HA, is kinematically possible and its cross section can be sizable. The HA pair production cross section does not depend on tan β at the tree level. Thus, the four top-quarks production rate depends on tan β only through the decay branching ratio of H and A.
On the other hand, for √ s < m H + m A , the pair production is kinematically forbidden, but the single production process can still open as long as √ s > 2m t +m H(A) . The cross section of this process can be increased by the enhanced Yukawa coupling of H and A to the top quarks. Followed by the decays of H and A into tt, four top-quarks events occur from these processes.
Through the decay of top quarks, the signature of four top-quarks production can be observed as all-hadronic, single lepton plus jets plus missing momentum, dilepton plus jets plus missing, trilepton plus jets plus missing, tetralepton plus jets plus missing channels. Among dilepton plus jets plus missing channels, there are same-sign and opposite-sign dilepton final states, where the former is expected to have small backgrounds. The branching fractions for these channels are listed in Table III. In the SM, the leading production mechanism of four top-quarks events is e + e − → ttg * → tttt via QCD interactions, thus the cross section is O(α 2 α 2 s ). The next-to-leading production mechanism is full electroweak process, O(α 4 ). When we consider the final states including the decay of top quarks and their detection at real experiments, there enter reducible backgrounds via e + e − → tt, ttbb, ttℓ + ℓ − , etc. We estimate the contributions from these processes in the following simulation analysis.
The SM contribution to the e + e − → tttt process is estimated to be very small, giving e + e − → ttbb, e + e − → ttℓ + ℓ − .
To analyze the gererated events, we follow the designed performance of the ILC detectors [11]. We take all detectable particles whose pseudo rapidity satisfies |η| < 1.5. For charged particles, we further require their transverse momentum satisfies p T > 0.3 GeV.
Four momenta of those particles are smeared by using the Gaussian distribution with Among those particles, we select isolated leptons, e and µ, whose energy satisfies E cone ≤ 6(E ℓ − 15) where E cone and E ℓ are given in an unit of GeV. E cone is the summation of energies of particles inside the cone around the lepton defined as cos θ cone ≥ 0.98 except the lepton itself [65].
After removing the isolated leptons from the list of particles, we perform a jet clustering by using the Durham algorithm [66] with fixed Y cut = 5 ×10 −4 with the help of Fastjet [67].
Thus, the number of jets in an event is flexible according to the event structure. For each clustered jet, we perform a flavour tagging. If a jet contains only photons, it is tagged as a photon-jet. B-tagging is performed stochastically by using the decay history of particles which is available in the Monte-Carlo simulation. If a jet contains B-hadrons (D-hadrons) in the decay history of constituent particles, we tag it as a b-jet randomly with a probability of 80% (10%). A probability of mis-tagging a jet which does not contain B or D-hadrons as a b-jet is set to be 3%. These probabilities correspond to loose tagging criteria given in Ref. [11]. We found that this loose criteria works better than rather tight criteria to collect more signal events in the circumstances of small backgrounds. In addition, a jet is tagged as a tau-jet, if it contains 1 or 3 charged tracks and satisfies E cone /E jet > 0.95 where E cone is the summation of energies inside the small cone around a direction of jet three momenta with R = 0.15. The other jets are assumed to be light-jets. The number of leptons in an event is counted as N lep = N iso e + N iso µ + N τ j , where N iso e(µ) is the number of isolated e (µ) and N τ j is the number of tau-jets. The number of jets in an event is counted as N jet = N lj + N bj , where N lj(bj) is the number of light-jets (b-jets).

Cross sections
Accumulated efficiencies   To extract the signal events out of the SM background, we impose following selection cuts; (1) small thrust, T < 0.77, (2) N bj ≥ 3, and (3)  We find that large tt backgrounds are excluded by the thrust cut, and a large amount of tt, ttℓ + ℓ − contributions is excluded by the N bj cut. Furthermore, all the backgrounds are suppressed by applying the cut on N T .
The background reduction and signal detection efficiencies are summarized in Table IV where the background process Eq. (12) and the SM four top-quarks production processes are also included for the reference. In our simulation, the background reduction rates by the above three cuts are O(10 −6 ) for tt, 0.66% for ttbb, 1.4% for ttℓ + ℓ − , and 3% for ttW + W − .
With the integrated luminosity of L = 1 ab −1 , only around 47.8 events are expected to be observed. From the SM four top-quarks production, we expect 1.6 events. On the other hand, for the signal process of additional Higgs bosons, around 34% to 47% of events are remained after these cuts, depending on the mass.
By using the signal detection efficiency ǫ S with the expected number of background rate B = 49.4 ab at L = 1 ab −1 , we can estimate the minimum value of the total cross section for the signal process to be identified in a certain accuracy. We take into account only the statistical uncertainties due to the presence of backgrounds, since at lepton colliders systematical uncertainties can be expected to be well under control. Thus, the uncertainty of observing the total cross section of signal events is estimated as We find that the signal process can be detected at the 2σ (5σ) CL if the total cross section We note that, however, the result for Type-I is due to the fact that we take the SMlike limit, sin(β − α) = 1, where no H → W W , ZZ, hh or A → Zh decay is induced.
For example, if we take sin(β − α) = 0.99, these decay modes become non-zero, and even dominant for larger tan β [14]. The value of sin(β − α) = 0.99 can be detected by the precision measurement of hV V coupling constants at the ILC with √ s = 500 GeV and L = 1.6 ab −1 at the 5σ CL [8]. In this case, the four top-quarks events can be observed up to about tan β ≃ 8 (5) at the 2σ (5σ) CL for the four types of Yukawa models. The discovery reaches for sin(β − α) = 0.99 are also shown in each figure in Fig. 4 [17]. By observing several decay modes and their event rates, tan β can be determined experimentally [69]. In the case of sin(β − α) < 1, the decay modes of H → hh, W W , ZZ, and A → Zh can be sizable, especially for Type-I. By the combinations of the measurements of these modes, experimental determination of sin(β − α) may be performed.
Finally, we give some comments on the searches at the CLIC [13]. At the CLIC, the collision energy of multi-TeV, such as 3 TeV, is proposed. With √ s = 3 TeV, the mass reach would be extended up to about 1.5 TeV. This is totally above the scope at the LHC.
Thus, the direct searches at the CLIC would have a great impact in any decay mode of additional Higgs bosons. The top quarks from the decay of such heavier Higgs bosons are more energetic so that the mass reconstruction by using boosted top-jet measurement can be realistic. In the case that H and A are produced with large velocity, the decay products of each Higgs boson are well separated into different hemispheres. Therefore, the mass of additional Higgs boson can be reconstructed by using the invariant mass of all decay products in one hemisphere [70].