# Studying Same-Sign Top Pair Production through Top-Higgs FCNC Interactions at the HL-LHC

Authors: O. M. Ozsimsek; V. Ari; O. Cakir
Journal: Advances in High Energy Physics
 (2022)

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## Abstract

We investigate the potential of the HL-LHC for discovering new physics effects via the same-sign top pair signatures. We focus on the semileptonic (electron and muon) decay of the top quarks and study the reach for a simplified model approach where top quark flavor changing could occur through a neutral scalar exchange. A relatively smaller background contribution and clean signature are the advantages of the leptonic decay mode of the same-signW bosons in the same-sign production processes of top quark pairs. Assuming the FCNC between top quark, up-type quark, and scalar boson from the new physics interactions, the branchings could be excluded of the order O10−4. We use angular observables of the same-sign lepton pairs and the top quark kinematics in the process which provide the possibility of separation of new physics signal from the SM backgrounds using machine-learning techniques. We find that the same-sign top quark pair production is quite capable of testing the top-Higgs FCNCs at the HL-LHC.


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## Body

## 1. Introduction

Among all fundamental fermions in the standard model (SM), top quark has the largest mass and causes the most serious hierarchy and plays an essential role in the metastability of the Higgs boson potential [1]. Top quark is also the last corner stone of the family structure of the SM with a huge mass gap with other members of quark content of the SM. It is the most sensitive particle for TeV scale physics in SM with Higgs boson, therefore researching the interactions of top quark is a crucial part of BSM physics.The flavor-changing neutral currents (FCNCs) among the up or down sector quarks are not present at leading-order in both Yukawa and gauge interactions within the standard model (SM) framework. However, extremely small FCNC couplings could be generated from loop-level diagrams, which are strongly suppressed due to the Glashow-Iliopoulos-Maiani (GIM) mechanism [2]; and it is one of the unique characteristics of the SM. Besides, it sets a new horizon for new researches.The essence and importance of GIM mechanism’s veto and studying FCNC interactions lies in the decision of dropping or keeping the FCNC preventing unique feature of SM model to new physics. FCNC searches will deduce its ultimate fate without any doubt. If one can show its possibility, that would be a great progress at BSM researches.The phenomenology of FCNC couplings has been discussed in many studies. There are scenarios including top-Higgs FCNC within supersymmetry models (including MSSM and RPV) [3–6]: the two-Higgs-doublet models (both flavor violating and conserving) [7–10], quark-singlet models [11], composite Higgs models [12], and warped extra dimensions models [13]. However, we use an effective Lagrangian formalism for top-Higgs-q (thq) FCNC interactions [14, 15] for a model-independent research and discuss our results with the expectations of present models. Then, the top quark FCNCs can also show up in the processes through the exchange of a new neutral scalar. To be specific about the branching ratio from models that are expected, we would like to summarize them at Table 1.Table 1
Expected FCNC branching ratios from models [16].
t⟶uHt⟶cHSM2×10−173×10−15QS4.1×10−54.1×10−5MSSM≤10−5≤10−52HDM (FC)−≤10−52HDM (FV)6×10−62×10−3RPV SUSY≤10−9≤10−9Production of two positively charged top quarks viauu⟶tt resulting in an excess of same-sign lepton pairs has already been searched by the ATLAS [17]. Systematic uncertainties for the main backgrounds, including charge misidentification and fake/nonprompt leptons, are presented about 28%, 33%, and 30% for the ee, eμ, and μμ channels, respectively. The limit on the cross section leads to a limit of BRt⟶uH<0.01. Another search for flavor-changing neutral current processes in top quark decays has been presented again by the ATLAS Collaboration from proton-proton collisions at the LHC with s=13 TeV [18]. The observed (expected) upper limits are set on the t⟶cH branching ratio of 1.1×10−3 (8.3×10−4) and on the t⟶uH branching ratio of 1.2×10−3 (8.3×10−4) at the 95% confidence level. A search for flavor-changing neutral currents (FCNCs) in events with the top quark and the Higgs boson is presented by the CMS collaboration [19]. The observed (expected) upper limits at 95% confidence level are set on the branching ratios of top quark FCNC decays, BRt⟶uH<7.9×10−4 (1.1×10−3) and BRt⟶cH<9.4×10−4 (8.6×10−4), assuming a single nonzero FCNC coupling. These prior works the basically constitutes the starting point of FCNC researches at post-Higgs era researches for FCNC. More recently, the limits given by CMS collaboration have been further improved as BRt⟶uH<1.9×10−43.1×10−4 and BRt⟶cH<7.3×10−45.1×10−4 [20].Especially, we focus on the limits by CMS collaboration [20]; we use same effective Lagrangian up to a factor of weak coupling constant g and follow their limits on coupling constants which are 0.037 for ηu and 0.071 for ηc. In the case of ATLAS collaboration [18], they give a lower bound around 0.065 for both coupling constants. However, bear in mind that the differences mainly come from using different effective Lagrangian, which is discussed at Model Framework section. We investigate the problem by setting coupling constant 0.07 for scenarios about to introduce at following sections and try to improve the limits.In recent years, many new collider ideas such as HL-LHC/HE-LHC/FCC [21–23] have been reported, and technical design report of HL-LHC has been published. Most promising feature of the HL-LHC collider for BSM searches is increased COM energy (14 TeV) and especially its luminosity [21] of up to 3ab−1. Some phenomenological researches for future colliders and HL-LHC have already been started up; for tqH couplings, which have been explored at a high-luminosity ab−1ep colliders (with the possibility of electron beam having a polarization of 80% and electron energy being of 60 GeV), the 2σ upper limits on Brt⟶uH have been obtained as 1.5×10−3 and 2.9×10−4 these future colliders LHeC and FCC-eh, respectively [24].Development of such a collider has notable effects on the BSM literature evidently since it offers new possibilities for phenomenological studies and gives a large room for potential discoveries/exclusions. It offers an opportunity to rule out flavor-violating 2HDM fort⟶cH case and penetrate the other regions foreseen by other models (such as Randall-Sundrum model) [25]. As a consequence, exploiting the physics potential of HL-LHC is crucial for next phase of BSM searches.The phenomenological researches and simulations based on new colliders started to make predictions about new physics scenarios and set new limitations. To be specific at HL-LHC for FCNC interactions [26–30], branching ratios are updated as BRt⟶qh<O10−4 using different analyses from different channels and processes; thus, couplings are expected to go below ηq=0.04, which is roughly below the known limits from experiments. FCNC interaction projections are also available for FCC-hh. The branching ratios suggested by current phenomenological research for this collider changes at the O10−6 and O10−5 [31]. Expected FCNC decay widths and branching ratios are given at Figures 1 and 2, respectively, according to three scenarios which are important and handled separately to set limits for couplings in following sections.Figure 1
The FCNC decay width of top quark according to two scenarios, foru+c case top quark can decay into both, otherwise decays into only one of them.Figure 2
FCNC branchings of top quark for three scenario presented:u+c indicates top quark can decay them both via Higgs. Only u or only c assumes top quark can decay only one of them and the other channel is closed. At last case, top both channels are accessible but only one of them is preferred. To access beyond the FCNC regions excluded by LHC Brt⟶qh~O10−3, one needs to set bound for the coupling constant roughly below ηq=0.04.In this study, we would like to investigate the problem and seek for the new limits at HL-LHC. To do so, we restrict ourselves to production mechanisms of same-signttt¯t¯ pairs (signal processes pp⟶tt⟶W+W+bb⟶l+l+bb+MET, pp⟶t¯t¯⟶W−W−b¯b¯⟶l−l−b¯b¯+MET) including the exchange of Higgs boson at the HL-LHC. In addition, because the analysis was carried out in the HL-LHC, with the anticipation that the systematic uncertainties described in the literature would, in general, reduce, a value of 20% was used for the systematic uncertainties, which is still near to the limitations given in the literature and discussed in the findings section. This was done in light of the fact that the analysis was carried out in the HL-LHC. We introduce the kinematical variables to enhance the signal (S) and background (B) ratio. Angular separation of the two same-sign leptons could indicate the new physics effects in ttt¯t¯ production process and separate the signal from background processes.In order to make this research more detailed and similar to other studies in the literature (for comparison purposes), three different scenarios were designed for the signaling process. These are theu+c, only u, and only c scenarios. As the nomenclature suggests, FCNC transitions are made possible from the top quark to the other two quarks in the u+c case; while in other cases, the transitions are limited to just one quark.


## 2. Model Framework

The flavor-changing neutral current interactions of the top quark with other particles of the SM have been described in a general way as an extension [14, 15]. This provides a direct connection between experimental observables and the new anomalous couplings. The Lagrangian describing FCNC tqH interactions in model-independent manner is given as
(1)LH=12Ht¯ηuLPL+ηuRPRu+h.c.+12Ht¯ηcLPL+ηcRPRc+h.c.,where the ηqL/R couplings set the strength of the coupling between the top quark, the Higgs boson, and up or charm quark, as well as the chirality of this coupling. They can be complex in general; however, we take into account real parts of the couplings to reduce the free parameters. In literature, this interaction can be seen as modeled without the constant 1/2 thus gives higher top branchings a factor of 2 [32]. The FCNC processes that corresponds to tqh interactions have been described by a similar Lagrangian [19] with an extra factor of weak coupling constant. To switch between models, we just need to remind this conversion factor. We keep that constant here in order to make bounds more strict meanwhile keeping the conversion to other models in our mind. Note that it effects cross section and number of events naturally, thus it would make signal process more realistic. The decay width for FCNC channels can be calculated as
(2)Γt⟶qh=ηqL2+ηqR264πmt2−mh22mt3,and its numerical value depends on the coupling values related to Γt⟶qh≃0.1904ηqL2+ηqR2 GeV. The branching ratio to an FCNC channel can be expressed as BRt⟶qh=Γt⟶qh/Γt⟶all. Since the dominant decay mode of top quark is Γt⟶Wb, this branching ratio mostly related to ηqL2+ηqR2 factor especially for smaller coupling values.The model framework can also be compared with the formalism assumed that the FCNC interactions occur via a weak sector. The relevant effective interaction Lagrangian including a new flavor-changing scalar (ϕ) is given
(3)Lϕ=ϕt¯au+buγ5u+ϕt¯ac+bcγ5c+H.c.,where the coupling parameters au,c and bu,c denote the scalar and axial couplings between top quark and up-type light quarks (u,c) which proceeds through the exchange of a scalar ϕ. To compare different formalism for the top-scalar FCNC, we find the correspondence of the couplings aq=ηqL+ηqR/22 and bq=ηqR−ηqL/22. Assuming no specific chirality dependence (same value for left- and right-handed couplings) of the process, we may set aq=ηq/2 and bq=0.In this study, we use a template model. The parameters that appear in the top FCNC_UFO [33, 34] model are complex numbers in general and their real and imaginary parts can be set manually. In this work, we restrict ourselves to real parameters in order to reduce the free parameters.


## 3. Cross Sections of Signal and Background

At the first step before event generation, we calculate the cross section for FCNC processes includingtqh, which vertices lead to same-sign signal final state as shown schematically at Figure 3. Since the cross section is proportional to the modulo quartic of the value of the anomalous couplings, in Figures 4 and 5, we can see due to presence of up-type quarks in proton, pp⟶tt process is much more favorable than pp⟶t¯t¯. Although the contribution from the signal pp⟶t¯t¯ to same-sign lepton signal compared to the signal from pp⟶tt is nearly less than one order of magnitude, we also use that contribution to enhance the signal.Figure 3
Feynman diagram of leptonic decay of top-Higgs FCNC process: for sake of simplicity, we give a compact form of the process which includes two new physics vertex. Dominant contribution will come frompp⟶tt process due to the large values of PDF of up-type quarks in proton.Figure 4
Estimated cross sections according to coupling constant of two same-sign lepton signal in FCNC processes. As we can see, the main contribution comes from positively charged top pair due to higher parton distributions of valance quarks at proton which differs nearly one order of magnitude. Nevertheless, addingt¯t¯ production, we use negatively charged lepton pair to enhance the signal process. We assume all FCNC coefficients are the same and all channels are open (to state exactly we use u+c⟶ηu=ηc case).Figure 5
Cross section for the final state including two same-sign lepton at HL-LHC. Comparison of three FCNC scenarios: the matrix element of the FCNC process includes two new physics vertices which are proportional toηq2, hence the cross section is proportional to ηq4. If c quark does not involve in interactions then cross section depends only on ηu4. Since the PDF of valence u quarks are high, the contribution to cross section from u quarks are consideribly high. In the case of a forbidden u quark interaction, cross section completely depends on ηc4 while cross section is lower. In the case of u+c scenario, both u and c actively participate in interactions, there is cross term in addition to the contributions from only u and only c scenario. However, the total cross section is expected to be relatively higher than the case of only u (as shown in Figure 5), showing that the majority of interactions carry the signature of u quark distributions in the proton.After setting model parameters, the signal samples and background samples are generated with MadGraph5 [35]. In the partonic and hadronic level simulations, we use the parton distribution function (PDF) set NNPDF2.3 [36] at MadGraph5’s default energy scale. PYTHIA 8 [37] is used for shower and hadronisation processes, and finally, DELPHES 3 [38] is used for detector level simulation. Result files are analyzed with ROOT6 [39].As mentioned before, the same-sign lepton signal has relatively low background, which is advantageous and many of the background processes fall into reducible background category, which means, although they are present due to similarities between signal process, by applying proper analyze cuts, their contributions can be well reduced. However, there still exist tough irreducible backgrounds. The contributions from various backgrounds are listed below.Characteristics of signal events are two jets (b-tagged if possible), two same-sign leptons, and missing transverse energy. We choose our background processes by considering three fundamental features:(i)
Similarity of final state particles as much as possible with signal processes(ii)
High cross section compared to signal(iii)
Having same reconstruction inputs as for the signalAt Table2, backgrounds have at least one of these characteristics, and several have two (at Table 3, they are grouped for simplicity). Backgrounds given in tables have at least one of these properties, besides some of them have two. As long as all processes have their own unique nature, they more or less differ at least one criterion or partly one or two criterion.Table 2
Signal and background processes with leptonic decay channels: We consider the positively and negatively charged leptonic final states for maximal imitation of signal process. So background events generated with this regard, we force particles to givel+/l− final states if possible. Otherwise, we let particles to decay any channel. For W boson at intermediate states, we always take leptonic decay modes in getting the maximal similarity with signal.
ProcessCross section (pb)Intermediate statespp⟶ttt¯t¯WWbbηu=ηc=0.073.439×10−5ηu=0.075.257×10−4ηc=0.071.976×10−5pp⟶tt¯W±1.647×10−2WWWbbpp⟶W±W±jj1.357×10−2WWjjpp⟶W+W−Z1.581×10−3WWZpp⟶tt¯l+l−1.827×10−2WWbbllpp⟶ZZW±1.938×10−4WZZpp⟶tt¯W+W−8.466×10−2WWWWbbpp⟶tt¯Z1.846×10−4WWbbZpp⟶ZZjj1.267×10−2ZZjjpp⟶tt¯H4.242×10−5WWbbHTable 3
Content of background groups: here, we grouped backgrounds to increase clarity of our histograms. The most important feature of these backgrounds are four of them includes top pair as backbone, and others only bosons. Onlypp⟶tt¯l+l− process is left as own. That behavior of backgrounds leads us the categorization of them in this table.
Group nameProcessesDefinitiontt¯ w/wo boson (s)pp⟶tt¯W±Top pair with or without bosons or bosonpp⟶W+W−tt¯pp⟶tt¯Zpp⟶tt¯HBosons w/wo jetspp⟶W+W+jjBosons with or without jetspp⟶W+W−Zpp⟶ZZW±pp⟶ZZjjThe processespp⟶W±W±jj; pp⟶tt¯W±; pp⟶tt¯l+l−; and pp⟶tt¯W+W− with same-sign dilepton decay modes which are most similar to our signal process are directly background to our signal process and they are all irreducible. Although they give same final state content with the signal, pp⟶tt¯W± reconstruction region is slightly different. This process also gives similar products at final state. However, its cross section is high. In the case pp⟶W±W±jj, on the one hand, reconstruction region is significantly different; on the other hand, its particle content is exactly the same. In addition to previous two discussions, as an advantage for analysis, pp⟶tt¯l+l− procces has low cross section compared to other two. Nevertheless, its reconstruction region is fairly same. pp⟶tt¯W+W− with leptonic decay modes directly produce signal content; however, its reconstruction region is noticeably distinct. Besides, its cross section is quite high. Similar arguments can easily be expanded to other backgrounds. Others are reducible backgrounds: even though their particle contents are similar to signal, either their cross sections are low and reconstruction region significantly different. In that regard, they satisfy only one criterion, while irreducible ones fulfill two or more.Further, we select decay channels of background events as such to give same-sign2l± with 2j and MET. Jets include at least one b-tag jet. This ensures the maximum cross section for background and gives more contribution to histograms, when we consider the detector effects such as misidentification and over counting of particles.Inability to distinguish between signal and background processes increases with misidentification of particles and loss of particles due to detector effects. These effects causes the fuzzing of characteristics of signal, while imitating the features of signal for background processes. Moreover, b-tag efficiency plays also an important role for analyzing the signal and background events since two b-tagged jets are a major property of signal. Nevertheless, two b-tagged jets requirement is so strict for observability of signal while reducing background effects too. Therefore, we confined ourselves to at least one b-tagged jet while recognizing characteristics of our signal and background processes. It is also important to note that there is no interference between signal and background at this level of calculation.


## 4. Analysis

At first stage, we have started with the known limits from current LHC experiments that put a limit on the FCNC coupling constant valueηq=0.07 which is already reached; and then, use benchmark value ηq=0.07 to insvestigate the limits for upgrading HL-LHC detector to search for a possible FCNC signal outcome. After that, we seek edge values to limit and finalize our research. We will look forward to push the limits for ηu+c, ηu, and ηc, separately.We use the statistical significanceSSdisc(4)SSdisc=2S+Bln1+SB−S,and SSexc(5)SSexc=2S−Bln1+SB,for discovery and for exclusion as given in [40–43]. For the exclusion of a parameter value, we are looking for SSexc>1.645 corresponding to a confidence level of 95% CL. In order to make it complete, we will give limits for discovery relation too. Both relations reduce to S/B at large background limit. In addition, we will conduct an evaluation in which systematic uncertainties are estimated in order to comprehend how systematic uncertainties influence our results. For these calculations, we will use the following formula for discovery with systematic uncertainties
(6)SSwSdisc=2S+BlnS+BB+S2B2+S+BS2−B2ΔB2ln1+ΔB2SBB+ΔB21/2,and for exclusion case, we use the equation
(7)SSwSexc=2S−BlnB+S+x2B−B2ΔB2lnB−S−x2B−B+S−x1+BΔB21/2,where x being
(8)x=S+B2−4SBΔB2B+ΔB2.When it comes to our analysis path, the first thing we’ll do is focus on the key points for analysis and talk about the unique characteristics of the signaling process. These characteristics will then be disclosed by presenting the kinematic variables, and the method to be used in the study will be determined. Following that, the analysis will be performed, and the results will be provided.Here, we will track exactly two positively/negatively charged leptons as same-sign lepton pairs since we investigate the caseW±⟶l±νl± followed after tt¯⟶W+bW−b¯. Missing transverse energy is also an essential characteristics of the process too. We note that despite we have only two b-jets in our signal, when we consider the nature of interaction, more jets must be generated and we need to distinguish them from bottom quarks to reconstruct two top quarks. That point needs a little bit attention when we think of backgrounds and to make it clear, we would like to go deeper: as we know, our background events have more particles; in addition, the nature of interaction also dictates numerous jets which give more hadronic transverse energy. When we consider both, a cut that is limiting the number of jets seem to be advantageous. The best choice at first glance is limiting jet number as two, so we conclude with exact event selection. Nonetheless, taking into account detector effects, in a situation where two leptons are detected individually, if there are no jets or only one jet, these jets are more likely to escape from the detector. Working with a small number of jets is useful in this regard, as backdrops are highly prominent when working with a large number of jets. Furthermore, because the top quark is the source of leptons in the processes, it can be assumed that every case in which two same-sign leptons are seen belong to the signal event, again taking charge conservation into account. Again, b-tagging serves a purpose here. Of course, without jets, this labeling is not conceivable. However, in single-jet (or fat jet) scenarios, this criterion can be used to provide the analysis a boost.For lepton flavors, we have 2 possibilities, namely,e± and μ± for l± case since τ lepton disintegrates before reaching the detector, so its analysis is out of scope. In that respect, we divide the analysis region to three, which includes three possibilities of same-sign lepton pairs (e±e±,μ±μ±,e±μ±) with exactly two jets, while at least one of them is b-tagged, and lastly, the presence missing transverse energy in events.Decay of top quarks in their rest frame gives rise to highpT b-jets larger than about 80 GeV as a prediction in addition same happens for W+ bosons, and daughter particles should have at least 40 GeV. These particles also carry momentum, thus we expect boosted behavior at histograms for mother and daughter particles.To sum up at the beginning of the analysis, we have divided signal analysis into three regions with exact event selection, followed by simple cuts given in Table4. Here, the η cuts were chosen to work with the more sensitive regions of the detector for leptons especially. Furthermore, ΔR cuts were established as the minimum lepton isolation criteria. For triggering and good object selection criteria for jets and leptons, missing transverse energy and pT cuts are minimally incorporated. To avoid a fat-jet scenario, ΔR cut was regarded appropriate for jets, although jets reaching the detector were tolerated by avoiding an η limiting cut. As previously stated, it was noted that at least one of the jets entering the depicted histograms was b-tagged. Here, we give the kinematical distributions for lepton pT at Figures 6–8, lepton η at Figures 9 and 10, HT and MET at Figures 11 and 12, and lastly jet pT and η at Figure 13–16, belonging the signal process. In addition to the variables specified, the ΔR distributions of leading jets and leptons that are useful for analysis are provided at Figures 17 and 18. Finally, we present histograms showing the characteristics of jets produced and little comments on them. These histograms compare the behavior of signal and background events without delving into a detailed investigation. Except for a few cuts relevant to the study, the segments utilized for event production have been transferred to the detector level in order to provide the histograms in their simplest form, while some variables reflect differences. Although it is possible to separate the signal process, which includes two new physics vertices (and lowers cross section drastically), in the background, due to the high cross section of the tt¯W± background and its similarity to the signal, it is not possible to make a discrepancy after a point and provide the desired improvement in the analysis.Table 4
List of basic cuts.
Event selection and basic cutsNjets≥2Nl±=2 (same sign)pTjets>20GeVpTl±>10GeVMET>20GeVηl<2.5,ηj<5ΔRl1,l2>0.4ΔRj1,j2>0.4At least one b-tagged jetFigure 6
For the signal process, leptonpT distributions e±e±,μ±μ±,e±μ± event regions: histogram clearly shows that e±μ± final state is more favorable. The e±μ± pair comes from the disintegration of W± pairs which have about 80 GeV rest mass. Hence, that energy and momentum shared by final particles give a peak around 40 GeV with boosted behavior. However, the same flavor final states shows an asymmetry originates from the following reasons: detector always discriminates lower and higher pT particle which gives a gap between first and second highest pT object. Nevertheless, they all have boosted behavior and give peaks close to 40 GeV as well.Figure 7
pT distribution of signal and background processes for leading leptons.Figure 8
pT distribution of signal and background processes for secondary leading leptons.Figure 9
Leptonη distributions for signal and backgrounds: general detection is central.Figure 10
η distributions of the secondary lepton from signal and background. As can be observed, they do not form a clear cut, and their significance in the analysis is rather minor.Figure 11
ScalarHT distribution for the signal and background processes. Since more jet generated at backgrounds, they have relatively shifted to forward.Figure 12
Neutrinos are the main source of missing energy of the interaction. Here, we have two neutrinos coming fromW± decay. Thus, histogram gives a peak about 40-50 GeV and boosted too which are in complete consistency with our expectations.Figure 13
JetpT: even though we know our process gives mainly two b-jets, nature of process gives more jets as final state objects. Higher number of jets lowers pT values for the jets coming from leading and second-leading jets and squeeze their pT values below 60-70 GeV. The jets playing role at reconstructing top quarks energetic may have pT above that values. Additionally, the effect of the longitudinal component must not be overlooked.Figure 14
The overall behavior of the secondary jets in the backgrounds is highly forward, in contrast to the second jets in the signal.Figure 15
Leading jetη distribution at detector is central.Figure 16
Second-leading jetη distribution at detector is central.Figure 17
ΔRj1,j2 distribution between two jets. Although there is no significant difference between the signal and background ΔR distributions at this point, it stands out as one of the most important variables since the signal process is symmetrical in its stationary frame of reference. Jets have the direct top quarks’ back-to-back scattering structure.Figure 18
ΔRl1+,l2+ distribution between two leptons. The ΔR variable in leptons is very crucial for discrimination, as it is in jets, but their behavior is much looser in comparison to jets due to additional energy-momentum conservation constraints from the decay of the W boson.Although this makes the investigated process more appealing for exclusion, because the path forward with cut-based analysis is limited, better results can be obtained by utilizing machine-learning techniques with the help of variables defined after these basic cuts.The most fundamental variables in this analysis are thepT, η, and ϕ components of the jets up to 4th as well as the same kinematic variables as the first two leptons. Furthermore, variables such as missing ET, HT, and ΔR are used together with the invariant masses of the two jets and two leptons, the invariant and transverse masses in the quadruple state l1,l2,j1,j2, and finally mTW1,2, mTt1,2 reconstructions for the final state particles which are important for the result. For mTW and mTt variables, we have used the relations,
(9)mTt=pl+pb2+p⟶Tl+p⟶Tb2+p⟶Tνl−p⟶Tl+p⟶Tb+p⟶Tνl221/2,(10)mTW=2pTlETmiss−p⟶Tl.p⟶Tνl.During the generation of these variables, cuts identical to those in Table4 were utilized, with minor modifications. First, the event selection regions are separated immediately into two lepton regions with same signs, regardless of the number of jets. While the fundamental sections of the pT cuts were kept, the criteria for lepton and jet separation were abandoned. In addition, the pT cuts for the fifth jet remained at 15 GeV. Each η variable is set to a value less than 2.5. To contrast, the prominent signal regions in low jet number and low HT states with the dominant background processes in high jet number and high HT states; the number of jets is included up to a maximum of five and processes begin in nonjet states. In addition, the parsing of the ΔR variable was to be performed solely using machine-learning techniques [44].Finally, the findings of the BDT analysis are presented in Figures19 and 20. Observing the nonlinear behavior of the signal and background, suitable approaches were chosen. Since a method based on fluctuations, such as BDT, is employed. A decision tree takes a set of input features and splits input data recursively based on these features. Boosting is a method of combining many weak learnings (trees) into a strong classifier. It has been confirmed that the rate of discrimination gradually increases between the training and testing phases. Figure 19 demonstrates that, as a result of the employment of several variables with high event numbers, the distribution and height of the signal’s curve are significantly superior to the back one.Figure 19
By employing an appropriate cut, it is achievable to distinguish the signal from the background with great efficiency. (The curve was determined by analyzingηuc=0.07.)Figure 20
In the analysis, nonlinear approaches were predominantly employed. This is due to the fact that the structure of the signal and background distributions is more accurately reflected in this manner. In this regard, linear approaches such as Fisher’s and its derivatives are unsuitable for analysis. Again, similar procedures were not adopted since they did not produce successful results. However, other nonlinear approaches were incorporated in this context so that the analysis could be compared to other ways and its evolution could be observed. The results indicate that the inputs are uniformly distributed, no overtraining was seen, and the analysis produced a high level of diversification overall.


## 5. Results and Conclusions

In this study, we have searched for accessible limits for top-Higgs FCNC couplings using same-sign lepton channel at the HL-LHC (see Figures21 and 22). This channel gives clean signal signature in addition to its low reducible/irreducible background. However, this channel suffers from two new physics vertices. Thus, these effects lower the cross section drastically which is a disadvantageous feature of this analysis. Keeping these in mind, we can conclude that simulation of this process with the same-sign lepton channel turns into a laboratory for testing the mentioned scenarios in the text. In this respect, this channel determines the upper limit for couplings and benefits exclusion limits rather than discovery.Figure 21
Signal significance (SSdisc) versus ηq-coupling parameter for three different scenarios at 3ab−1-integrated luminosity.Figure 22
Signal significance (SSexc) versus ηq-coupling parameter for three different scenarios at 3ab−1-integrated luminosity.We have started with coupling constantηq=0.07 to demonstrate the characteristics of signal an catch the limits given in ref. [18] whose limits are more or less same as our benchmark value. Then, as stated at introduction section, we have tried to improve our results and get better limits for FCNC couplings.In Table5, we summarize our analysis results with the discovery and exclusion significance. Due to the sensitivity of the study to exclusion, examining exclusion instances first will expose the results more clearly. First, the results of the initial review have improved the known limits [18–20], with the exception of some channels [20]. In addition, although how the results will be compared with one another is discussed in the second chapter, these changes will be discussed in greater detail here.Table 5
Upper limits onηq parameter and corresponding branching ratio as a potential discovery scenario projection at HL-LHC with no systematics (left side) and with 20% systematics (right side) at 3ab−1 integrated luminosity.
ScenarioSSdisc≥220% sys.SSdisc≥2ηu=ηc0.0480.048ηu=ηc0.0506.52×10−4Onlyηu0.0530.053Onlyηu0.0557.88×10−4Onlyηc0.120.12Onlyηc0.123.74×10−3ScenarioSSdisc≥320% sys.SSdisc≥3ηu=ηc0.0547.60×10−4ηu=ηc0.0568.17×10−4Onlyηu0.0609.38×10−4Onlyηu0.0621.00×10−3Onlyηc0.134.39×10−3Onlyηc0.145.09×10−3ScenarioSSdisc≥520% sys.SSdisc≥5ηu=ηc0.0631.00×10−3ηu=ηc0.0651.10×10−3Onlyηu0.0701.28×10−3Onlyηu0.0731.39×10−3Onlyηc0.155.83×10−3Onlyηc0.166.63×10−3ScenarioSSexc≥1.64520% sys.SSexc≥1.645ηu=ηc0.0343.00×10−4ηu=ηc0.0363.38×10−4Onlyηu0.0363.38×10−4Onlyηu0.0404.17×10−4Onlyηc0.123.74×10−3Onlyηc0.123.74×10−3As expected, theηu+c instance produced the best results. Cases ηu and ηc followed these outcomes, respectively. Theoretically and empirically, the results vary little in the idealized scenario, assuming a total of 20% systematic uncertainty. This means that the background in the study has been eliminated with great success, and these uncertainties will not significantly impact the outcomes. In the case of exclusion, we have improved the coupling constant limits for ηu+c and ηu situations, although our limits for ηc are more stringent. However, the branching ratios for the ηc situation appear to have already been exceeded. Similarly, the ηu and ηu+c scenarios exceed the LHC constraints by a small amount. At this point, as the effective Lagrangiande utilized by CMS contains a weak interaction constant, it is apparent that the results may stray further from the known limitations with this factor, despite the fact that the analysis indicates the reverse. From the obtained coupling constants, the resulting branching ratios are determined. The minimum values coupling constants attained are proportional to the number of events in the analysis, or indeed the cross section. When the analyzed process consists of two vertices, it is dependent on constants of the fourth order and has an advantage proportionate to the inverse square of the coupling constant size when compared directly. In fact, this circumstance nullifies the influence of the weak interaction constant and drastically decreases the results below the known levels. In this regard, it becomes evident why the channel is superior for exclusion and why it establishes very strict upper limits. Nonetheless, these constraints also limit other studies of top quark-Higgs FCNC interactions. Since these restrictions are precluded for this channel with two vertices, it stands to reason that studies with a single vertex will go below this limit, at least proportional to the obtained coupling constant value. Note that, we have also caught the phenomenological limits for HL-LHC expected [26–31]. At that studies ηq varies near 0.04 [27–29] (bear in mind that models does not include additional 1/2 factor and we would like to point out that some of these research focus on luminosity variation rather than limit values).Concerning the scenario of discovery, the limits reached for discovery coincide with the limits reached by the CMS and ATLAS Collaborations at lower total luminosity values. In this instance, if further data is obtained, this value indicates that exploration is feasible up to the region’s limit. However, it should not be forgotten that due to the nature of the analysis channel, they are still upper limitations. In this context, it has been proven that the values for an analysis involving a single FCNC vertex can be reduced.Lastly, upcoming colliders will provide better visions for FCNC interactions [23]. To compare them with each other, we may say HL-LHC and FCC-eh are expected to work at same region. Moreover, HL-LHC offers better limits when we compare it with ILC/CLIC [23]. So our results have some implications on the analysis have been done for both FCC-eh and ILC/CLIC. In support of this, studies give similar results to ours done for FCC-eh [24]. Even though results of HL-LHC will give direction to new researches without any doubt, there is a gap in COM and luminosity values between HL-LHC and FCC-hh. It is expected to take down limits even further by FCC-hh. FCC-hh can possibly rule out RS models and start to penetrate the MSSM region.To sum up our findings, we may say, while these limits are compatible with the expectations from HL-LHC, which enforce limitations for findings on other channels since on the one hand, this channel gives its clean signal fingerprint; on the other hand, even lower cross section, the same-sign lepton channel provides upper limits and provides hints to other detectors and thanks to its clean signal fingerprint, it also imposes partial limitations on other channels. Our limits can also be combined with the other sensitive channels for similar scenarios.



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