Four-top as probe of light top-philic New Physics

We study the four-top (tt¯\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \overline{t} $$\end{document}tt¯\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \overline{t} $$\end{document}) final state at the LHC as a probe for New Physics (NP) effects due to new particles that couple predominantly to the top quark and whose masses are below the top-quark-pair production threshold. We consider simple NP models containing a new particle with either spin 0, spin 1, or spin 2, and find benchmark points compatible with current experimental results. We find that interference effects between NP and QED amplitudes can be large, pointing out the necessity of NLO contributions to be explicitly computed and taken into account when NP is present. We examine kinematic differences between these models and the Standard Model (SM) at the parton level and the reconstructed level. In the latter case, we focus on events selected requiring two same-sign leptons and multiple jets. We investigate how the different Lorentz structure of the light NP affects the kinematic hardness, the polarization, the spin correlations, and the angular distributions of the parton-level and/or final-state particles. We find that spin-2 light NP would be identified by harder kinematics than the SM. We also show that the angular sepa- ration between the same-sign leptons is a sensitive observable for spin-0 NP. The spin-0 and spin-2 NP cases would also yield a signal in tt¯\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \overline{t} $$\end{document}γγ with the invariant mass of the photons in- dicating the mass of the new particle. The spin-1 NP would be identified through an excess in four-top signal and slight or not modification in other observables, as for instance the lack of signal in tt¯\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \overline{t} $$\end{document}γγ due to the Landau-Yang theorem. We comment on the opportunities that would open from the kinematic reconstruction of some of the top quarks in the tt¯\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \overline{t} $$\end{document}tt¯\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \overline{t} $$\end{document} state. Our results provide new handles to probe for light top-philic NP as part of the ongoing experimental program of searches for four-top production at the LHC Run 2 and beyond.


Introduction
The LHC is already a very successful machine. It has discovered a Standard Model (SM)like Higgs boson [1,2], which was one of the main drivers of its design and construction, and it has pushed our frontiers of knowledge to extraordinary limits by excluding the existence of new particles over a broad range of masses and couplings in a wide variety of New Physics (NP) models. The current state-of-the-art in High Energy Physics (HEP) research can be depicted as a vast and challenging ocean, of which we are practically clueless, between the current TeV energy frontier and the Planck energy scale. Over the next two decades, while the LHC completes its Run 3, the HEP community will be devoted to the scrutiny of all available LHC results, as well as to the proposal of new promising experimental directions. Among these upcoming LHC results, there are few processes that are beginning to be tested experimentally using the full Run 2 dataset, and whose measurement is directly sensitive to NP contributions. Of particular interest are Higgs-boson pair (hh) production [3][4][5], the associated production of a Higgs boson with a top-antitop-quark pair (tth) [6][7][8], and fourtop (tttt) production [9][10][11]. The first two processes, hh and tth, will deliver crucial direct information on the Higgs potential and the top-quark Yukawa coupling, respectively. The

NP models
The aim of this article is to study how simple NP models would affect the four-top phenomenology at the LHC, and how could they be recognized and distinguished. We focus on models whose effects are expected to be more important in four-top production rather than in other processes. To this end, we consider new particles whose couplings are predominantly to the top quark and whose mass M is below the tt threshold (M < 2m t ) to avoid resonance effects in tt production. In addition, we restrict ourselves to new particles which are color neutral to avoid interactions with gluons that would yield a large QCD-mediated production cross-section. For this purpose we study the following simple models that are described below: i) Scalar, ii) Pseudo-scalar, iii) vector Z , and iv) Graviton.
It is not the objective of this work to develop the UV completion of the proposed simple NP models. However, it can be argued that having a new resonance with couplings to SM particles dominated by the top quark is feasible, as for instance in two-sector models [34] or Composite Higgs Models (CHM) [35]. In these models the SM is accompanied by a heavier strongly interacting sector; the details and phenomenology of this kind of NP can be found elsewhere [34]. In CHM models, to avoid experimental constraints and to explain the fermion mass hierarchy, it is customary to implement partial compositeness, where the degree of compositeness of each physical fermion depends on its mass [36]. Given Electroweak Precision Tests on SU(2) L it is convenient to set in the model the right-chiral top quark (t R ) with large compositeness [34]. Then, depending on the particular realization of each model, one can obtain for different cases some new light resonances that couple predominantly to t R . For the case of a spin-0 field, however, the Lorentz structure requires a left-chiral top quark (t L ) as well. Vertices of this kind are found in ref. [15], and ref. [37] discusses a UV complete model with additional scalars that presents this kind of phenomenology.
For the sake of simplicity, and to address qualitative aspects of four-top production phenomenology, throughout this work we make the assumption that the new light resonance couples only to the top quark, as described in the following paragraphs.

NP interaction Lagrangian
Scalar NP: φ. For the scalar case we study the following simplified Lagrangian L tree φ = g φttL φt R + h.c. . (2.1) A one-loop effective coupling to gluons (φgg) and to photons (φγγ) is added to the Lagrangian through a top-quark loop. The NP effective interaction Lagrangian therefore reads Details on the one-loop effective Lagrangian are described in appendix B.
Pseudo-scalar NP: A. The pseudo-scalar case has the following Lagrangian L tree A = g AttL Aiγ 5 t R + h.c. .

JHEP12(2019)080
Including the one-loop effective Lagrangian describing Agg and Aγγ interactions that can be found in appendix B, the full pseudo-scalar Lagrangian reads Z Vector NP: Z . For the purpose of our work, the only interaction considered for Z reads Since Z is a spin-1 particle, it cannot couple at any order to a γγ final state due to the Landau-Yang theorem [38,39]. However, recent works claim that a spin-1 particle can couple to a gg state since gluons are colored [40][41][42][43]. Since we expect that limits coming from resonance searches in di-jet (jj) production and tt+jets production (tjj or ttjj) do not have sufficient sensitive to probe the relevant parameter space for the models considered, we ignore this possibility. As pointed out in ref. [15], having the Z coupled to an unconserved current such ast R γ µ t R yields a factor (m t /M ) 2 , due to the longitudinal polarization of the vector propagator. For small M this translates into an enhancement in the cross-section, as discussed below. We have explicitly verified that if we use the conserved fermionic current instead, then this enhancement for small M disappears and the behavior is more similar to the spin-0 case, where the coupling is to a conserved current.
Graviton NP: G. We consider an effective Lagrangian for a spin-2 graviton with field G µν . The tree-level interaction Lagrangian reads [44] Contrary to the previous NP models, the spin-2 Lagrangian needs dimensional couplings, hence the dimensional constant Λ in the denominator. The constant Λ can be understood as the energy scale up to which the theory as described here is valid. Throughout the remainder of this article we set Λ = 3 TeV.
It is interesting to notice that in this model, in addition to the coupling between the resonance and the top-quark pair, SM gauge invariance introduces 4-point interactions that include the resonance, the top-quark pair, and a SM gauge boson. This represents a distinctive feature of the model, since there are Feynman diagrams in pp → tttt production that are not present in the other models (see figure 1c).
Therefore, the full spin-2 Lagrangian reads where the one-loop effective Lagrangians due to gluons and photons can be found in appendix B.

Constraints on the NP models
Since we restrict our study to cases where the mass of the NP resonance is below the tt production threshold, M 350 GeV, the constraints on the model would mainly come from NP loop corrections to tt near threshold, γγ resonance searches, and four-top production at the LHC. We examine these constraints in the following paragraphs.
Loop corrections to tt production have been studied for Higgs and electroweak gauge bosons [45]. Although it is not possible to directly extract bounds on the presented NP models from the available results, adapting these computations for spin-0 and spin-1 NP contributions, as well as including spin-2 corrections and the corresponding interference with SM contributions, could provide relevant constraints on the models. This objective lies beyond the scope of this work; however, given the precision reached in tt production and its recent application in constraining the top-quark Yukawa coupling [46], we estimate that results near the tt threshold should be interesting concerning the presented NP models.
New particles with spin = 1 can be created in gluon fusion through a top-quark loop and decay into a γγ or di-jet final state through a top-quark loop, as discussed previously. A massive spin-1 particle cannot decay to γγ due to the Landau-Yang theorem [38,39]. Since parton-level calculations yield a ratio of S/B (S/ √ B) between γγ and di-jet final states of ∼ 10 5 (∼ 10), and since there are no updated di-jet resonance searches in the relevant region of invariant masses, we only consider γγ resonance searches. The latter represent an extensive program by both ATLAS [47][48][49] and CMS [50,51]. We have scanned the parameter space of the relevant models and compared the predicted cross-sections with the available experimental bounds. The details of the simulations are described in appendix C. We present these bounds in figure 2. We find that γγ resonance searches provide important bounds for the spin-0 NP model, being more restrictive for the pseudo-scalar case. On the other hand, for the spin-2 model, we find that the four-top cross-section is enhanced by the extra Feynman diagrams compared to the other NP scenarios. Thus for regions in parameter space with same four-top cross-section as in the spin-0 models, the γγ process has smaller cross-section in the spin-2 model. As a result the spin-2 model remains rather unconstrained by the available γγ resonance searches.
Some representative Feynman diagrams for the pp → tttt process are presented in figure 1. As discussed in section 1, the most sensitive SM four-top search to date [11] excludes at the 95% CL values of the four-top cross-section larger than approximately a factor of two larger the SM prediction (under the assumption of SM kinematics), thus still leaving enough room for light top-philic NP contributions. We show in figure 2 the contourlevels of the predicted SM+NP cross-sections in units of the SM cross-section. Simulations are in equal conditions for SM and NP, which is equivalent to using the same NLO kfactor for both scenarios. Details on the simulation process are given in appendix C. It is interesting to notice that, although LO electroweak corrections represent a minor correction of ∼ 5% to the SM cross-section, their fractional contribution is enhanced when NP effects are included. This could be expected, since it has been shown in ref. [33] that SM LO contributions of O(α 3 s α) and O(α 2 s α 2 ) are both sizable but have opposite sign, leading to a large accidental cancellation. Therefore, any NP contribution that affects the interference  terms may break this cancellation at this order, thus resulting in larger contributions to the total cross-section. As stated in ref. [33], a similar behavior is also expected at NLO, where there is also a cancellation between SM contributions of different order. In general we find that this enhancement at LO is due to the interference of the SM particles with those NP particles with the same quantum numbers. Figure 3 displays the fractional contribution of the SM+NP interference to the total four-top cross-section, in the parameter space for each of the NP models considered. For many of the relevant benchmarks defined below (see section 2.3), the inclusion of electroweak diagrams can account to a modification in the four-top cross-section of up to ∼ 30%, all at LO. The Z and Graviton models exhibit a larger four-top production cross-section dependence on the resonance mass since the NP is coupled to an unconserved current, as explained in the text. Values of the predicted cross-section above about 2×SM are excluded at the 95% CL by the latest four-top search at the LHC (under the assumption of SM kinematics). The gray shaded area represents the region excluded by γγ resonance searches. The light-blue shaded region corresponds to an interpolation since there are not available general γγ searches in the 110 GeV-150 GeV range, where the H → γγ signal is measured and no other excesses are observed. In the case of the Z and Graviton models, such γγ resonance searches do not yield significant constraints: the Z resonance cannot decay into γγ, whereas the Graviton model considered is less sensitive to γγ searches as explained in the text.

MZ' [GeV]
gZ' t (c) Figure 3. Fraction of the contribution to the total pp → tttt cross-section due to interference between SM (QCD+QED) and NP. It is important to stress that the interference is enhanced by including QED corrections, as discussed in text. In the Pseudo-scalar benchmark points the interference may reach up to ∼ −70% of the total SM LO cross-section. The interference for the Graviton benchmark points -not shown -is negligible in the relevant region.

NP benchmark points
In order to study the NP phenomenology in four-top production, we define in each NP model a set of Benchmark Points (BP) for a representative sample of NP masses and couplings still allowed by the available data. For each assumed mass (M ) in a given NP model, we define a tight (T) and a loose (L) BP for which the four-top production crosssection equals 1.5 and 2 times the SM cross-section, respectively. We denote them as BP N P T,L (M ). Since the spin-0 NP models are excluded by γγ resonance searches for masses above 65 GeV we choose the BPs below this mass value. For other NP models we consider masses of 50 GeV, 150 GeV, and 300 GeV where possible. In table 1 we display the values for the couplings and masses in each NP model, which define the BPs.

Phenomenology of non-resonant light NP in four-top production
The four-top final state at the LHC represents an exciting opportunity to search for light particles that couple preferentially to the top quark. In this section we highlight several features in four-top production that are sensitive to this kind of NP contributions.
After decay of the top quarks, a four-top event features a very busy final state with at least 12 energetic partons, including eventual neutrinos. Therefore, it is extremely challenging the kinematic reconstruction of the final state. In the case of the highest sensitivity channels, 2LSS and ML, the presence of multiple neutrinos makes very difficult the kinematic reconstruction of the leptonically decaying top quarks, although the hadronically decaying top quarks can potentially be reconstructed, particularly if they have significant boost.
For definiteness, in the following we will restrict our study to the 2LSS channel, which features two same-sign leptons, significant E miss T because of the presence of two neutrinos, and at least eight jets, four of which are b-jets. This choice is appropriate, since the 2LSS Table 1. Benchmark Points selected to study NP effects in four-top phenomenology. Subscripts T and L stand for tight and loose, for which the four-top production cross-section is 1.5 and 2 times larger than the SM cross-section, respectively.
channel is one of the most sensitive search channels, although most of our findings will also be applicable to the ML channel, which is dominated by events with exactly three leptons. We consider several inclusive observables, assuming that kinematic reconstruction is either not available, or too inefficient to be helpful. One of such observables is the total transverse energy H T , defined as the scalar sum of the transverse momentum of all jets, leptons and missing energy in the event. This observable is an trivial extension of the H jets T variable, which only the jets in the sum, which is typically used by the ATLAS and CMS collaborations in their four-top analyses. 1 However we find that H T , including more information on the event final state objects, is slightly more sensitive. In any case, we have verified that the results are qualitatively similar when using either of the two variables. We also define and investigate tt (ortt) spin correlations using the angular separation between the same-sign leptons. We study the feasibility of using these observables to distinguish NP contributions from the SM, and to discriminate among different NP scenarios.
For this study, we generate pp → tttt at LO, including all SM and NP diagrams, for each of the BPs defined in section 2.3. The generated events properly account for the helicity transmission in the decay of the two same-sign top quarks, and are showered and processed through a simplified simulation of the ATLAS detector, followed by the reconstruction of detector-level physics objects (see appendix C for details). The simulated events are then preselected using requirements based in ref. [29], which can be summarized as: exactly two same-sign leptons, H jet T > 300 GeV, E miss T > 50 GeV, and either ≥ 5 jets of which at least three are b-tagged, or ≥ 6 jets of which at least two are b-tagged.

Total transverse energy
The total transverse energy H T is a variable that provides a measure on how hard the event is, and usually a lower cut in H T is used in searches for very massive final states JHEP12(2019)080 such as those from four-top production, since it suppresses important backgrounds such as tt. The aim of studying this variable in the context of light NP contributions in four-top production is not only to distinguish NP signatures, but also to explore whether H T cuts guided by SM four-top searches may inadvertently suppress NP contributions. Figure 4 displays the H T distribution for each of the NP models considered. Interestingly, in the case of the spin-0 and spin-1 NP models, the H T distribution for SM+NP is found to be slightly softer than that expected for the SM only. This kind of deviation in the H T would typically be attributed to a background mismodeling, and thus potentially missed by current experimental searches. In contrast, the SM+NP distribution for the spin-2 NP model is distinctly harder than the SM prediction, possibly more in line with what is typically expected for ultra-heavy NP, described via an EFT, although in this case we are considering a very light particle. This can be attributed to the presence of diagrams such as in figure 1c, where there is a symmetry such that the available energy is in average equally distributed among the top quarks in the center-of-mass frame. Using Lagrange multipliers it can be shown that the maximization of the scalar sum of the top-quark 3momenta, while constrained to be all on-shell, is obtained for equally distributed energies. This this an effect that increases with the mass/energy ratio of the top quarks.

Spin correlations in four-top events
A second observable that is interesting to study in four-top events, and that does not require to reconstruct the four-top system, is the spin correlation between a pair of top quarks. It is easy to appreciate that, depending on the type of the NP particle X exchanged in figure 1a, the ttX vertex has a different Lorentz structure, which in turn affects the spin correlation between the top and antitop quarks in the same fermionic line. This effect is also transmitted to the same-sign top quarks in different fermionic lines. In this section we study the spin correlation between same-sign top quarks via their corresponding reconstructed leptons in the 2LSS channel.
We first investigate the spin correlation at the parton level by constructing an asymmetry between like and unlike same-sign top-quark helicities. Then, we select events in the 2LSS channel, and study the azimuthal separation in the laboratory frame between the reconstructed same-sign leptons, ∆φ( ± , ± ). In the following paragraphs, we present results for same-sign top quarks (tt) and for same-sign positive leptons ( + + ), but the same conclusions apply to same-sign antitop quarks (tt) and same-sign negative leptons ( − − ).
At the parton level one can quantify the spin correlation between the top quarks by defining an asymmetry between the cross-sections for Like (L) and Unlike (U ) top-quark helicities, as given by: where σ(t i t j ) denotes the cross-section for tttt production with the two top quarks (tt) having helicities i and j, respectively, summed over the antitop-quark helicities.  to A L/U tt-hel in the Scalar case, a slight negative contribution in the Pseudo-scalar case, a positive (negative) contribution in the Z case with high (low) mass, and a large positive contribution in the Graviton case. The two latter results could be expected, since the Z and Graviton contributions include only right-chiral top quarks which, at higher energy, are likely to have positive helicity.
In contrast to tt production, since tttt is a four-body final state, the translation from these top-quark polarization asymmetries to the angular separation between leptons is not straightforward. In fact, the angular separation between the top quarks, which depends on the underlying dynamics, also affects the angular separation between the final-state leptons. This distribution, together with A L/U tt-hel (see figure 5), provide some insights of what can be expected for the angular distribution of the top-quark-decay products. In figure 6 we display the azimuthal separation between the two same-sign top quarks, ∆φ(t, t), for the dominant helicity configurations in the each of the NP scenarios considered. In particular,    for the Z and Graviton modes we show the t + t + configuration because this final state represents 33% and 47% of the total cross-section, respectively. A suppression (enhancement) in the back-to-back configurations for the top quarks in these helicity configurations tends to suppress (enhance) the back-to-back configuration between their corresponding same-sign leptons.
When considering spin-correlation observables in four-top events, the simplest observable is the azimuthal separation between same-sign leptons, ∆φ( + , + ), in the 2LSS and ML channels. Figure 7 shows a comparison of the predicted ∆φ( + , + ) distribution in the 2LSS channel after preselection, between the SM and the tight benchmark points (i.e. giving σ = 1.5σ SM ) of the NP models considered. As can be appreciated, the Scalar and Pseudo-scalar models are characterized by a depletion of back-to-back SS leptons compared to the SM. In the case of Z model, there is an enhancement (depletion) of back-to-back SS leptons for high (low) mass. Surprisingly, the Graviton model does not display a signif- icant difference with respect to the SM distribution. This appears to be (at least partly) explained by an accidental cancellation of effects in the parton-level polarizations (see figure 5) and the parton-level angular distributions (see figure 6).

Discussion
The four-top signal at the LHC is a relatively new subject and the community is in the course of acquiring and processing knowledge on the many aspects of this final state. We have presented a set of results that raise new questions and challenges, which we discuss in the following paragraphs. We begin with a discussion concerning parton-level four-top production and then we examine the results concerning final state particles and detectorlevel results.
In this work we have simulated four-top production at LO, and we have applied a k-factor to estimate NLO corrections to the total cross section. However, we have found that for the studied benchmark points at LO, the interference between SM QCD+QED and NP amplitudes can account for a large fraction of the total cross-section, ∼ 30%. This suggests that a simulation of four-top production at NLO, including NP contributions, is required for more precise interpretation of experimental results in terms of the parameter space of the NP models considered. This conclusion had been envisaged in previous NLO studies of SM four-top production [33,52].
Since the reconstruction of the four-top final state is very challenging, one of the interesting observables after event selection is the distribution of the total transverse energy, H T . The presented NP scenarios with light resonances that cannot be produced on-shell, tend to produce an H T spectrum softer than the SM in the cases of spin-0 and spin-1 NP, whereas the spectrum is harder in the case of spin-2 NP. Interestingly, the latter is analogous to the effect from a heavy off-shell resonance [17]. The spin-2 NP model differs from the other models in the presence of extra Feynman diagrams that involve four-point interactions (see figure 1c). A softer H T spectrum for spin-0 and spin-1 NP could lead to a bias in the measured four-top cross-section [11], since SM kinematics is usually assumed to estimate the acceptance and shape of the final discriminating variable. Further work in this direction would be interesting. Nevertheless, our results suggest that H T is a useful observable to discriminate possible NP contributions, even in the case of new light particles.
The combined study of the parton-level polarization asymmetries and angular distributions, e.g. ∆φ( + , + ) in the 2LSS channel, is suggestive of a rich and exciting program yet to be developed related to the use of this kind of observables. Whereas the ∆φ( + + ) distribution can be used to probe spin-0 NP scenarios, the Graviton and Z models would be better probed by studying the angular separation between two reconstructed top quarks. This means that new opportunities arise if one could reconstruct the top quarks. This could be achieved with large statistics in the 2LSS channel, using some of the sophisticated -14 -

JHEP12(2019)080
reconstruction algorithms already in use by the experimental collaborations. Alternatively, in the ML channel, useful information could also be extracted from the angular separation between one lepton and the reconstructed top quark. In general, the study of polarization effects in four-top production is an attractive field that requires further investigation.
Our study has focused on the spin correlation between same-sign top quarks in the 2LSS channel. We have shown that this observable is sensitive to NP, even though these same-sign top quarks do not share a common vertex in the Feynman diagrams. We consider that a similar analysis, but in the opposite-sign dilepton channel -i.e. with leptons coming from opposite-sign top quarks, -could be potentially interesting. This has the advantage that opposite-sign top quarks can share a vertex in the Feynman diagrams, and therefore their relative spin would be sensitive to the Lorentz structure of the underlying physics. On the other hand, the 2LOS channel has significantly lower signal-to-background ratio than the 2LSS and ML channels, plus in half of the cases the opposite-sign top quarks would not share a common vertex in the Feynman diagrams, thus potentially affecting the sensitivity.
The observables studied in this work could be helpful towards establishing an eventual deviation in four-top production. The level of model discrimination of these observables indicates that they could be exploited by the experimental analyses using LHC Run 3 data and beyond. In any case, the smoking gun for a light new particle with spin-0 (H or A) or spin-2 (G) could come from pp → H/A/G → γγ resonant production searches. Even more promising could be the study of the di-photon invariant mass spectrum in pp → ttH/A/G(→ γγ) production, owing to the more favourable signal-to-background ratio. We note that the ttγγ final state has been studied so far only for a resonance in the SM Higgs mass region, and thus the extension of this search to a broader mass range would be extremely interesting. In the case of a light resonance with spin-1 (e.g. a Z ), potentially interesting processes would be pp → Z j and pp → ttZ , with Z → γγ * → γ + − . Observe that the one-loop Feynman diagrams gg → Z g and Z → ggg with tops running in the internal lines, whose features can be found in ref. [53], are key ingredients to study the previous processes. Further studies in these directions would be interesting as well.

Conclusions
We have studied the phenomenology of four-top production at the LHC for a variety of simple NP models consisting in a top-philic resonance whose mass is below the tt threshold. We have analyzed observables at parton and detector level and studied how they could be used to probe NP contributions, as well as discriminate among them.
The investigated NP models include a light Scalar, Pseudo-scalar, vector Z , and Graviton. Lorentz invariance in spin-0 resonances requires both top-quark chiralities in the interaction, whereas spin-1 and spin-2 models can be set to couple only to t R , being less constrained by SU(2) L precision tests. The Graviton non-renormalizable Lagrangian includes an extra set of four-point interactions -involving two top quarks, a Graviton and a gauge boson -which provides a distinguishing feature for the model.
We have focused our study in regions of parameter space where the four-top production cross-section is 1.5 and 2 times the SM-expected cross-section, which is consistent with -15 -JHEP12(2019)080 the latest experimental results. We have found that these regions are very sensitive to tree-level QED corrections when NP contributions are included, indicating that full NLO predictions including NP contributions would be an important development for the correct interpretation of future experimental results. We have found that available γγ resonance searches exclude masses above 65 GeV for the spin-0 models, while the spin-2 model remains largely unconstrained. In the remaining allowed parameter space, we have defined some benchmark points and studied a set of observables and their phenomenology.
We have studied the 2LSS channel, which is one of the most sensitive final state signatures being probed experimentally, We have studied the distribution of the scalar sum of all objects p T , H T , which is widely used by the experimental searches at the LHC. We have found that, in comparison to the SM, the spin-0 and spin-1 models predict a softer spectrum, whereas the spin-2 model predicts a harder spectrum. We conclude that such a change in shape towards the softer spectrum region for spin-0 and spin-1 could be translated into an incorrect estimation of the measured four-top production cross-section. On the other hand, the harder H T -spectrum in the Graviton model would be a valuable discriminating feature for this model.
Given the different Lorentz structure of the interactions in each NP model, we have also investigated the spin correlation in four-top production, and its traces in the finalstate particles. At the parton-level, we have studied the relative helicity of both top quark by defining a top-quark Like/Unlike helicity asymmetry (see eq. 3.1) and comparing the predictions from the SM and the different NP models considered. We have found negative contributions to the asymmetry for the spin-0 models and positive contributions for a high-mass Z and Graviton. In order to relate this helicity asymmetry to the azimuthal separation between same-sign leptons, ∆φ( ± , ± ), we have also studied the parton-level azimuthal separation between the same-sign top quarks. We have found that the ∆φ( ± , ± ) distribution can be particularly sensitive to spin-0 NP.
We have included a discussion section where we examine the results in the article. We consider that the available results provide in principle a set of tools that would be useful, not only to detect the presence of light non-resonant NP in four-top production, but also to determine the nature of this NP. We find that to convert clues from these observables into hard evidence, resonance searches in the γγ and ttγγ channels would be crucial in all cases, except for the spin-1 NP. In the latter case, the corroboration could come by resonance searches replacing γγ by γγ * → γ + − . This article should be considered a first approach in studying the aforementioned observables within the presented simple NP models. To have a more realistic estimation on the significance of to what extent the available results could probe the NP in four-top production, a more comprehensive analysis including NLO calculations and backgrounds should be performed on the channels and observables as described above. Nevertheless, the outcome of our work shows that such a study would be very relevant for the upcoming four-top phenomenology.
Four-top studies at experimental, phenomenological, and theoretical levels are becoming a powerful tool to investigate light top-philic NP. The community is currently at an stage of learning and developing new tools and features on this interesting final state. We expect four-top to be an important field in the forthcoming years and for the HL-LHC.

Acknowledgments
We thank Leandro Da Rold, Daniel de Florian, Mariel Estévez and Manuel Szewc for useful conversations.

A Complementary plots
We present in this appendix the plots which complement the results in the main body. Figures 8, 9, 10, 11, 12, 13 and 14 contain the same or similar analysis as those presented in text, for all the benchmark points. In particular, results for loose benchmark points are only presented in this appendix.   Δϕ(ℓ + ,ℓ + )

B Loop functions
We provide some more details about the NP models presented in section 2.

C Simulation details
Along the article we have used MadGraph5 aMC@NLO [54] for matrix level generation, Pythia [55,56] for showering, hadronization and ISR and FSR, and Delphes [57] for detector simulation. We have used Madspin [58,59] to decay top quarks while preserving the spin orientation. The NP models have been implemented through FeynRules [60].
In all cases we have included in the simulation QCD and Electroweak leading order effects. Although Electroweak corrections are a minor correction of the order ∼ 5% in SM pp → tttt production, it can account up to ∼ 30% for some studied NP Benchmark Points. In general the interference is enhanced with the Electroweak particles of the same Nature as the NP. For the sake of obtaining reasonable results in a reasonable time we have restricted the proton partons to the gluon, the valence quarks u and d, and their anti-particlesū andd. This approximation is converted into a difference in cross-section of about 1%. The spin-0 and spin-1 NP models contain 524 Feynman diagrams to produce a four-top final state in the aforementioned conditions, whereas spin-2 NP model requires 588 Feynman diagrams. These extra 64 diagrams are because of the 4-particle vertices needed to conserve gauge invariance in the spin-2 NP Lagrangian.
In section 2.2 we have simulated SM and NP processes using MadGraph5 aMC@NLO in its original tune. Since it is the ratio of NP to SM what we compute, we have not required a k-factor. We have not applied cuts on the pp → tttt process, whereas for the di-photon generation we have used the same cuts as the cited searches.
In section 3 we have simulated tops decaying to final state using Madspin, Pythia and Delphes. All simulations are at leading order using NNPDF30 lo as 0118 PDF and a k-factor of 1.26 is extracted from refs. [11,33]. For the sake of computational resources we have only decayed the tops using Madspin. We have set Delphes parameters as in ref. [61] which is tuned for CMS results in ref. [29].
Objects at the detector level are defined as follows. Electrons are required to have p T > 20 GeV and |η| < 2.5. Muons are required to have p T > 20 GeV and |η| < 2.4. Hadronically decaying taus p T > 20 GeV and |η| < 2.5. Jets are required to have p T > 40 GeV and |η| < 2.4. Whereas b-tagged jets are demanded to have p T > 25 GeV and |η| < 2.4.

C.1 Computational resources overview
Four-top is a very populated final state, and with ∼ 500 Feynman diagrams when the proton PDF is restricted to g, u,ū, d andd. If in addition this partonic state is decayed with correlated spins in at least two of the partons, the simulation becomes still more involved. When simulating only SM the simulation includes QED tree corrections. When including NP, the Feynman diagrams are increased because of new diagrams. The following table is a representative sample of the computational resources used to simulate some of the results in the manuscript.  Open Access. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.