Constraining scalar resonances with top-quark pair production at the LHC

Constraints on models which predict resonant top-quark pair production at the LHC are provided via a reinterpretation of the Standard Model (SM) particle level measurement of the top-anti-top invariant mass distribution, $m(t\bar{t})$. We make use of state-of-the-art Monte Carlo event simulation to perform a direct comparison with measurements of $m(t\bar{t})$ in the semi-leptonic channels, considering both the boosted and the resolved regime of the hadronic top decays. A simplified model to describe various scalar resonances decaying into top-quarks is considered, including CP-even and CP-odd, color-singlet and color-octet states, and the excluded regions in the respective parameter spaces are provided.

Heavy scalar resonances that decay into a pair of top quarks are predicted by several NP scenarios, in particular the Two Higgs Doublet Model (THDM), supersymmetric theories and models of dynamical EWSB. In this paper, we provide a framework to reinterpret the SM tt differential cross section measurements as exclusion limits for signatures of NP resonances decaying into tt. The framework relies on the comparison between particle-level data with state-of-the-art event simulation and the interpretation of deviations in terms of NP models.
It is based on four main ingredients 1. A Monte Carlo event generator which allows the precise and realistic description of particle-level observables.
In order to theoretically describe top-quark pair production at the LHC, we make use of state-of-the-art event simulations provided by the Sherpa [10] event-generator framework. This implies the usage of techniques to match leading and next-to-leading order QCD matrix elements with parton showers and merging different parton-multiplicity final states.
2. The precise measurement of SM processes from fiducial kinematical regions provided as differential particle-level observables by LHC experiments, and available through the Rivet package [11]. Here we used the ATLAS analyses of top-quark pair production in the boosted [12] and resolved [13] regimes. 3. A general parametrization of NP whose predictions for colliders can be computed efficiently. We adopt a Lagrangian which describes scalar resonances that can be CPeven or odd and color singlet or octet. We devise a reweighting method to describe the model prediction in the m(tt) distribution for a wide range of the parameter space in a fast and efficient manner. 4. A statistical interpretation to decide what regions of parameter space of the model are ruled out at a given confidence level. We adopt here a simplified χ 2 analysis.
A similar method to constrain NP with SM measurements in several other channels has recently been presented in Ref. [14]. These approaches are complementary to model-specific searches in the respective final states. They provide systematic methods for the theory community to derive more realistic exclusion limits for any particular model, not relying on the experiment-specific assumptions.
In the rest of the paper we explain these 4 points in detail. In Sec. II we describe the set-up of our event simulation. In Sec. III we give details on the analyses used in the boosted and the resolved regime and validate our SM predictions by comparing them to experimental data. In Sec. IV we introduce our simplified model of beyond the SM scalar resonances and describe the implementation in our simulation framework, based on an event-by-event reweighting. In Sec. V we present a statistical analysis to assess the region in parameter space accessible by the LHC experiments and provide interpretations in terms of some specific models. We finally conclude in Sec. VI.

II. SIMULATION FRAMEWORK
When searching for imprints of resonant contributions in top-quark pair production at the LHC, a detailed understanding of the SM production process is vital. In particular, as there are non-trivial interference effects between NP signals and SM amplitudes that determine the shape of the resulting top-pair invariant-mass distribution. In order to obtain realistic and reliable predictions for the top-pair production process, we make use of state-of-the-art particle-level simulations, based on higher-order matrix elements matched to parton-shower simulations and hadronization.
Our analysis focuses on observables in the semi-leptonic decay channel of top-quark pair production, i.e.
pp → tt → bbjj ν + jets , where denotes muons or electrons, ν the corresponding neutrinos, b are bottom quarks and j light quarks or gluons. These decay products and the associated radiation might be reconstructed as well-separated objects, i.e. light-flavour jets, b-jets and a lepton, or, in the boosted regime, as a large-area jet, containing the hadronic decay products, additional jets and a lepton. In either case, to realistically simulate the associated QCD activity, higher-order QCD corrections need to be considered.
To describe the SM top-pair production process we use the Sherpa event-generation framework [10,15]. We employ the techniques to match LO and NLO QCD matrix elements to Sherpa's dipole shower [16] and to merge processes of variable partonic multiplicity [17,18]. Leading-order and real-emission correction matrix elements are obtained from Comix [19]. Virtual one-loop amplitudes, contributing at NLO QCD, are obtained from the modelled at leading-order accuracy through Sherpa's decay handler, that implements Breit-Wigner smearing for the intermediate resonances and preserves spin correlations between production and decay [23]. We treat bottom-quarks as massive in the top-quark decays and the final-state parton-shower evolution [24].
To validate the SM predictions we also consider leading-order simulations in the Mad-Graph aMCNLO framework [25]. The hard-process' partonic configurations get showered and hadronized through Pythia8 [26]. The spin-correlated decays of top quarks are implemented through the MadSpin package [27]. Samples of different partonic multiplicity are merged according to the k T -MLM prescription described in [28].
For the top-quark and W -boson, the following mass values are used and the corresponding widths are calculated at leading order, assuming for the remaining electroweak input parameters m Z = 91.19 GeV and G µ = 1.16637 × 10 −5 GeV −2 . In the following section we present a comparison of our simulated predictions against ATLAS measurements and discuss their systematics. Alongside, we give details on the QCD input parameters and calculational choices used there.

III. ANALYSIS FRAMEWORK
In what follows we describe the event selections used to identify the top-quark pairproduction process, used later on to study the imprint of resonant NP contributions.
Thereby, we closely follow the strategies used by the LHC experiments. Our simulated events from Sherpa and MadGraph aMCNLO are produced in the HepMC output format [29] and passed to Rivet [11] where we implement our particle-level selections.
We consider two analyses, based on measurements performed using the ATLAS detector of the differential tt production cross sections in proton-proton collisions at √ s = 8 TeV with an integrated luminosity of L = 20.3 fb −1 [12,13]. Both analyses select events in the leptons+jets decay channel. The two measurements indicated in the following as Resolved and Boosted are optimized for different regions of phase space. The Boosted analysis, cf.
Ref. [12], is designed to enhance the selection and reconstruction efficiency of highly-boosted top quarks with transverse momentum p T > 300 GeV, that might originate from the decay of a heavy resonance with mass m > 600 GeV. In such events the decay products of the hadronic top overlap, due to the high Lorentz boost. In turn, they cannot be reconstructed as three distinct jets. The Resolved analysis, based on Ref. [13], measures the differential cross section as a function of the full kinematic spectrum of the tt system and is useful to identify and reconstruct rather light resonances.
The selection requirements are applied on leptons and jets at particle level, i.e. after hadronization. In our simulated data we discard any detector resolution, i.e. smearing effects. All the leptons used in the analyses, i.e. e, µ, ν e and ν µ must not originate from hadrons, neither directly nor through a τ -lepton decay. In this way the leptons are guar- Jets are clustered using the anti-k T algorithm [30] with a radius of R = 0.4 for small-R jets and R = 1.0 for the large-R jets, using all stable particles, excluding the selected dressed leptons, as input. All small-R jets considered during the selections are required to have p T > 25 GeV and |η| < 2.5, while for large-R jets we demand p T > 300 GeV and |η| < 2. The small-R jets are considered b-tagged if a b-hadron with p T > 5 GeV is associated to the jet through a ghost-matching procedure [31,32]. To remove most of the contribution coming from the interaction of the proton remnants, i.e. the underlying event, and to reduce the dependence on the generator, large-R jets are groomed following a trimming procedure with parameters R sub = 0.3 and f cut = 0.05, for details of the procedure see Ref. [33]. The presence of at least one small-R jet with ∆R(lepton, small-R jet)< 1.5 is required. In case more than one jet fulfills this requirement the jet with higher p T is considered as the jet originating from the leptonic top decay, dubbed lep-jet candidate. Furthermore, it is required the presence of a trimmed large-R jet with mass m R=1.0 j > 100 GeV and [34,35] between the two subjets in the last step of the jet reclustering, i.e. √ d 12 = min(p T 1 , p T 2 ) ∆R 1,2 . If more than one large-R jet fulfills these requirements the one with highest transverse momentum is considered as the had-jet candidate. The had-jet candidate must furthermore satisfy certain kinematic requirements: ∆φ(had-jet, lepton) > 2. 3 and ∆R(had-jet, lep-jet) > 1. 5

. The final requirement in the
Boosted selection is that at least one b-tagged jet in ∆R(had-jet, jet) < 1 is found or that the lep-jet candidate is b-tagged. The Resolved and Boosted event selections are summarized in Tab. I.
For the selected events the tt system is reconstructed based on the event topology: • Resolved analysis: The leptonic top is reconstructed using the b-tagged jet nearest in ∆R to the lepton and the missing-momentum four vector, the hadronic top is reconstructed using the other b-tagged jet and the two light jets with invariant mass closest to the W mass.
• Boosted analysis: The leptonic top is reconstructed using the lep-jet candidate, the lepton and the missing-momentum four vector, the had-jet candidate is directly considered as the hadronic top.
In order to validate our simulations of SM top-quark pair-production we compare our predictions against ATLAS data for the Boosted and Resolved selection, supplemented by studies of systematic variations. To begin with, we check the impact of the grooming procedure on the reconstructed hadronic-top candidate mass, i.e. the mass of the had-jet candidate in the Boosted event selection. We consider event samples from Sherpa and MadGraph aMCNLO, based on the leading-order matrix element for top-quark pair production, labelled as 0j. In these calculations, i.e. without merging-in higher-multiplicity matrix elements, we set the renormalization (µ R ) and factorization scale (µ F ) to with p T,t (p T,t ) the transverse momentum of the decaying (anti) top quark.
In Fig. 1  p T > 25 GeV, |η| < 2.5 ≥ 1 large-R jet: -∆R(lepton, small-R jet) < 1.5 -∆R(small-R jet, large-R jet) > 1.5 -∆R(large-R jet, b-tagged jet) < 1 or, -the small-R jet is b-tagged. nominal top-quark mass. However, due to parton-shower radiation and non-perturbative corrections from hadronization and underlying event the peak is rather broad and sizeable differences are observed when comparing the predictions from Sherpa and Mad-Graph aMCNLO+Pythia8. Note that the uncertainty bands shown represent the statistical uncertainty of the samples only. When applying the trimming procedure to the had-jet candidates the mass distributions agree to a much better degree, both in the tails of the distribution and the peak region. Therefore, trimming of the large-R jets significantly reduces the dependence on the generator and the details of its parton-shower formalism and the modelling of non-perturbative effects.  shower [17]. The merging-scale parameter is set to Q cut = 20 GeV. The MEPS@NLO sample combines QCD matrix elements at NLO for tt + 0, 1jet and tt + 2, 3jets at LO according to the methods described in [18,36], again using a merging scale of Q cut = 20 GeV.
Both methods share the event-wise reconstruction of an underlying jj → tt core process through consecutive clusterings of the external legs. For this reconstructed core process the renormalization and factorization scales are set to µ R = µ F = µ core , with For the reconstructed clusterings the strong coupling is evaluated at the respective splitting scale. The scale µ core is furthermore used as the resummation, i.e. parton-shower starting scale, denoted µ Q . To assess the scale uncertainty of the predictions we perform variations by common factors of 2 and 1/2 for the core scale and the local splitting scales, using the eventreweighting technique described in [37]. In the figures the resulting uncertainty estimate is represented by the red band, while the blue band indicates the statistical uncertainty.  data taken from [12]. In the right panel the reconstructed invariant mass of the tt system in the Resolved event selection is depicted, with data taken from [13].  For the boosted-top selection we show the transverse-momentum distribution of the hadronic-top candidate in the left panels of Figs. 2 and 3, respectively. Notably, both samples, i.e. the MEPS@LO and the MEPS@NLO prediction, describe the ATLAS measurement [12] very well, both in terms of the production rate and in particular concerning the shape of the distribution. For the MEPS@LO result the scale uncertainty is quite significant, reaching up to 50%. However, the dominant effect is a mere rescaling of the total production rate, the shape of the distribution stays almost unaltered. This is also observed for the MEPS@NLO sample, however, the scale uncertainty reduces to ±20%. In what follows we want to study the imprint of New Physics resonant contributions on the top-pair invariant mass distribution. To this end we currently rely on a leadingorder description of the signal, interfering with the corresponding SM amplitudes. However, from the considerations above we can conclude that the MEPS@LO calculation of the SM production process captures the dominant QCD corrections, which are of real-radiation type.
To illustrate this further, we present in Fig. 4 a comparison of MEPS@LO samples using different parton-multiplicity matrix elements for the mass and the transverse momentum of the tt system in the Boosted selection. These results get compared to the corresponding MEPS@NLO prediction described above.  greatly improves the 0jet sample. As might be expected, for the transverse momentum of the tt system, the inclusion of higher-multiplicity matrix elements improves the agreement with the MEPS@NLO result. The MEPS@LO calculation based on tt + 0, 1jet predicts a somewhat softer spectrum, i.e. is lacking configuration corresponding to multiple hard emissions. However, the bulk of the events in the Boosted selection is reasonably modeled by this simple LO merging setup and describes the data presented above very well. We will therefore rely on this setup when invoking New Physics contributions.
In the following we also introduce a simple Parton Analysis, used to quantify the effect of the NP without any smearing due to the reconstruction of the top quarks. In the Parton Analysis no cuts are applied to the events and the two top quarks are identified, before any decay, using truth-level information from the generator. It has been shown in [39] that the most general scalar extension of the SM which couples to fermions and maintains naturally small flavour changing neutral currents is provided by scalars with the same quantum numbers of the Higgs doublet or that transform as a color octet (8, 2) 1/2 under the SU(3)×SU(2)×U(1) SM gauge group. Color neutral and octet scalars arise also naturally in several models of dynamical EWSB, such as in the seminal Farhi-Susskind model [40] and models where the top is partially composite [41]. Although the specific origin of the scalar-top couplings is important, determining the relation to other couplings and their magnitudes, we here adopt a more phenomenological simplified approach relevant for top-quark pair production, in which the left-handed top is stripped off from its doublet and couples directly to the scalars. In our simplified model we assume the only light state running in the loop to be the topquark. This is a good approximation if two conditions are fulfilled: (i) -the bottom-quark contribution is suppressed; and (ii) -the extra states contributing significantly to the gluon-scalar couplings are heavy (at least as much as the scalar resonance itself). This is a good approximation in many models beyond the SM. In the THDM [42] for example, there is no new particle living at higher scale apart from the new scalar sector. Moreover, the loop of bottom-quarks is usually suppressed in the cases relevant for tt production. Specializations of the THDM such as the Minimal Supersymmetric Standard Model (MSSM) where the super-partners are heavy enough to be integrated out can also be described in this framework.
Composite models typically predict relatively degenerate spectra of first excitations, thus they can be usually described by the effective point-like interaction. Similarly, for the color octet in the model of Manohar and Wise [39] the scalars are produced purely by top and bottom loops. In some other models intermediate states much lighter than the first scalar excitations are present, e.g. top partners and stops may be light in some models of partial compositeness and SUSY -in these cases our approximation is not applicable.
Under this assumption we can describe the scalar sector interactions relevant for tt production via the following Lagrangian: It contains a CP-odd isosinglet scalar η, a CP-even isosinglet scalar σ, a CP-odd color octet scalarη and a CP-even octet scalarσ which we collectively call φ. G µν is the gluon fieldstrength tensor, G µν = 1 2 µνρσ G ρσ , λ a are the SU(3) generators and d abc = 1 4 T r[λ a λ b , λ c ] is the fully symmetric SU(3) tensor.
The top-quark loops generate form factors that describe the gluon-scalar interaction. The loop triangles contribute to the trilinear ggφ vertices in the form with Similar expressions for the color octet top-quark loop generated form factor can be found e.g. in [43].
As a matter of fact, resonant top pair production is accompanied by other signatures.
In particular, diphoton, dijet, γZ, ZZ and W + W − signatures are generated via diagrams induced by a top-quark loop, and in general by high-scale physics. Tree-level ZZ, W + W − decay channels are typically present for a scalar state, while decays into lighter fermions are typically suppressed. Color octets decays into gγ and gZ might give striking signatures. The detailed analysis of these channels is not in the scope of this work, however, we provide some qualitative discussion about the regions in parameter space where they can be competitive in sensitivity to tt search.
Loop (or anomaly) induced decays are typically suppressed and might be competitive to tt searches only for small Yukawa couplings c t . They are often the only possible decay channels for pseudo-scalars besides that into tt. As an example, consider some partial widths of a color-singlet pseudo-scalar Here we parametrize the photon interaction with η by the following gauge invariant operators with c η γ ≡ c η W + c η B . These operators also give rise to decays into weak bosons, but not competitive in sensitivity to diphoton searches (unless there is some cancellation in c W +c B ).
From the above expressions it can be noticed that the gg partial width is much larger than γγ, however, the corresponding search is not as competitive to the diphoton channel due to the clean signature of the latter.
On the other hand, scalar resonances tend to decay into weak bosons at tree level, with large contributions to their decay width and good sensitivity in the corresponding channels.

A. Model description and simulation
Our goal is to achieve accurate predictions for a wide parameter range of our generic model in an efficient and fast way. For this purpose, the Lagrangian given in eq. (5) has been implemented into the FeynRules [46] package to produce a corresponding UFO model file [47].
The required helicity amplitudes have been extracted to C++ codes via the Madgraph [48] program and incorporated in the Rivet analyses in order to perform a reweighting method and reproduce the signal line-shape. To this end, each event of the Sherpa SM event sample is given a weight, w, proportional to the ratio of the amplitudes, where |M SM | 2 is the SM amplitude squared summed and averaged over color and spin. In the numerator the amplitude M φ corresponding to the resonant diagrams depicted in Fig. 5 is added on top of the SM diagrams. The further decay of top quarks is included neglecting non-resonant diagrams. Therefore, the full process in eq. (1) -including possible extra hard radiation -is considered with full spin correlation of the top-quark decays.
We note that our signal includes not only the purely resonant contribution. The complete squared amplitude can be split into three contributions: The last term defines the SM background (B M ), the pure signal (S M ) and the interference between signal and SM (I M ).
We use as the test observable the m(tt) distribution of the signal hypothesis H normalized bin-by-bin to the SM QCD prediction, cross section subtracted by the SM prediction. Such normalized distribution is less affected by systematic errors, i.e. theoretical uncertainties [49].
In order to assess the importance of the interference we study both the full signal including interference dσ S+I /dm and the pure signal hypothesis neglecting interference dσ S /dm. To simplify the notation in the remaining of the text we use the following definitions: Interference between signal (Fig. 5) and QCD diagrams are known to be important in this process. In fact, they can completely change the line-shape of the resonance from a pure Breit-Wigner peak to a peak-dip structure, or even dip-peak, pure dip or an enhanced peak [50][51][52][53][54][55]. QCD corrections to this effect have recently been computed [56][57][58] and shown to be important. A pilot experimental analysis investigating such interference effects has been presented recently [59].
The form factors in eq. (7) have been implemented in the helicity amplitudes used in the reweighting step. However, the corresponding box diagram contributing to the four-gluonscalar coupling was kept as an effective vertex without momentum dependence. For the color octet the form factor is approximated by a fixed momentum flowing through the loop that is equal to the mass of the resonance. The interference between top-quark loops and point-like interactions is also manifest in the calculation.
Higher-order QCD corrections are partially taken into account through the radiation of extra gluons in the MEPS@LO simulation. The contribution from real-emission ttj matrix elements also get reweighted with the NP theory hypotheses.
We note however that the method neglects the signals' color-singlet color flow contribution when attaching parton showers, which affects the subsequent radiation pattern only.
We nevertheless found that these effects are small in the description of the top-pair mass distribution. In Fig. 6

V. RESULTS
Resonant top-quark pair production at the LHC has been analyzed for several of the models mentioned above already. Color neutral resonances decaying into tt have been studied in several works for a large number of models [50,51,[53][54][55], even including interference effects at NLO in QCD [56][57][58]. The case of a color-octet signal has been considered in [43,52,60,61], also considering other production channels, e.g. via bb initial states, or even double scalar production [62][63][64]. Our approach differs from previous studies because we adopt the strategy of directly comparing to data which has been shown to agree well with the SM prediction, and therefore, can be used to put direct limits on the model parameters, in the same spirit as [14]. Indeed, the recent ATLAS measurement of the top-quark pair differential cross section at √ s = 13 TeV shows good agreement with various SM Monte Carlo generators [65]. However, there are no measurements of the tt invariant mass in the boosted regime at this energy yet. Moreover, the uncertainties are still quite large, since only the 2015 data, corresponding to 3.2 fb −1 , were used, but we expect that an update of the analysis will be available in the near future, with improved systematics and statistical uncertainty (comparable to the ones presented in this paper) allowing to derive real exclusion limits. We assume in what follows that data will be well described by the SM expectation, and take the SM prediction from Sherpa as mock data.
The method proposed allows theorists to derive realistic exclusion limits on a variety of NP scenarios without a dedicated and expensive experimental analysis. It opens a new path to search for NP, with the experiments providing precision measurements of SM processes.
With respect to dedicated experimental searches, it can serve as check and as an alternative (less-expensive) approach to look for more general parametrizations of deviations caused by New Physics. For instance, in the ATLAS and CMS collaborations' analyses [8,9,59,66,67], only a leptophobic Z' bosons (present for instance in topcolor scenarios), a Kaluza-Klein excitation of the gluon and heavy states in THDM were searched for. Moreover, interference effects were considered only in Ref. [59]. With our technique we are able to provide limits for a whole wealth of models.
In order to assess the possibility to observe the signals described above we perform a simple χ 2 analysis using the bins of the r distribution. We consider the mass window m φ − 200 GeV < m(tt) < m φ + 200 GeV and compute with N the number of bins taken into account, according to the assumed resolution of the measurement. r i (H) is the r(H) distribution integrated over bin i and H is the hypothesis (either S or S + I). σ 2 i is the variance on each bin of the distribution. The variance is derived according to the rules of propagation of uncertainties and is estimated by the second for systematic uncertainties of experimental sources, and the third for theoretical uncertainties. We assume a flat distribution for theory and systematic uncertainty, and that statistical uncertainties are dominated by the background, with a small ratio signal over background. We take T H = 1% for both H σ = S σ and H σ = S σ + I σ , assuming other errors are strongly correlated and will be canceled when taking the ratio distribution. The experimental uncertainty is more important and we consider three benchmark estimates for SYS : 1. In Ref. [59] the total systematics on the background were estimated as 10% and 11%.
2. As an optimistic scenario we vary it to lower values considering a future improved understanding of the uncertainties and the reduction in uncertainty associated to normalization. Since we are using a normalized distribution many of the uncertainties estimated in the previous benchmark are strongly correlated and will be canceled out.
3. As the most optimistic case we assume experimental uncertainties can be drastically reduced to the level of theoretical, which according to Ref. [49] results in SYS = 1% − 2%.
We consider N = 1 for a bad resolution case, assuming the experiment can resolve only the full window of 400 GeV in m(tt), and N = 10 assuming a mass resolution in m(tt) of 40 GeV.
We consider χ 2 ≥ 2 as a criterion for exclusion, which corresponds roughly to an exclusion at 95% of confidence level.
This simple analysis is intended to be a first approximation to a full statistical data analysis that will be carried out eventually. In particular we assume the same uncertainty for every bin without correlation between them, and we assume only two cases of resolution independent of the bin. In the following we discuss some benchmark scenarios and the respective results.
A. Pseudo-scalar color octet The first scenario we consider is when the resonance φ represents a pseudo-scalar color octet ( η) with total width dominated by the decays to pairs of tops and gluons In Fig. 7 we show the resulting r distribution assuming a color octet resonance with mass mη = 500 GeV and the parameters c t = 1, c g = 1 (left) and c g = −1 (right) at parton level, i.e. using the Parton Analysis described in sec. (III). We show both the full line-shape, which comprises signal and interference with QCD background (S+I), and the pure signal (S) for comparison. The importance of taking into account interference effects can clearly be noticed. Similarly, in Fig. 8, we present the effect of a resonance with mass mη = 1700 GeV and couplings c t = 1, c g = 1 (left) and c g = −1 (right), reconstructed using the Boosted Analysis.
The excess reaches more than 10%, which indicates that even a pessimistic estimate of the uncertainties is sufficient to exclude the existence of this state for values of c g of order 1.
We thus use the most pessimistic value for the systematic error, SYS = 10% − 15%. In Fig. 9 the corresponding exclusion limits are shown, assuming a fixed value of c t = 1.
The bands correspond to a systematic uncertainty on the measurement running from 10% to 15%. The limits are evaluated considering the interference effect (dashed lines) or neglecting it (continuous lines). The interference has a significant effect in the low mass region (mη < We expect striking signatures in other channels, but little has been studied. For instance, in the analysis of γ+jets in Ref. [45] a color octet has not been considered.

B. Pseudo-scalar singlet
For the benchmark scenario of a pseudo-scalar color singlet we again assume the resonance' width is dominated by the top and gluon decays, as in eq. (21).
We show in Fig. 10  In Fig. 11 we show the exclusion limits in the (m η , c g ) parameter space plane for c t = 1.
The band represents the different assumptions for the systematic uncertainty, 5% and 10%. For very low masses the Resolved analysis can be slightly more powerful than the Boosted.
In Fig. 13 on the left we show an example of a line-shape and on the right the exclusion limit provided by the Resolved analysis. Compared to fig. (11) it can be noticed that the low mass region m η 600 GeV can be better covered by the Resolved selection. We note as well that the case of negative c g is less excluded due to the fact that larger cancellations between top-quark loop and effective vertex happens for these masses. Exclusion limit (χ 2 = 2) in (m η , c g ) parameter space for c t = 1. The color scheme is the same as in Fig. 11. In both panels the Resolved analysis has been employed.
Diphoton and dijet searches might be relevant in extreme regions of parameter space, i.e.
for very small c t ∼ 0.2, and large masses, due to the dependence of the γγ and gg partial widths on m 3 as opposed to the linear dependence of the tt decay width. In fig. (14) we show the 95%CL excluded region derived from the limits provided by the ATLAS collaboration in the dijet search [68]. We used the case σ G /m G = 0 and assumed an acceptance of 50%.
In the same figure we show the 95%CL excluded region in the diphoton channel using the exclusion limits by the ATLAS analysis in Ref. [69]. We used the case Γ X /M X = 6% and the spin-0 selection. To derive cross sections we used the N 3 LO result for Higgs production cross section σ h [70] and rescale by the LO decay width, Γ η→gg is given in eq. (13) and the form factors in eqs. (8)(9)(10). The shaded area in the figure represents the region where σ η ×BR is larger than the excluded line in the respective references, and BR is the corresponding branching ratios. We can notice that these channels get competitive in sensitivity to tt analysis at low c t and large mass, but only if c γ is particularly large. In particular, even for c t = 1, for m > 3 TeV the dijet search seems to be more sensitive to New Physics.

Interpretation for Composite Higgs models with Top Partial Compositeness
As an ultra-violet realization of the pseudo-scalar scenario we consider the composite models M3, M8 and M9 of Ref. [41]. These models are constituted by two additional confining fermions, ψ and χ, which form several composite states among which a top partner that can generate a mass to the top quarks through the partial-compositeness mechanism.
In addition, they present two iso-singlet pseudo-scalar mass eigenstates a and η . In general, the observation of such pseudo-scalar state decaying into top quarks can shed light on the mechanism of fermion mass generation [71]. These models present extra parameters which determine the couplings, given by a pair of integers (n ψ , n ξ ) and the relation between the mixing angle α and the ratio of scales and U(1) charges, ζ. We do not enter a discussion of the details of these the models and their parameters here but invite the reader to consult Ref. [41]. We choose α = ζ and the values of (n ψ , n ξ ) which provide the largest couplings to the tops, (n ψ , n ξ ) = (2, 0), (−4, 2) and (4, 2). We neglect contributions to the resonance width from the decays into Z, W and γ, which are sub-dominant. The relevant couplings are summarized in Tab. II.
In Fig. 15 we show the value of c t and c g for each model together with the exclusion region

C. Broad scalar color singlet
In this benchmark scenario we assume a CP-even color-singlet scalar that can, apart from top quarks and gluons, also decay into other particles and is thus much broader than the previous scenarios. We choose a total width of 20% of the resonance mass Γ σ = 20% m σ .
The rationale for choosing a larger width is the fact that the scalar tends to decay also to weak bosons. Indeed, we expect a large sensitivity in this decay channel which might be competitive w.r.t. top pair production.
In this scenario the signal is very weak and thus hard to be observed unless the systematic uncertainty is improved to values below 5% or higher values of c g > 3 are considered. In Fig. 16 on the left we show the line-shape for m σ = 900 GeV, c t = c g = 1. It can be noticed that the yields are always below 5%. On the right panel we show the χ 2 10 = 2 contours in the (m η , c g ) parameter space plane for c t = 1. Varying the assumed systematic uncertainties between SYS = 1% − 2% determines the band of the exclusion limit. The integrated luminosities are L = 20 fb −1 (blue line) and L = 300 fb −1 (black). Limits are given considering interference (dashed lines) and neglecting it (solid lines). A large interference effect can be noticed, which is in fact larger than the pure signal. and c t = 1 for such scalar state. The color scheme is the same as in Fig. 11. In both panels the Boosted analysis have been adopted.

VI. CONCLUSION
In this work we have provided a framework to reinterpret the SM tt differential cross section measurements in terms of exclusion limits for signatures of NP scalar resonances decaying into tt. The method relies on the detailed simulation of the SM prediction at particle level with the Sherpa Monte Carlo, the subsequent analysis in the Rivet framework, which can be directly compared with the measured distributions provided by the experimental collaborations, a modeling of the NP scenarios efficient enough to allow a scan over a large range in parameter space, and finally a statistical analysis to determine the excluded regions.
In the simulation of top-pair production we take into account higher-order QCD corrections through matching LO or NLO matrix elements to parton showers and merging partonic processes of varying multiplicity. To validate our simulation we compare to data from the ATLAS collaboration, finding very good agreement. As New Physics contributions we consider CP-even and CP-odd scalar resonances, being either color-singlets or octets. To model the signal we devise an efficient and fast reweighting method allowing to scan large regions of parameter space without the need of full re-simulation and re-analysis for each parameter point. For our simplified model we have derived exclusion limits based on a simple χ 2 analysis, that can subsequently be used to set limits on other specific models, and we consider a model of partial compositness as an example. We showed the importance of properly accounting for interference between the New Physics signal and the SM background in setting the exclusion limit, as well as of using a full line-shape analysis which is not necessarily a simple Breit-Wigner shape due to the interference effects.
By confronting SM precision measurements with hypotheses for New Physics models stringent exclusion limits on the parameters of the latter can be obtained, providing complementary sensitivity to direct searches. The methodology laid out here can be readily applied to other observables than the top-pair invariant mass considered here. It relies on a solid understanding of the respective SM expectation and the uncertainties related to the theoretical predictions and the experimental data.