On two-body and three-body spin correlations in leptonic $t\bar{t}Z$ production and anomalous couplings at the LHC

We study the anomalous $t\bar{t}Z$ couplings in the $t\bar{t}Z$ production in leptonic final state at the $13$ TeV LHC. We use the polarizations of top quarks and $Z$ boson, two-body and three-body spin correlations among the top quarks and $Z$ boson, and the cross section to probe the anomalous couplings. We estimate one parameter and simultaneous limits on the couplings of the effective vertex as well as the effective operators for a set of luminosities $150$ fb$^{-1}$, $300$ fb$^{-1}$, $1000$ fb$^{-1}$, and $3000$ fb$^{-1}$. The polarizations and the spin correlations are found to be helpful on top of the cross section to better constrain the anomalous couplings.


Introduction
The standard model (SM) of particle physics, though well established, requires corrections not only due to incompatibility with the experimental evidence of non zero neutrino mass, dark matter, and Baryogenesis but also the theoretical issues such as the hierarchy of mass scales, the strong CP problem, etc. Anomalies in recent experiments such as the muon (g − 2) anomaly [1], and W -mass anomalies [2], along with few fluctuations [3][4][5][6], have strengthened the requirement to go beyond the SM (BSM), although no direct evidence has been observed for any BSM degrees of freedom at experiments. Precision measurements at the electroweak (EW) scale are, thus, essential to look for the remnant of BSM physics sitting at a high energy scale. Top quark interactions play a key role in exploring BSM theories because of their heavy mass, which is the same order as the electroweak scale. Because of the almost bare nature of the top quark, i.e., it decays before hadronization, observables associated with or induced by its spins are useful tools in the precision measurement of the top quark interaction.
In this study, we use the polarizations of top quarks and Z boson, spin correlations of tt pair, tZ pair,tZ pair, including ttZ triplet, and the total cross section to probe anomalous ttZ interaction in the ttZ production process at the 13 TeV LHC. We work in the fully leptonic final state, i.e., in 4l + 2b + E T final state, for better reconstruction of three-body (t-t-Z) spin correlation. We then extrapolate the result by combining all semi-leptonic channels. We use the effective vertex factor parameterization for the anomalous ttZ interaction [63,108,109] to investigate them and translate their limit into the higher dimensional effective operators [63,105,108] to compare with the existing studies [89-91, 110, 111]. The polarizations and spin correlations provide complementary sensitivity to the anomalous ttZ interaction to the existing approaches. The use of a large number of polarization and spin correlation observables allows us to extract more information from a given measurement with low statistical correlation and may eventually help to isolate the contribution of individual interaction parameters.
The rest of the article is organized as follows. In section 2, we present the formalism for the three-body spin correlations among t,t, and Z and the method to obtain them in experiments or in a Monte-Carlo (MC) simulation. We discuss the signal process in section 3, along with the effect of neutrino reconstruction on the polarizations and spin correlations in the SM. In section 4, we investigate the effect of anomalous ttZ interaction on the observables, followed by extracting simultaneous limits on them. Finally, we summarize in section 5.
Asymmetries for the polarizations of t,t and Z, and the spin correlations for t-t and t/t-Z are described in Ref. [112]. These formulas can be used to estimate the three-body spin correlations with real data from experiments or with events generated by a Monte-Carlo simulation. In the next section, we calculate these polarization and spin correlation parameters from their asymmetries with events generated at MADGRAPH5 aMC@NLO [114] after reconstructing the two missing neutrinos.

Signal process, polarizations and spin correlations in the SM
We are interested in the signal topology of ttZ production in the fully leptonic decay channel at the 13 TeV LHC. The ttZ process comprises gg and qq initial beams coming from proton as partons, see Fig. 1 for the representative Feynman diagrams at leading order (LO), where a Z radiation from t leg is also assumed implicitly. The production cross section of the ttZ process is estimated to be σ LO ttZ 0.59 fb at LO for √ s = 13 TeV with the package MADGRAPH5 aMC@NLO v2.7.3, while the experimentally measured cross section by CMS [90] is 0.95 ± 0.05 stat. + 0.06 syst. , much larger than the LO estimate. We thus estimate the ttZ production cross section at next-to-leading order (NLO) in QCD in MADGRAPH5 aMC@NLO v2.7.3; the NLO cross section is σ NLO ttZ 0.86. Thus an NLO to LO factor of κ NLO = 1.46 will be used for the SM process including the decay later on [92]. We use NNPDF31 [115] set for the parton distribution functions (PDFs) with α s (m Z ) = 0.118. A fixed renormalization (µ R ) and factorization (µ F ) of µ F = µ R = m t + m Z /2 is used along with the following SM input parameters [116]:  Signal events (100 million) for the ttZ production and their leptonic decays are generated in MADGRAPH5 aMC@NLO v2.7.3 at LO with generation level cuts of with the input parameters discussed above. We generated the events in MADGRAPH5 aMC@NLO as i.e., tops are decayed in muonic flavors, while the Z boson is decayed in electronic flavor for simplicity. A flavor factor of 8 for the complete leptonic channel is accounted for in the analysis. The parton level events are then passed to PYTHIA8 [117] for showering and hadronization followed by fast detector simulation by Delphes-3.5.0 [118]. The events are selected at the Delphes level with at least two oppositely charged muons, two oppositely charged electrons, and two b-tagged jets using the default isolation criteria, p T and η cuts given by The detection efficiency of the 2b + 2µ + 2e + E T events with the above selection criteria is about ε sel. 10.2%. The estimated number of events in a fully leptonic channel, i.e., including the flavor factor, adjusted with an NLO k-factor of 1.46, after the selection criteria is about N SM = 403 for an integrated luminosity of L = 3000 fb −1 . These events are then used to calculate all the polarizations and spin correlations and their asymmetries after reconstructing the two missing neutrinos needed to obtain the top quarks' rest frame. The method for reconstruction of the two neutrinos is described in the following section, followed by comparing the reconstructed variables to the truth level variables. We reconstruct the two neutrinos with detector level events for the polarizations and spin correlations in the ttZ process in the decay channel given in Eq. (3.6) as follows [81,119,120]. At first, the two b-quarks are assigned with the correct lepton (here muon) such that m 2 bµ + + m 2 bµ − is minimum. The four momenta of the two neutrinos are then solved using the constraints,

Reconstruction of the neutrinos
(3.8)  These constraints provide multiple sets of solutions for the components of neutrinos' momenta consisting of real as well as imaginary values due to the quadratic nature of the constraint equations. In case all solutions are imaginary, the values of m W and m t are varied 1000 times following the Gaussian distribution with mean at m W and m t and variance 10 GeV and 40 GeV, respectively, until at least one set of real solution for neutrinos momenta is obtained. The events are rejected if no set of real solutions is found within the iteration of 1000, which is only about 0.2%. In an event consisting of several real sets of solutions for neutrinos momenta, the set is chosen with minimum m tt .
We study the goodness of the reconstruction method of the neutrinos in the SM by comparing the detector level results with the truth level results for the angular variables related to polarizations and spin correlations of t,t and Z, as described in section 2. Normalized distributions for some variables are shown in Fig. 2 for the polarizations and two-body spin correlations of the top quark and Z boson, and in Fig. 3 for three-body spin correlations as representative for the following three cases.
I. Parton-Truth: In this method, observables are calculated with the parton level events with MC truth information of the final state particles, including the neutrinos.
II. Parton-Reco: In this method, we use the parton level events, but the two neutrinos are reconstructed using truth level pairing of b-quarks.
III. Delphes-Reco: Here, we use the events selected at the Delphes detector simulations to reconstruct the neutrinos using the above mentioned approach.
The distributions for the polarizations of the top quark seem to be distorted in Parton-Reco compared to the Parton-Truth case, see  Table A in appendix A for completeness. Though we can recover some of the polarization and spin correlation variables with good accuracy, we do not obtain a good accuracy for many variables after reconstructing the neutrinos at the detector level simulations. Nevertheless, for the sake of realistic analysis, we will calculate the polarization and spin correlation asymmetries at the Delphes level by reconstructing the missing neutrinos with the above mentioned method with anomalous couplings and higher dimensional operators. We investigate the new physics effect on the polarizations and spin correlations in the following section.
Z boson reconstruction and reference z-axis One needs to identify the leptons coming from Z in order to reconstruct the Z boson to evaluate its polarizations and spin correlations with the top quarks. The 3e + µ and 3µ + e channels suffer a two-fold ambiguity, while the 4µ and 4e channels suffer four fold-ambiguity for the identification of Z candidate leptons. Nevertheless, by demanding a same flavor oppositely charged lepton pair with an invariant mass closest to m Z , these ambiguities can be resolved with reasonable accuracy. We use the 2e + 2µ channel as the proxy for the 4l final state for simplicity. We need a reference z-axis and x-z plane to measure the angular orientations of the leptons for the polarizations and spin correlations. We consider the direction of the reconstructed boost as the proxy for the positive z-axis. The t-t production plane can be safely considered as the x-z plane or the φ = 0 plane to estimate polarizations and spin correlations.

Probe of anomalous ttZ interaction
In this work, we are interested in studying the anomalous interactions, i.e., a contribution that can be received from beyond the SM, of t,t, and Z in the ttZ production process. We neglect the effect of the four-point contact interaction of four quarks that can enter into the ttZ production at the LHC, as these are better constrained in tt production process. The ttZ interaction Lagrangian, including new physics, is generally parameterized in a model independent way as [63,108,109], −0.60. The couplings C V 2 and C A 2 (CP-odd) are the source of weak magnetic and electric dipole moments of the top quark, respectively and are highly suppressed in the SM [102,104,108].
In the effective field theory (EFT) approach with higher dimension operators (O), the interaction Lagrangian is expressed as, with index n summing over higher dimensions (> 4) and index i summing over all the operators in a givendimension; C i are the Wilson coefficients (WCs) corresponding to operator O i . The Λ is the cut-off energy scale up to which the EFT is valid. The gauge invariant operators, made of the SM fields, are low energy remnant of some new physics theory at a higher energy scale (> Λ) with heavy fields, i.e., the heavy degrees of freedom are integrated out to the WCs at low energy. The anomalous ttZ interactions in Eq. (4.1) receive contribution from the following dimension-6 operators [63,105,108], Here, i, j are the flavor indices; Q is the left-handed quark doublet and u are the right-handed singlet quark; τ I are the Pauli matrices, ϕ is the Higgs doublet with its dual ϕ = iτ 2 ϕ ; B I µν and W I µν are the U(1) Y and SU(2) L filed strength tensor, respectively; D µ ( ← − D µ ) is the covariant derivative acting on the right (left) and The couplings in Eq. (4.1) are related to the WCs of the operators listed in Eq. (4.3) as [63,108,121], ϕQ . (4.5) Here, θ W is the Weinberg mixing angle, and v 246 GeV is the vacuum expectation value (VEV) of the Higgs. We define ∆C 1,SM and treat them as anomalous couplings in the rest of the article.  With the setup of anomalous ttZ couplings and EFT operators discussed above, we proceed to probe them in our desired channel of 4l + 2b + E T final state with the polarization and spin correlation asymmetries along with the total rate (expected number of events with selection level cuts). We generated events (10 million) in MADGRAPH5 aMC@NLO of the process in Eq. (3.6) as a proxy for the 4l + 2b + E T final state for a set of anomalous couplings in Eq. (4.1) validated with FeynRules [122] for the UFO model with the same set up of input parameters (SM inputs in Eq. (3.1), µ F , µ R , and PDFs) and generation level cuts (Eq. (3.5)) as discussed in Section 3. The parton level events are then passed through PYTHIA8 for showering and hadronization followed by detector simulation in Delphes. We, first, study the effect of the anomalous couplings on the   1)), proide higher excess in events after the peak compared to ∆C V /A 1 with no momentum dependence. The excess in events is larger at the peak, and thus no rectangular cuts on the √ŝ will be able to enhance the signal to background ratios. The case is true for E T and p T (Z) along with the p T s of all the particles, although not shown. We, thus, do not impose any rectangular cuts on the kinematic variables other than the selection cuts for our analysis; this will also help us not to diminish the statistics for the asymmetries. However, we use four bins in the p T (Z) for the cross section using the fact that C (4.6)

Normalized Events
We will be using the same NLO to LO k-factor of 1.46 for the four bins in p T (Z), although it is higher for higher p T (Z) [92] . For the asymmetries, however, we use the un-binned cross section to avoid losing the statistics. We now investigate the effect of anomalous couplings on the angular distributions corresponding to polarizations and spin correlations, which are shown in Fig. 5 and Fig. 6, respectively as representative with the same benchmarks for anomalous couplings as used for kinematic variables. The top quark polarization (p t z ) (Fig. 5 left-top panel) shows deviation only for the ∆C V 1 benchmark, while p Z z (Fig. 5 right- Fig. 6. The three body spin correlations shown in Fig. 6 (excluding left-top panel) show visible deviation from the SM for all the anomalous benchmark points as representative of many such spin correlation variables which are not shown. We use all the polarization and spin correlation variables to study the sensitivity to the anomalous couplings and estimate their limits in the following subsection. We use the Delphes level events after selection cuts, given in Eq. (3.7), to calculate all the asymmetries for the polarizations and spin correlations discussed in Section 2 for a set of anomalous couplings in order to obtain a semi-analytical expression for the observables. We use twenty six such benchmark couplings (five linear for each ∆C 1 , four linear for each C 2 , four for ∆C A 1 -∆C V 1 cross terms, and four for C A 2 -C V 2 cross terms) to obtain the semi-analytical expressions for the cross sections in four bins (Eq. (4.6) and all asymmetries. For the cross sections, the following expression is used to fit the data [48]:

Constraints on the anomalous couplings and the operators
, σ i as the linear/interference terms for couplings C i , and σ i j as the quadratic or cross terms for couplings C i and C j . The numerators of the asymmetries (∆σ ) are fitted separately using the same form of the expression in Eq. (4.7) and used in the asymmetries as With the obtained semi-analytical expression for the observables in hand, we study the sensitivity of all observables to the anomalous couplings by varying one parameter at a time in terms of χ 2 . The χ 2 for a coupling C i is defined as follows, where N is the total number of observable O, and δ O is the estimated error in O. The error for the cross section (σ ) and asymmetries (A i ) are respectively with L as the integrated luminosity; ε σ and ε A are the systematic uncertainty for the cross section and the asymmetries, respectively. We assume a flat systematic uncertainty of 10% for the cross sections, i.e., ε σ = 0.1 [90] for all four bins in the four-lepton channel. For asymmetries, we use an absolute uncertainty of ε A = 0.01 [81] as a conservative choice. The sensitivity of polarization, spin correlation parameters, and their combinations are studied in terms of χ 2 , and they are shown in Fig. 7  couplings. The spin correlation asymmetries show a smaller effect compared to the polarization asymmetries for an obvious reason related to the relation of the asymmetries to the polarization and spin correlation parameters. There are extra factors in the spin correlation asymmetries compared to the polarization asymmetries (see Ref. [112] for details), reducing the sensitivity to anomalous couplings compared to polarization asymmetries.
We now compute the χ 2 for the cross sections combining all four bins (XSec), XSec combined with the polarizations and spin correlations successively and show them in Fig. 8 by varying one parameter at a time for the comparison. The sensitivity or the χ 2 for the cross section in the binned case is better compared to the un-binned cross section, see appendix B. The dashed horizontal lines at χ 2 = 3.84 indicate the 95% C.L. bound on the couplings. The polarizations play a crucial role compared to the cross section in constraining the limits on the couplings, particularly for the couplings ∆C V /A 1 . The polarizations improve the limits on the couplings better on the positive side when added to the cross section for both ∆C V 1 and ∆C A 1 . The cross sections create two patches for ∆C A 1 within 95% C.L. limit; The dip in the right patch reduces when polarizations and correlations are added successively, see right-top panel in Fig. 8. For the couplings C V /A 2 , the cross sections dominate in constraining them; the polarizations and correlations improve the limits a little on top of the cross section. These behavior are further illustrated in the 95% C.L. contours (χ 2 = 5.991 [123]) in ∆C V 1 -∆C A 1 and C V 2 -C A 2 planes in Fig. 8, bottom-panel. The cross section allows large values of simultaneous couplings for ∆C V 1 and ∆C A 1 , e.g., ∆C V 1 = −1.2 and ∆C A 1 = 1.5. This is due to a large cancellation of cross sections for ∆C V 1 and ∆C A 1 . The polarizations reduce the allowed parameter space to two narrow regions in the ∆C A 1 direction when added to the cross section, one of them includes the SM (0, 0) point. The spin correlations further reduce the two regions of parameter space; the region not containing the SM point shrinks more, making less allowable region at 95% C.L. limit. In the C V 2 -C A 2 plane, however, the regions are circular, and the polarizations and spin correlations have a comparatively smaller effect in shrinking the region compared to ∆C V 1 -∆C A 1 plane. We computed the one parameter 95% C.L. limit on the couplings using cross sections, polarizations, and spin correlations for four sets of integrated luminosity, such as L = 150 fb −1 , 300 fb −1 , 1000 fb −1 , and 3000 fb −1 , and listed them in Table 1. We also obtained the limits on the operator's Wilson coefficients by changing the expression for the observable using relation given in Eq. (4.4) and listed them for the same set of luminosities in Table 1. For a complete analysis, one could use all the leptonic channels of the ttZ process provid-ing better limits on the couplings. All the polarizations and spin correlations can be obtained in different decay channels as follows: • Z → l + l − , t/t → hadronic (2l) : Only the Z polarizations are obtained in this case, • Z → l + l − , t → leptonic,t hadronic (3l): Top quark polarizations are obtained along with the t-Z spin correlations by reconstructing the missing neutrino [48]. Thet polarizations andt-Z spin correlations are obtained by reversing the top and anti-top decay, • Fully leptonic (4l): In this case, tt and ttZ spin correlations are obtained.
The hadronic Z-decays are avoided to reconstruct the ttZ topology better. We estimated the cross section and the detection efficiency for the 2l and 3l topology in the SM and adjusted the statistics for all the polarizations and spin correlations in accordance with the above categorization. The cross sections in 2l and 3l channels increase by a factor of ∼ 9.9 and ∼ 2.6 from the 4l channel, respectively. We then estimate the one parameter projected limits at 95% C.L. on the couplings by combining the three channels, i.e., in the 2l + 3l + 4l channel for the set of luminosity of L = 150 fb −1 , 300 fb −1 , 1000 fb −1 , and 3000 fb −1 and listed them in Table 2. The limits in 2l + 3l + 4l channels are tighter roughly by a factor of 2 compared to the 4l channel. We use systematic uncertainties of 0.13 and 0.16 for the cross sections in the 3l and 2l channels, respectively, and the same uncertainty of 0.01 for the asymmetries as used for the 4l channel. We also redraw the 95% C.L. contour for the 2l + 3l + 4l channel in ∆C V 1 -∆C A 1 plane at L = 3000 fb −1 to see the improvement, see Fig. 9. The parameter space is tighter compared to only the 4l channel, as depicted in Fig. 8. Unlike the 4l channel, the cross sections divide the parameter space into two regions. The region not containing the SM point is smaller than the point containing the SM point when polarizations are added to the cross sections. The region not containing the SM point further disappears when spin correlations come into play, allowing the parameter space only in the neighborhood of the SM point.
Simultaneous limits : We have estimated the limits above by varying one parameter at a time, fixing others to their SM values. More realistic bounds on the couplings can be obtained by simultaneously varying all the parameters followed by marginalizing them. Here, we extract simultaneous limits on the couplings using the Markov-Chain-Monte-Carlo (MCMC) method and GetDist [124] package for marginalization. The simultaneous 95% C.L. limits in 4l + 3l + 2l channel are shown in Table 3 for the same set of luminosity L = 150 fb −1 , 300 fb −1 , 1000 fb −1 , and 3000 fb −1 . The simultaneous limits are diluted by roughly a factor of 2 for almost all the couplings compared to the one parameter limits ( Table 2). The corresponding marginalized Bayesian Credible Interval (BCI) at 95% C.L. are shown for the benchmark luminosities in Fig. 10 in the ∆C V 1 -∆C A 1 and C V 2 -C A 2 planes. As the luminosity increases to 300 fb −1 from 150 fb −1 , the region of parameter space get divided along ∆C A 1 direction in ∆C V 1 -∆C A 1 plane. The two region shrinks at 1000 fb −1 further, and finally, we only have one region centering SM point at 3000 fb −1 . This behavior is translated to the C ϕt -C − ϕQ plane. The contours in the C V 2 -C A 2 plane (C tZ -C I tZ plane) shrink as the luminosity increases remaining circular with the SM point at the center.   Figure 9: The two-parameter 95% C.L. contours in ∆C V 1 -∆C A 1 combining all the leptonic channel, i.e., ttZ : 2l + 3l + 4l channels for √ s = 13 TeV and integrated luminosity L = 3000 fb −1 . The legends are the same as in Fig. 8.
Effect of systematic uncertainties : The simultaneous limits change due to changes in systematic uncertainties. Increasing the systematic uncertainties loosen the limits on the couplings. A comparison of the limits is shown in 95% C.L. BCI contours in Fig. 11 for different combinations of systematic uncertainties for cross sections and asymmetries at 3000 fb −1 luminosity. The contours (dashed/red lines) get tightened up by little when systematic uncertainties for cross sections are considered to be 0.1 for all 4l, 3l and 2l channel keeping ε A = 0.01 as compared to the benchmark systematic uncertainties of ε σ (4l, 3l, 2l) = (0.10, 0.13, 0.16), ε A = 0.01 (solid/green lines) in both ∆C V 1 -∆C A 1 and C V 2 -C A 2 planes. The ε A has comparatively large effects on the limits; The contours enlarge for ε A = 0.02 keeping the ε σ s to their benchmark values. A second region way from the SM point appears along the ∆C A 1 direction in the ∆C V 1 -∆C A 1 plane, drastically changing the limits on ∆C A 1 . The final one parameter limits that we estimated in 4l + 3l + 2l channels on the operators' couplings for L = 150 fb −1 (second-column, Table 2) are better compared to observed one parameter limits by CMS with L = 77.5 fb −1 [90] and L = 138 fb −1 [91]. Our simultaneous limits for L = 150 fb −1 (second-column, Table 3) are also better compared to the simultaneous limits  observed by CMS [91]. Our one parameter limits on the operator for L = 150 fb −1 are better in contrast to the one parameter limits obtained by SMFiT [111] collaboration in a global analysis of the top quark sector. Our simultaneous limits are also better, except C − ϕQ , compared to the marginalized limits obtained by SMFiT [111].
We did not account for backgrounds other than the SM ttZ process but used a large systematic uncertainty (10%, 13% and 16% for 4l, 3l and 2l channel) in our analysis. Further, we use the default isolation criteria in the Delphes, which are relatively strict compared to what is used in CMS analyses giving us fairly conservative results. We note that the authors in Ref. [63] also study anomalous couplings in ttZ production process, where the polarization of top quarks and spin correlations of top and anti-top pair are estimated in a truth level simulation. In contrast to Ref. [63], we estimate polarization of Z boson including the top quarks, spin correlation of top and anti-top system, top and Z system as well as the top, anti-top, and Z system, i.e., all possible two-body and three-body spin correlations, by reconstructing the top quarks in a detailed detector level simulation. The marginalized constraints on the operator, including a CP-odd operator, in our study are tighter as compared to what was obtained in Ref. [63], where Run 2 and Run 2+Run 3 limits can be compared with our limits for L = 150 fb −1 and 300 fb −1 , respectively.

Summary
In summary, we studied the anomalous ttZ interaction in leptonic channel of the ttZ production process at the 13 TeV LHC with the help of polarizations, two-body and three-body spin correlations of t,t and Z on top of the cross sections binned in p T (Z). We showed how the reconstruction of two neutrinos at the detector level affects the angular distributions corresponding to polarizations and spin correlations compared to the parton level distributions. We identified a few polarization and spin correlation parameters sensitive to only one kind of anomalous couplings, helping us disentangle the effect of the four anomalous couplings that we have considered. The sensitivity of the couplings to polarizations and spin correlations are studied in the form of χ 2 for a luminosity of L = 3000 fb −1 . The improvements of limits on the couplings are studied over the binned cross sections by successively including the polarization and spin correlation asymmetries. We estimated the one parameter and simultaneous limits at 95% C.L. on the anomalous couplings as well as the effective operators for a set of luminosities of 150 fb −1 , 300 fb −1 , 1000 fb −1 , and 3000 fb −1 . Our limits on the couplings (except ∆C A 1 / C ϕt ) are better compared to the existing limits obtained by CSM [90,91]. The polarizations and spin correlations help in tightening the region of parameters space, especially for the vector and axial-vector couplings (∆C V 1 -∆C A 1 ) in comparison to the cross section by a considerable amount. The parameter space becomes even tinier in the 2l + 3l + 4l channel neighboring only the SM point. Our strategy in this analysis can serve as an extra handle in interpreting anomalous interactions on the data at the high energy and high luminosity LHC.
ACKNOWLEDGEMENT The author would like to acknowledge support from the Department of Atomic Energy, Government of India, for the Regional Centre for Accelerator-based Particle Physics (RECAPP), Harish Chandra Research Institute.
A Standard model values of polarizations, spin correlations, and their asymmetries Table 4: Standard Model values of various polarizations and spin correlations along with their asymmetries above in parton level as well as in detector level in the ttZ production in the 4l channel at the √ s = 13 TeV LHC. The values are listed with asymmetries more than 5σ MC error of 10 million events (δ A = 0.001) in Delphes level. PT, PR and DR stands for Parton-Truth,

B Binned cross sections versus the un-binned cross section
Here, we compare the cross sections binned over reconstructed p T (Z) with the total un-binned cross sections in terms of χ 2 as a function of anomalous couplings, shown in Fig. 12. The combined binned cross section (solid/green lines) performs better compared to the total un-binned cross section (dotted/red lines) in constraining the couplings. Some individual bins even perform better compared to the total un-binned cross sections. For example, Bin 1 (blue lines) for ∆C V /A 1 ; and Bin 2 (magenta lines ) together with Bin 3 (brown lines) for C V /A 2 provide tighter limits as compared to the total un-binned cross sections.  Figure 12: Comparison of the total un-binned cross section with the binned cross sections (binned in p T (Z), see Eq. (4.6)) in terms of χ 2 as a function of ttZ anomalous couplings at √ s = 13 TeV and integrated luminosity of L = 3000 fb −1 .