Study of top quark dipole interactions in $t\bar{t}$ production associated with two heavy gauge bosons at the LHC

In this paper, we investigate the prospects of measuring the strong and weak dipole moments of the top quark at the Large Hadron Collider (LHC). Measurements of these couplings provide an excellent opportunity to probe new physics interactions as they have quite small magnitudes in the Standard Model. Our analyses are through studying the production cross sections of $t\bar{t}WW$ and $t\bar{t}ZZ$ processes in the same sign dilepton and four-lepton final states, respectively. The sensitivities to strong and weak top quark dipole interactions at the $95\%$ confidence level for various integrated luminosity scenarios are derived and compared with other studies. In addition to using the total cross sections, a novel handle based on an angular observable is introduced which is found to be sensitive to variations of the top quark strong dipole moments. We also investigate the sensitivity of the invariant mass of the system to the strong and weak dipole moments of the top quark.


Introduction
The search for new physics beyond the Standard Model (SM) is one of the main purposes of the CERN Large Hadron Collider (LHC). At the LHC, the impacts of beyond the SM physics could be directly seen, providing that the characteristic scale would be below the center of mass energy of the related hard processes. If not, the new physics effects need to be explored via the accurate measurements of the couplings of the SM particles. According to the recent LHC results, all measurements are found to be in agreement with the SM predictions [1]. This could be a hint that possible new degrees of freedom are separated in mass from the SM fields. As a result, the available energy in the LHC collisions is not enough for direct production of the heavy degrees of freedom coming from beyond the SM. Therefore, one could parameterize the effects of all new physics by a series of SU (3) c × SU (2) L × U (1) Y gauge invariant operators O i constructed out of the SM fields [2][3][4][5]. These operators should be of dimension d > 4 and typically the leading effects for collider observables show up at d = 6. Their coefficients are suppressed by inverse powers of the scale of new physics Λ: where L SM denotes the SM Lagrangian and c i are the dimensionless Wilson coefficients. Such a model independent parameterization has the possibility to be linked to ultraviolet completions and the results could be interpreted in various beyond the SM theories. The dimension six operators O (6) i have been listed in Refs. [2][3][4]. Studies on the validity of the SM effective field theory (EFT) and the fact that the EFT validity range could not be obtained only on the basis of low energy information are available in Ref. [6].
From the theoretical point of view, top quark could provide a unique way into beyond the SM physics, since the top quark Yukawa coupling is the largest among all other SM fermions. Particularly, the CP properties of top quark interactions with the SM fields is one of the important subjects to study in the top quark sector [7]. Especially, it has been shown that the CP violating couplings of the top quark in the framework of a model with an extended scalar sector can explain the observed baryon asymmetry of the universe [8]. In the top quark sector, within a beyond SM theory, CP violating interactions may also show up through the form of electric, strong, and weak dipole moments. So far, there have been many studies of the potential for revealing possible effects of new physics in the top quark sector at the LHC, Tevatron and future colliders using the higher-dimensional operators [9][10][11][12][13][14][15][16][17][18][19][20].
With the LHC phase II upgrade, in which a large amount of data is going to be collected and several experimental efforts are going on to assess and reduce the systematic uncertainties, rare SM processes will become accessible [60][61][62]. In particular, final states containing several heavy SM degrees of freedom could be observed and new physics effects can be studied through them as they suffer from small amount of backgrounds. For instance, pp → ttV V processes, where V = Z, W ± are of the promising channels through which new physics beyond the SM can be investigated. Studying these processes has the advantage of having naturally high multiplicity final states and consequently the backgrounds are better under control. Large thresholds of 2(m t + m V ) with V = W, Z for ttW W and ttZZ productions, restricts the phase space and lead to small production cross sections at the level of few femto-barns. However, LHC is able to reach the threshold and its experiments are able to observe these processes as around 75 ttZZ and 420 ttW W events are expected to be produced per 30 fb −1 of integrated luminosity of data [60]. It is worth mentioning that so far the ATLAS and CMS experiments have measured the top pair production cross sections in association with a single W or Z boson [63,64]. Measuring the ttW W and ttZZ rates at the LHC is in particular remarkable in top quark sector as they provide the possibility to probe the top quark couplings with the SM heavy gauge bosons and even multi-gauge boson interactions. This allows direct probes for dynamics of electroweak symmetry breaking.
In this paper, our concentration is specially on studying the strong and weak electric and magnetic dipole moments of the top quark through the pp → ttW W and pp → ttZZ processes at the LHC. In the SM framework at tree level, the magnetic and electric dipole moments are zero and they could be generated at higher order electroweak corrections which have small magnitudes [65]. However, sizable enhancements are predicted in various extensions of the SM [33,65]. Therefore, observation of these moments with deviations from the SM predictions would be indicative of beyond the SM physics. A highly motivated task would be to investigate how precise these dipole moments can be measured at the collider experiments.
The plan of this paper is as follows. In Section 2, the top quark strong and weak dipole moments are defined in the context of the SM effective field theory and the relations of the dipole moments with the dimension-six operators are given. Section 3 is dedicated to estimate the sensitivity of the pp → ttW W and pp → ttZZ processes to the top quark dipole moments and prospects arising from the production rates. Section 4 concentrates on introducing sensitive observables to the top quark dipole moments. The conclusions and results are summarized in Section 5.

Top quark effective couplings
As we have mentioned in the previous section, within the SM effective framework, the effects of new physics can be parameterized by using higher-dimensional operators involving the SM fields, assuming they come from new degrees of freedom occurring at a large energy scale Λ. Considering dimension-six operators and following Ref. [3], we present the general expressions for the gluon-top-antitop (gtt) and Z-top-antitop (Ztt) vertices here.

gtt vertex
The most general gtt coupling considering dimension-six operators including the SM part could be parameterized as follows [3]: where g s denotes the strong interaction coupling, d g V and d g A are real parameters which are related to the top quark chromomagnetic and chromoelectric dipole moments, respectively. Gell-Mann matrices are denoted by λ a and G a µν is the strong field strength tensor. At leading-order, in the SM context, d g V and d g A are zero. The first term in Eq.2 is the SM interaction, second and third terms which consist of both gtt interaction and four-leg ggtt coupling come from the dimension six operator [3]: whereφ = iτ 2 φ * and φ is the weak doublet of Higgs boson field, q L3 is the quark weak doublet of left-handed quark and the right-handed top quark field is denoted by t R . It is notable that no corrections from dimension-six operators are received by the γ µ term in the Eq.2.
They are connected to the effective dimension-six operator couplings through the following relations [3]: where v is the vacuum expectation value and is equal to 246 GeV. The chromoelectric dipole moment d g A is corresponding to the imaginary part of C 33 uGφ . In this study, we consider both chromoelectric and chromomagnetic dipole moments.
In the SM context, the one-loop level QCD corrections can generate d g V through the exchange of gluons in two different Feynman diagrams. One of the diagrams is the same as QED case, replacing photon by gluon. Another diagram consists of an external gluon interacting with the internal gluons coming from the non-abelian nature of QCD. The same as QED case, these diagrams generate non-zero d g V which is proportional to α s /π [65]. It is worth indicating that in addition to QCD corrections, Z and Higgs bosons exchange also generate d g V . Including all SM contributions at one-loop, the value of d g V is equal to −7 × 10 −2 and non-zero value for d g A arises from contributions from beyond one-loop and is quite small [65,66].
At present, there are both direct and indirect bounds on the chromomagnetic and chromoelectric dipole moments of the top quark. The bound could be obtained from the inclusive and differential top quark pair cross section measurements at the LHC and Tevatron. In Ref. [20], we have shown that in particular the presence of top quark chromoelectric dipole moment increases the gluon-gluon fusion process contribution in tt production at the Tevatron and LHC. Bounds are derived on both top quark chromoelectric and chromomagnetic dipole moments using the measured ratio σ(gg → tt)/σ(pp → tt) and tt mass spectrum at the Tevatron [20].
The top pair events produced at the large invariant masses in proton-proton collisions at the center-of-mass energies of 13, 14, and 100 TeV in the semi-leptonic channel have been studied to probe the top quark dipole moments in Ref. [9]. It has been shown that in the boosted regime the QCD background can be considerably suppressed and stringent bounds are achievable. The CMS collaboration has derived limits on these dipole moments from the measured top pair spin correlation at the LHC at 8 TeV [21].
The single top quark production in association with a W boson (tW -channel) is shown to be also a sensitive process to the top quark dipole moments [11,19]. Constraints have been obtained using the measured cross section of tW -channel at the LHC with the center-of-mass energy of 7 TeV using an integrated luminosity of 4.9 fb −1 .
Amongst all searches, the strongest limits on d g V and d g A come from low energy probes like the neutron electric dipole moment (d n ) [67] and the rare decays of B mesons [65]. The constraint on the top quark chromoelectric dipole moment from d n is found to be: |d g A | ≤ 0.95 × 10 −3 at 90% confidence level (CL) [67]. The measured branching fraction of b → sγ leads to the limits of 3.8 × 10 −3 ≤ d g V ≤ 1.2 × 10 −3 at the 95% CL [65].

Ztt vertex
The effective Ztt vertex considering the SM contributions and the ones come from dimension six operators can be written as [3]: where m Z and Q t are the Z boson mass and the top quark electric charge, respectively. In the SM at tree level, X L = 1, X R = 0, and d Z V = d Z A = 0. The contributions to these Ztt coupling from the dimension six operators are: The contributions of dimension six operators to X L and X R are neglected in this analysis [3]. The constraints on d Z A and d Z V could be translated into limits on the combination of the effective operators. The couplings d Z A and d Z V are the weak electric and magnetic dipole moments. The weak electric dipole moment coupling is a CP violating coupling which appears at three-loops in the SM and the coupling d Z V corresponds to the weak magnetic dipole moment and is at the order of 10 −4 in the SM framework [68][69][70][71].
There are studies on d Z A and d Z V at the electron-positron colliders and at the LHC [28,72] to constrain these couplings. In Ref. [72], it has been shown that by combining the LEP1 data at Zpole with top pair cross section measurements and the electroweak precision data, the degeneracy between the involving operators in d Z A and d Z V could be broken. The top quark weak electric and magnetic dipole moments have been investigated at the LHC and the ILC from the ttZ production [28]. Both weak dipole moments are expected to be constrained to ±0.15 using 300 fb −1 of data and would be improved to ±0.08 with 3 ab −1 integrated luminosity of the data. Bounds at the same order can be obtained using the LEP electroweak precision data. The ILC with 500 fb −1 is expected to reach the limits of ±0.08 on the weak electric dipole moment and [−0.02, 0.04] on the weak magnetic dipole moment [28]. It has been shown in Ref. [26] that d Z V and d Z A can be well probed by the ratio of the cross section of ttZ to tt, because it allows to reduce several sources of the systematic uncertainties considerably.

LHC constraints from ttV V
The pp → ttW W and pp → ttZZ processes are interesting to study because of their small production cross sections in the SM [60] and the significant enhancement that could show up in their rates in several new physics scenarios. In this section, we examine the sensitivity of these processes to the strong and weak top quark electric and magnetic dipole moments at the 14 TeV LHC.
The SM ttW W and ttZZ processes produce an interesting set of the final states from which most of them giving rise to important signatures at the LHC. For ttW W (ttZZ) process, depending on the top quarks and W (Z) bosons decays between zero to four (six) charged lepton(s) might be produced. Lists of ttW W and ttZZ decay modes, with at least a charged lepton in the final state, and the related branching fractions are presented in Table 1 and Table 2, respectively.
For the ttW W process, the main decay channel is the mono-leptonic decay mode which has a branching fraction of 40%, followed by the dilepton, opposite-sign and same-sign (OS+SS) mode with branching fraction of 29.6%. The branching fractions of trilepton and four-lepton decay modes are 9.6% and 1.2%, respectively. Among all the above decay modes the mono-leptonic suffers from large background contributions. The channels in particular containing at least a pair of SS charged leptons seem to be the promising search channels for the ttW W process. For the ttZZ process, in addition to mono-lepton, dilepton, trilepton, and four-lepton channels five and six lepton multiplicities are among the possible decay channels. Although the topologies with high lepton multiplicities have small branching fractions, the contributing backgrounds for such cases are quite negligible.
In order to study the sensitivity of the ttW W and ttZZ processes to the top quark strong and weak dipole moments, we employ MadGraph5 aMC@NLO package [73] which automatically generates the necessary code for computing the cross section and other observables for the related process. The results are computed using the NNPDF3 PDF sets [74]. The top quark mass is set to 172.5 GeV and the mass of W boson is taken as 80.37 GeV. The calculations are performed at the LHC with the center-of-mass energy of 14 TeV.
To perform the calculations of the cross sections in the presence of the top quark strong and weak dipole moments, the effective Lagrangians are implemented into FeynRules program [75]. Then the effective model is exported into a UFO module [76] which is connected to MadGraph5 aMC@NLO. MadSpin is used to for decaying top quarks, W and Z bosons. Pythia 8 [77] is used for parton showering and hadronization. Jets are reconstructed using the anti-k t algorithm with a radius size of 0.4 [78]. All the results presented in this study are idealized and no object reconstruction and detector effects are included. These effects modify the shape of final state distributions, however the study of such effects is beyond the scope of this exploratory work and are left to a future analysis.

Top pair production in association with two charged gauge bosons W ± W ∓
In the SM, the production of top quark pair associated with W ± W ∓ come from either gluongluon fusion or quark-anti-quark annihilation. The main contributions are of order O(α 2 s α 2 ) and a partonic center-of-mass energy of at least 2m t + 2m W is necessary which causes a small production cross section at the LHC. Gluon and quark initiated representative Feynman diagrams at leading order contributing to ttW W production in the SM are depicted in Fig. 1. In our study the production of ttW W is calculated in four flavor scheme (4FS) as in the 5FS case there exists intermediate top quark resonances that must be subtracted [60,79]. It is to avoid of unnecessary complication in calculation of the production rate. The ttW W production cross section at the center-of-mass energy of 14 TeV is calculated using MadGraph5 aMC@NLO package. The next-to-leading order cross section is found to be 14.5 fb ± 3% (PDF) +12.3% −13.0% (scales). The NLO QCD effects are on the order of 10%. Complete details of the QCD NLO calculations can be found in Refs. [79]. We note that at the 14 TeV LHC, around 54% of the total cross section comes from the gluon-gluon fusion which goes higher at the larger center-of-mass energies because of growing of the gluon PDF.
The LO contributions of the top quark chromoelectric (d g A ) and chromomagnetic (d g V ) dipole moments, arising from O 33 uGφ operator, to the ttW W rate is calculated with MadGraph5 aMC@NLO. The relative corrections from d g A and d g V to the total cross section of σ(pp → ttW W ) has the following form: where σ SM is the SM cross section and α i is the interference term which its contribution is of the order of Λ −2 . The β i term corresponds to the pure O 33 uGφ contributions which has the power of Λ −4 . Without taking into account the dimension eight operators, such terms could be dropped because dimension eight operators generate contributions at similar order. However, we keep Λ −4 term as it is the first appearing term in the cross section for d g A and it is relevant to have it when obtaining constraints on d g V . Of course, it is expected that the cross section has a symmetric shape around d g A = 0 as it is a CP even observable leading to α A = 0. To extract the coefficients α i and β i in Eq.7, the calculations with d g A and d g V are performed assuming different values: 0.0, ±01, ±0.2, ±0.3 and fit the obtained cross sections to Eq.7. The coefficients α i and β i are presented in Table 3.
To derive a quantitative estimate of the constraints that could be optimistically reached under various integrated luminosity scenarios, we concentrate on the exactly two same sign charged lepton (e, µ) topology. To select the same sign dilepton events, we require to have exactly two SS leptons with transverse momentum greater than 20 GeV and |η l | < 2.5. The angular separation of the leptons, ∆R(l 1 , l 2 ) = (∆η) 2 + (∆φ) 2 , is requested to larger than 0.4. The event is required to contain at least four jets from which at least two have to be matched with a B-hadron. We continue to set an upper limit on the ttW W production cross section in the presence of strong chromoelectric or chromomagnetic dipole moments.
To derive constraints on d g V and d g A , a counting experiment technique is employed. The method is to begin with a Poisson distribution describing the probability for measuring N events: where σ ttW W , L, and B are the signal cross section in the presence of d g V and d g A , the integrated luminosity, the efficiency of signal after the selection criteria, and the expected background events corresponding to the assumed integrated luminosity. At 95% confidence level (CL), the upper limit on the signal cross section can be calculated with integration over the posterior probability according to the following: In this exploratory study, the number of background events is obtained as B = (σ SM ttW W +σ SM ttW )×L where σ SM ttW W and σ SM ttW are the SM production rate for ttW W and ttW processes after the selection cuts described above. To be more realistic, the SM production cross section of these backgrounds are scaled to their NLO value. Assuming 60% b-tagging efficiency and full efficiency for lepton reconstruction, the efficiency is found to be 33%. To have a realistic estimation of the efficiency , a detailed experimental simulation to consider full detector response must be done which is beyond the scope of this study. We obtain the expected upper limit at the 95% CL on the signal cross section and compare it with the theoretical signal cross section to find the upper limits on d g V and d g A . The resulting limits are calculated for three scenarios of integrated luminosities of 30, 300, 3000 fb −1 and presented in Table 4. For example, with an integrated luminosity of 30 fb −1 the upper limits of −0.027 ≤ d g V ≤ 0.028 and |d g A | ≤ 0.026 are derived. If we assume 10% uncertainty on the signal efficiency and 100% uncertainty on the number of background events, the bounds on d g V and d g A at 30 fb −1 are loosen to −0.037 ≤ d g V ≤ 0.038 and |d g A | ≤ 0.036. We note that including the other signatures of ttW W process such as trilepton and four lepton would increase the sensitivity of this channel to the strong electric and magnetic dipole moments of the top quark. In the end of this section, it should be indicated that in addition to gtt effective couplings, ttW W process is sensitive to the anomalous W tb and Ztt vertices. The effective Lagrangian up to dimension six operators explaining the anomalous W tb coupling as follows [3]: where V L,R and g L,R are dimensionless couplings. At tree level within the SM, V L = V tb and V R = g L = g R = 0. From the rare B-meson decay, the constraints on these couplings are found to be [80]: The 95% CL bounds derived from W boson polarization and measured cross section of the single top t-channel at the LHC are [81]: −0.13 < V R < 0.18, −0.09 < g L < 0.06, and −0.15 < g R < 0.01. The total cross section of ttW W process does not show considerable sensitivity to g L and g R . By setting g R = 0.1 and g L = 0.1, the relative change of ttW W rate is 4% and 0.24%, respectively. This means that no strong limits on g L and g R are expected to be obtained from ttW W channel 1 .
We also note that in ttW W production, there are diagrams containing Ztt vertex resulting to the fact that the weak dipole moments d Z V and d Z A contribute to ttW W cross section. We do not consider this in our analysis as the modification to σ(pp → ttW W ) due to d Z V,A is found to be at the level of less than 10% when these couplings vary up to the value of ±0.05.

Top pair production in association with two neutral heavy gauge bosons ZZ
In this section, we study the sensitivity of the ttZZ production to the top quark dipole moments. The representative Feynman diagrams at leading order of this process are depicted in Fig.2. The next-to-leading-order cross section of ttZZ process is calculated using MadGraph5 aMC@NLO is found to be: 2.6 fb±1.82% (PDF) +4.34% −8.78% (scales), where the first uncertainty gives the contribution from the dependence on the choice of parton distribution functions and the second part is the factorization and renormalization scale uncertainties [60,79]. The input parameters for the cross section calculation has been taken similar to the previous section. The NLO corrections to the ttZZ production is quite small resulting to a k-factor close to one [79]. The leading order cross section is proportional to O(α 2 s α 2 ) and a partonic center-of-mass energy of at least 2m t + 2m Z is necessary for such a final state at the LHC. The presence of α 2 and four heavy particles in the final state, which causes to reduce the phase space, lead to such a small rate for this process.  Figure 2: Representative Feynman diagrams for ttZZ production at leading-order.    Table 5. We see the interference term coefficient (for i = V ) is small and the pure new physics coefficients are almost close to each other. As expected due to the presence of q µ factor in the effective Lagrangian, the coefficients γ g,Z V,A are very large. As mentioned before, there are several signatures for ttZZ that all contain at least two b-jets which come from the weak top quark decay. Among all signatures, we take the four-lepton (lepton = e, µ) final state which is a clean signature. Requiring four leptons and two b-tagged jets in the final state should be enough to increase the signal-to-background ratio significantly. To select the signal events, we require to have exactly four leptons with p T > 10 GeV and |η| < 2.5. The missing transverse energy has to be larger than 30 GeV and each event is requested to contain at least two b-tagged jets. To have well isolated objects in the final state, it is required ∆R(l i , l j ) > 0.4, We follow the same method as described in the previous section to set upper limit on the signal cross section then the upper limit is translated into the limits on the top quark dipole moments. The SM ttZZ and ttZ are taken as the main backgrounds and the number of background events is obtained through B = (σ SM ttZZ + σ SM ttZ ) × L where σ SM ttZZ and σ SM ttZ are the SM rates after the selection cuts described above. Taking a 60% b-tagging efficiency and fully efficient lepton reconstruction, the efficiency is obtained to be equal to 32%. The bounds on d g V,A and d Z V,A are shown in Table  6 for 30, 300 and 3000 fb −1 integrated luminosity of data.
Assuming a 10% overall uncertainty on the efficiency of signal and 100% uncertainty on the number of background events make limits looser. Using 30 fb −1 integrated luminosity of data, the bounds on d g V and d g A become −0.033 ≤ d g V ≤ 0.036 and |d g A | ≤ 0.035. One can derive a lower limit on the new physics characteristic scale using the Eq.4 and taking the Wilson coefficient C 33 uGφ to be at most equal to 4π. Using for instance the obtained upper limit on d g V at 3000 fb −1 , a lower bound of Λ ∼ 9 TeV is deduced. Of course, choosing lower value of C 33 uGφ leads to looser limit on Λ.

Comparison of the results with other studies
In this section, we compare the sensitivity of the expected constraints from the ttW W (same-sign leptons) analysis and ttZZ (four-lepton) analysis with some other studies. The results of this study with two scenarios of integrated luminosities 300 and 3000 fb −1 are compared with others in Fig.3. The most stringent direct bounds from the FCC-hh, where protons are collided with √ s = 100 TeV, are based on the integrated luminosity of 10 ab −1 [9] and are derived from the events with central jets (|η| < 2) and transverse momentum larger than 1 TeV reconstructed using an anti-k T [78] algorithm with a radius size of 0.2. The FCC-hh limits are obtained in an optimal invariant mass region of the top quark pair mass of m tt > 10 TeV.
The indirect limits on d g V are based on rare B meson decay [65] which has been found to be −0.0038 ≤ d g V ≤ 0.0012. In particular, the upper limit is the most stringent one which is even stronger than the expected bound from FCC-hh. The combination of the measured top quark pair cross section at the LHC8 and Tevatron lead to −0.012 ≤ d g V ≤ 0.023 [9] and the expected limit derived from the tt spectrum and the inclusive cross section at the LHC14 based on 100 fb −1 is −0.0086 ≤ d g V ≤ 0.012 [9]. The limits from our analyses are comparable to these limits and could be even improved if the other signatures presented in Table 1 and Table 2 are taken into account.
For the d g A case, the indirect limits have been extracted from the upper limit on the neutron electric dipole moment. This indirect low energy limit which is |d g A | ≤ 0.00095 [67] is the strongest one. Again, among the direct limits, the one obtained from FCC-hh is the most stringent limit: |d g A | ≤ 0.0026. The combination of the measured tt cross section at the LHC8 and Tevatron implies |d g A | ≤ 0.087 [9] while the ones from tt spectrum and the inclusive cross section at LHC14  with 100 fb −1 are |d g A | ≤ 0.019 [9]. The combination of ttW W and ttZZ channels provides the limits of −0.006 ≤ d g V ≤ 0.005 and |d g A | ≤ 0.005 with an integrated luminosity of 3000 fb−1. The limits from ttW W (samesign leptons), ttZZ (four-lepton) and their combination are comparable to the limits from other studies and in some cases would be even better. The bounds obtained from this analysis could be improved by including the other signatures and taking into account the higher order QCD corrections in the signal channels. It should be indicated that while the indirect limits from the rare B decays and the neutron electric dipole moment are stronger but they are complementing each other. Now, we turn to the weak dipole moments d Z V and d Z A . The expected constraints from an electron-positron collider at √ s = 500 GeV with an integrated luminosity of 500 fb −1 , are |d Z V | ≤ 0.08 and −0.02 ≤ d Z A | ≤ 0.04 [28]. These limits are derived by exploiting the total cross section of the top quark pair production. The limits from the LHC top pair production at the center-ofmass energy of 14 TeV with an integrated luminosity of 3 ab −1 are |d Z V,A | ≤ 0.08 [28]. They are obtained from the p T,Z distribution in ttZ production. The expected limits from the present study as shown in Table 6 are comparable with the ones from ILC and LHC in ttZ channel. At the end, it should be mentioned that our bounds are purely based on statistical sensitivity calculations and no experimental effects, which would weaken them, are taken into account. However, the combination of different decay channels for each process and considering QCD higher order corrections would lead to have larger statistics and significant improvements.

Sensitive observables
Various types of vector, tensor and pseudo-tensor couplings in the effective Lagrangian of gtt and Ztt could lead to changes in differential distributions of the final state particles. Therefore, one can exploit the differential rates to design analyses for achieving improvements with respect to the total cross sections. Specially, it becomes very important for the cases that the reachable sensitivities from the total cross section in future prospects are not exciting enough.
There are already studies where the authors proposed several observables to reach more sensitivities to the effective couplings in the top quark sector and also to disentangle CP-even and CP-odd couplings [16,42]. Here, we construct an observable on the basis of the momenta of the final state in ttZZ channel before decaying of the top quarks and the Z bosons. Of course, for the reconstruction of the ttZZ, we need full information of the top quarks and Z boson decay products momenta. However, due to the presence of the missing neutrino when a top quark decays leptonically, it is impossible to reconstruct the top quark(s) completely and one needs to use W boson and top mass as constraints to find the full momenta of the top quarks. Furthermore, ambiguities arise in combination of the decay products when assigning each particle to its real mother. Such ambiguities would lead to large systematic uncertainties to the ttZZ system. In this exploratory work, we design observables using the momenta of ttZZ and leave the explained complications to a future study.

Invariant mass distributions
In this section, We examine the information that could be derived from measuring of the invariant mass of the system, i.e. M ttZZ . In the left side of Fig.4, we display the normalized distributions of M ttZZ for the SM and two cases of d g V = 0.05 and d g A = 0.05. One can see that the distribution of M ttZZ is peaked towards small masses for the SM case. While, in the presence of either d g V or d g A the peak substantially moves toward large values. This could be traced back to the momentum dependence of these couplings. In the bottom plot of Fig. 4, the average value of M ttZZ distribution is presented in terms of d g V and d g A . As it can be seen, < M ttZZ > starts from around 1.42 TeV for the SM and grows significantly with d g V,A coulings and reaches up to around 2.45 TeV for d g V = 0.05 and 2.59 TeV for d g A = 0.05. We see an explicit rapid raise in the < M ttZZ > with a small change in either d g V or d g A that certainly allows us to deeply probe the gtt structure. We note that the difference between < M ttZZ > for the cases of d g V = 0.05 and d g A = 0.05 is around 150 GeV. The right panel of Fig.4 shows again the invariant mass distribution of the ttZZ system for the SM and two cases of d Z V = 0.05 and d Z A = 0.05. As it can be seen, the distributions are similar to the SM and almost we see no considerable change in the peak positions. The < M ttZZ > value for the cases of d Z V = 0.05 and d Z A = 0.05 are 1.47 TeV and 1.48 TeV, respectively. The growth with respect to the SM value is at the level of 50 to 60 GeV which is not comparable with the one received in cases of d g V or d g A . The presented distributions are idealized, as no effects of parton showering, hadronization, object identification and reconstruction, etc. are included. Also, the selection cuts and background contamination are not considered. In the definition of observable z 2 , the first cross in the nominator is between the top quark and the Z boson with highest p T and the second cross is between the anti-top quark and the other Z boson. For illustration, the shapes of z 1 and z 2 for the SM case (all couplings are set to zero) and for instance for d g V = 0.05 and d g A = 0.05 are depicted in Fig.6. As it can be seen, switching on the strong top quark dipole moments leads the the z 1 and z 2 distributions to become wider and to have less peaked behavior with respect to the SM case. A measure which reflects the heaviness of the tail of the z 1,2 distributions in the presence of d g V and d g A couplings is kurtosis. The size of kurtosis for the SM distribution for z 1 (z 2 ) is found to be 0.172 (0.270) while for d g V = 0.05 and d g A = 0.05, we find 0.430 (0.431) and 0.432 (0.465), respectively. As expected, the kurtosis grows as the tail becomes heavier. It is notable that z 1 receives more change in kurtosis with respect to the SM case than z 2 .
From the z 2 distributions, we also see that the presence of d g V and d g A couplings would lead events to be more distributed to z 2 < 0.0 region than z 2 > 0.0 region. To quantify that we define an asymmetry as: The denominator is the total number of events. The value of A(z 2 ) for the SM is found to be 10% and for SM+d g V (d g V = 0.05) is −7.5%. For SM+d g A (d g A = 0.05), A(z 2 ) amounts to −9.0%. As it can be seen, switching on d g V or d g A leads to a migration of events from z 2 > 0.0 to z 2 < 0.0 and consequently change the sign of asymmetry A(z 2 ) from a positive to negative values. As a  Figure 5: The angle α is shown which is the angle between two planes of ( p t , pt) and ( p Z 1 , p Z 2 ). result, the measurement of A(z 2 ) asymmetry will provide valuable information on the new physics effects. We have examined the sensitivities of the above angular observables to d Z V and d Z A and no serious distortion is observed.  Figure 6: The z 1 and z 2 distributions for the SM, d g V = 0.05 and d g A = 0.05 cases in the pp → ttZZ process.

Summary and conclusions
Rare SM processes involving multi-top-quark and multi-gauge-boson final states at the LHC provide an exciting opportunity to search for new physics effects. To assess those effects, searches could be performed using the effective field theory approach which could affect both the total cross sections and the differential distributions. Particularly, the impacts would be expected to be significantly visible in processes containing heavy particles in their final states. In this paper, for the first time, we study the strong and weak electric (d g,Z A ) and magnetic (d g,Z V ) dipole moments of the top quark through the ttW W and ttZZ channels at the LHC14. As the SM values for d g,Z V and d g,Z A are very small, in case of facing a situation with d g,Z V,A large enough, ttW W and ttZZ channels provide promising ways to observe the corresponding excess over the expectation of the SM.
Based on the top quarks, W bosons and Z bosons decays, various signatures are available from which we have concentrated on the much cleaner same-sign dilepton and four-lepton topologies for ttW W and ttZZ channels, respectively. Therefore, we assume the signals considered here are adequately distinguishable from the SM backgrounds and a comprehensive study with including the backgrounds and detector effects are left for a future work. We find constraints of −0.09 ≤ d Z V ≤ 0.08, |d Z A | ≤ 0.08 for the weak dipole moments and −0.005 ≤ d g V ≤ 0.006, |d g A | ≤ 0.005 for the strong dipole moments using 3 ab −1 of the integrated luminosity of data. The results are comparable with the prospective ones reachable from tt and ttZ at the LHC. However, there are rooms for significant improvements of the bounds which could be achieved by including different topologies and by taking into account the higher order QCD corrections to signal processes. Going beyond the total production cross section, new angular observables are proposed to probe the effects top quark dipole moments. We have found that the presence of top quark dipole moments could affect the final state angular configuration. We also show that the invariant mass distribution of ttZZ system is substantially sensitive to d g V and d g A , pushing the peak to large mass region. More investigation to examine the sensitivity to new couplings considering the impacts of final state reconstruction and detector resolution are left to a future work. Another feature that is also to be studied will be the disentanglement of CP-even and CP-odd operators through new observables.