Signs of new physics in top quark pair production associated with a neutrino pair at the LHC

In this paper, we examine the interactions of the top quarks with the $Z$ boson using the top quark pair production associated with neutrino pair ($t\bar{t}\nu_{l}\bar{\nu_{l}}$) at the LHC. In particular, potential constraints on the anomalous electroweak top-quark interactions are determined by considering two opposite-sign charged leptons, missing energy, and two b-tagged jets in the final state. The analysis is performed for a High Luminosity scenario of the LHC with an integrated luminosity of 3 ab$^{-1}$ of proton-proton collisions at a center-of-mass energy of 14 TeV. The $95\%$ confidence intervals are computed on the anomalous couplings considering a realistic detector simulation of an upgraded CMS detector including an average of 200 proton-proton interactions per bunch crossing. We find that the $t\bar{t}\nu_{l}\bar{\nu_{l}}$ channel can provide stringent bounds on the relevant Wilson coefficients and has the potential to serve as an additional handle beside the $t\bar{t}Z(Z\rightarrow l^{+}l^{-})$ and other channels to search for new physics.


Introduction
The main task of the Large Hadron Collider (LHC) is to make inquiry for possible effects of new physics beyond the Standard Model (SM). As the collected data by the LHC experiments have increased, the motivated models beyond the SM are being studied in detail and are strongly constrained. As a result, the phenomenological studies have become largely model independent and data are interpreted in the framework of SM effective field theory (EFT) [1][2][3]. The effective field theory extension of the SM has become a popular theoretical framework to look for beyond the SM effects and has received a lot of attention during the last years .
The effective field theory extension of SM is a power tool which could be considered as a bridge between the measurements at low energy scale and the unknown UV completion theory. The LHC experiments could observe the impacts of non-SM physics provided that its energy scale would be below the energy of the related hard processes. Otherwise, the new physics effects should be probed through the precise measurements of the interactions of the SM particles. As all the measurements have been found to be consistent with the SM predictions, one expects that the possible heavy degrees of freedom are apart from the SM content in mass. Within the framework of the effective field theory of the SM, the new physics effects can be parameterised by series of SU(3) c × SU(2) L × U(1) Y gauge invariant dimension-six operators O i built out of the SM fields. The coefficients of the operators are suppressed by the inverse power of the new physics characteristic scale Λ [2,3]: where L SM is the known SM Lagrangian and C (6) i 's are the so-called Wilson coefficients which are dimensionless. The leading contributions arise from the operators of dimension-six and the Wilson coefficients are considered as a priori free parameters when we constrain a generic model beyond the SM. List of dimension-six operators O (6) i could be found in Refs. [2,3]. The validity of the effective field theory extension of the SM has been investigated in Ref. [47] where it has been shown that the validity range of EFT could not be derived only on the basis of low energy information and the conditions for an EFT to provide an appropriate low-energy description of an underlying model beyond the SM are discussed.
In the present work, we perform a search for beyond the SM effects in the context of the SM effective field theory (SMEFT) through the production of tt in association with a neutrino pair at the LHC. The Wilson coefficients of the relevant dimension-six operators are constrained. There are 59 operators of dimension-six that form the so called Warsaw basis [3], among them the four most relevant linear combinations, as represented in Ref. [9], are selected. The study is performed for a High Luminosity scenario of the LHC at a center-of-mass energy of 14 TeV using an integrated luminosity of 3 ab −1 . Constraints at 95% confidence level are obtained on the relevant Wilson coefficients using the dilepton channel of the top pair events considering an upgraded CMS detector [48] and an average of 200 proton-proton interactions in each bunch crossing.
The production cross section of ttZ(Z → l + l − ) has been measured by the ATLAS and CMS collaborations using proton-proton collisions at √ s = 13 TeV and constraints have been applied on the Wilson coefficients [49,50]. The expected sensitivity of the CMS experiment for the anomalous electroweak top quark interactions has been provided for a HL-LHC scenario with 3 ab −1 at a centre-of-mass energy of 14 TeV in Ref. [51]. The constraints have been obtained based on the measurements of the differential cross section of the ttZ process in the three lepton final state. This article is organised as follows. In section 2, the theoretical framework and the contributing dimension-six operators which affect ttν lνl are discussed in short. Section 3 presents the production of ttν lνl process. The present constraints on the electroweak anomalous top-Z interactions are given in Section 3. In Section 4, we discuss the event generation, detector simulation and the analysis strategy. The estimated sensitivity that could be achieved from the HL-LHC are presented in section 5. A summary and conclusions are given in Section 6.

Effective Lagrangian
As it was mentioned, in the case that possible new particles are too heavy with respect to the LHC energy scale and are not produceable on-shell, one can use a low energy effective theory to describe the observables and look for possible new physics effects. In this section, the effective Lagrangian up to dimension-six operators which modify the top quark and Z boson interactions is introduced. The anomalous interactions between the top quark and gluons are not considered here as they have been strongly constrained using the tt+jets process [52]. We also neglect the anomalous W tb coupling in the current analysis due to the tight bounds obtained by single top quark production and W -polarisation measurements [53]. The most general effective Lagrangian describing the ttZ interaction can be written as [54,55]: where σ µν = i 2 [γ µ , γ ν ] and q = p t − pt. Within the SM at tree level the vector and axial couplings are: where θ W is the weak mixing angle, Q t is the top quark electric charge which is equal to 2/3, and in the SM are 0.244 and −0.601, respectively. In the SM, at tree level, C 2,V and C 2,A are zero however C 2,V receives corrections of the order of 10 −4 from one-loop diagrams and C 2,A gets corrections from three-loop diagrams [56][57][58]. Following the parametrisation of Ref. [9], the relevant Wilson coefficients are c tZ , c tZ , c φt , and c − φQ . These coefficients have a simple translation to the Wilson coefficients in the Warsaw basis [3] which can be found in the following [9]: Similar to the recent CMS experiment analyses [49, 51], we consider c tZ , c tZ , c φt , and c − φQ in this work and set other Wilson coefficients to zero. Setting C 3(33) φq and C (33) uW to zero guarantees the W tb vertex is consistent with the SM.

Production of ttν lνl at the LHC
In this section, the production of ttν lνl in proton-proton collisions at the LHC is discussed. Within the SM framework, at leading order, the production of ttν lνl proceeds via gluon-gluon fusion and quark-antiquark annihilation in both s-and t-channel, where the pair of neutrino comes from the Z boson decay. Figure 1 shows the representative Feynman diagrams at leading order at the LHC. At √ s = 14 TeV, the leading order cross section of the ttν lνl process is 143 fb from which around 72% comes from the gluon-gluon fusion. The next to leading order (NLO) QCD cross section, obtained with MadGraph5-aMC@NLO [59,60] is 195 fb. The new physics Lagrangian introduced in Eq.2 affects the ttZ vertex in the ttZ production in proton-proton collisions. The impacts of the anomalous couplings on the total cross section and the differential distributions of ttZ production have been extensively studied in Refs. [23,55]. According to these studies, in the presence of the defined Wilson coefficients in Eq.2, the production rate receives remarkable modification with respect to the SM case. In addition, the kinematic distributions of the final state particles are strongly affected by the anomalous couplings. Particularly, the electroweak dipole couplings C 2,V and C 2,A are expected to lead an enhancement in the tail of the momentum distributions of the final particles. This is because of the Lorentz structures of these couplings in the ttZ vertex which contains the Z boson momentum. As a result, in this study where the Z boson in ttZ production decays to a pair of neutrino, we expect an enhancement in the tail of missing transverse energy (E miss T ) distribution. Therefore, in the next sections we focus on the E miss T distribution to constrain the Wilson coefficient. The observed sensitivity of the anomalous electroweak top quark interactions have been determined based on the measurements of the differential cross section of the ttZ process in the three lepton final state. The limits at 95% CL are [49]: These bounds have been obtained using 77.5 fb −1 of the LHC data at a center-of-mass energy of 13 TeV. Expected 95% CL limits for a HL-LHC scenario with 3 ab −1 at a centre-of-mass energy of 14 TeV are [51]: These constraints have been derived for an upgraded CMS detector with the same analysis strategy followed in Ref. [49]. In this work, the calculations for the cross sections are performed at leading-order using MadGraph5-aMC@NLO package in the context of SMEFT following the parameterisation adopted in Ref. [9]. The model implementation has been performed with the FeynRules package [61] for generation of the related UFO file model that is inserted into the MadGraph5-aMC@NLO 1 . The details of simulations, analysis strategy and determination of the constraints on the Wilson coefficients are discussed in the next sections.

Simulation and analysis strategy
In this section, the details of simulation and the analysis strategy for probing the effective SM in tt production associated with a pair of neutrino are described. In order to have a clean signature, we consider the dileptonic decay of the tt. Consequently, the final state consists of two isolated charged leptons (electron and/or muon), two jets originating from the hadronization of bottom quarks, and large missing transverse energy. The major background processes which are included in this analysis are tt, ttZ(→ ν lνl ), single top tW -channel, ttW ± , ttH, W ± W ± , ZZ, and W ± Z.
The generation of signal and background events are done with MadGraph5 aMC@NLO. Then, the events are passed through PYTHIA [62,63] to perform parton showering, hadronisation, and decays of unstable particles. The events are generated at √ s = 14 TeV at the LHC with the NNPDF2.3 as the proton parton distribution functions [64]. The SM input parameters for generation of the events are: m t = 173.3 GeV and m Z = 91.187 GeV, m W = 80.385 GeV, m H = 125.0 GeV. Before we perform an analysis with a realistic detector simulation, it is worth presenting the distribution of the missing transverse momentum which is one the main characteritstic of the signal process. Missing transverse momentum distribution (| i ( p ν i ,T + pνi ,T )|) is depicted in Fig.2. The signal distribution is presented for the case of c tZ /Λ 2 = 0.5 TeV −2 and for comparison the distributions for the major backgrounds like tt, ttW , tW , ZZ, W + W − , and SM production of ttν lνl are shown. It can be seen that the tail of missing transverse momentum distribution is highly sensitive to the signal so that most of backgrounds are peaked towards low missing transverse momentum. Therefore, in this work to perform the search and study the sensitivity we concentrate on the tail of the missing transverse momentum distribution.
The detector response simulation is done using Delphes [65] package for an upgraded CMS detector [66]. The events are simulated by taking into account the additional proton-proton interactions for each bunch crossing (pile-up) with a mean number of pile-up interactions of 200. The jet finding process is performed using FastJet package [67] and the anti-k t algorithm [68] is utilised for reconstruction of jets with a distance parameter of 0.4 considering pile-up correction.    where the transverse momentum p T is in GeV unit. The efficiency of b-tagging for a jet with transverse momentum of 30 GeV is around 55% and the c-jet and light flavour jets misidentification rates are 12% and 1%, respectively.
In order to select signal events, it is required to have two opposite sign charged leptons with transverse momenta p T and pseudorapidity η l satisfying p T > 20 GeV and |η l | < 3.0. This requirement fulfils the high level trigger (HLT) condition [70]. The accepted charged leptons (muon and/or electron) are required to have a relative isolation I Rel < 0.15, where I Rel is defined as the scalar sum of transverse momenta of all particles inside a cone of size 0.4 around the lepton direction except the lepton, divided by the p T of lepton. Events are demanded to have exactly two b-jets with p T > 30 GeV and |η| < 4.0. To make sure all objects are well-isolated, the angular separation between the leptons and jets are required to satisfy ∆R(l ± , b-jet) > 0.4, where ∆R = (∆η) 2 + (∆φ) 2 . In order to reduce the SM background contributions, an additional cut is applied on the missing transverse energy so that the signal-to-background ratio is good enough to achieve the best sensitivity. The efficiencies of the cuts for the signal scenario c tZ /Λ 2 = 0.5 TeV −2 and the main background processes are presented in the Table 1. In particular, the efficiencies are given for illustration in a region of missing transverse energy above E miss T ≥ 400 GeV. The contributions of background processes such as ZZ, W ± W ∓ , and W ± Z, ttH are found to be negligible in this region. As the contribution of background processes overwhelm the signal at low values of cut on the magnitude of missing transverse energy, the concentration is on a region where the ratio of signal-to-background is large enough to find the exclusion limits. Because the signal events tend to have larger E miss T values with respect to the background, the E miss T region above 200 GeV will be chosen to obtain the limits.
The enhancement of the cross section in the presence of the anomalous couplings leads violation of the unitarity at very high energies. One needs to ensure the validity of the SM effective theory in this analysis. There are studies where the authors discussed the validity of effective theory which for instance could be found in Refs. [9,47,71]. In the present study, an upper bound of E miss T < 1.5 TeV is applied to avoid unitarity violation.

Results
This section is dedicated to present the potential sensitivity of the top pair production in association with a pair of neutrino to the Wilson coefficients. The results are presented for the collisions at a center-of-mass energy of 14 TeV and are corresponding to an integrated luminosity of 3 ab −1 . The Lagrangian introduced in Eq.2 consists of new momentum dependent tensor structures which affect the Z boson energy spectrum. Consequently, the missing transverse energy receives considerable impact from the effective Ztt couplings. The strategy to derive constraints on the Wilson coefficients is based on the fact that operators contribute to the tail of missing transverse energy distribution. We consider E miss T distribution in three bins of 200-300, 300-400, 400-1500 GeV to set limits where the contributions of SM background are remarkably suppressed. In order to obtain the expected limits at 95% CL on the Wilson coefficients, a binned likelihood function is constructed as a product of Poisson probabilities over three bins of the missing transverse energy. Expected 95% CL intervals from this study for the Wilson coefficients c tZ /Λ 2 , c tZ /Λ 2 , c φt /Λ 2 , and c − φQ /Λ 2 are presented in Table 2. The limits have been derived including only statistical uncertainties. Considering detailed systematic uncertainties is beyond the scope of this work and must be performed by the experimental collaborations. The observed 95% CL intervals from the CMS experiment measurement [51] and the expected results from a HL-LHC with 3 ab −1 [49] are shown for comparison. Table 2: The expected sensitivities on dimension six operator coefficients using 3 ab −1 integrated luminosity of data at the LHC with the center-of-mass energy of 14 TeV. The 95% CL upper bounds derived from ttZ(→ l + l − ) from Ref.
[49] with 77.5 fb −1 of data and the projection with 3 ab −1 are presented as well. The constraints are given in the unit of TeV −2 .
Coupling Limit from ttZ(ν lνl ) Observed limit from ttZ(l + l − ) [ A comparison of the limits from ttν lνl and the expected bounds from the projection of the ttZ(Z → l + l − ) rate suggests that ttν lνl is an additional channel that can provide the same order sensitivity as ttZ(Z → l + l − ) on the Wilson coefficients. Better sensitivity to c φt /Λ 2 and c − φQ /Λ 2 from this analysis is achievable with respect to the ttZ(Z → l + l − ) channel.
The expected intervals at 95% CL for the Wilson coefficients from this study, the observed CMS experiment result with 77.5 fb −1 from the ttZ measurement as well as the CMS experiment projection for a HL-LHC scenario are shown in Fig.3. The direct constraints from the TopFitter Collaboration and those within the framework of SMEFiT [4] and the indirect bounds at 68% CL from the electroweak precision data [72] are also shown. The SM prediction is shown as vertical line.

HL-LHC, 3 ab
TopFitter SMEFiT Indirect Figure 3: The expected 95% CL intervals for the Wilson coefficients from this study, the current CMS experiment results based on the ttZ(Z → l + l − ) cross section measurement [49], and the CMS projection results at high-luminosity. The constraints within the SMEFiT framework [4] and from the TopFitter collaboration [10] are presented. The indirect bounds from electroweak data at 68% CL are also given [72].
Contours of 68% (red) and 95% (blue) CL are also obtained for 14 TeV with an integrated luminosity of 3000 fb −1 . Figure 4 shows the complementary scan of the c tZ /Λ 2 and c [I] tZ /Λ 2 as well as c φt /Λ 2 and c − φQ /Λ 2 Wilson coefficients in the 2D plane. The two-dimensional scan shows that correlations are present in the sensitivity of ttν lνl to c φt ,c − φQ and c tZ ,c tZ .

Summary and conclusions
So far, the LHC experiments in Runs I and II have found no significant deviation from the SM expectations. In particular, all top quark and Higgs boson properties have been found to be in agreement with the predictions of the SM within the uncertainties. Consequently, for the sake of searching for the effects of possible new physics beyond the SM, one may concentrate on the SM effective field theory framework in which dimension-six operators are considered. The contributions of these operators are suppressed by the second power of the energy scale of new physics Λ. In the analysis presented here, we have probed the anomalous electroweak top quark using the tt production associated with neutrino pair process at the LHC. The 95% CL limits on the Wilson coefficients are computed by focusing on a final state consisting of two oppositesign charged leptons, missing energy, and two b-tagged jets. A fast simulation of detector effects for an upgraded CMS detector including an average of 200 proton-proton interactions per bunch crossing, is considered. It is found that the ttZ(Z → ν lνl ) production provides the same order sensitivity as ttZ(Z → l + l − ) channel in a HL-LHC scenario with an integrated luminosity of 3 tZ /Λ 2 ) and (c φt /Λ 2 ,c − φQ /Λ 2 ) are depicted. The contours of 68% and 95% CL are shown in red and blue. The star displays the SM prediction. ab −1 . Better limits are obtained on c φt and c − φQ with respect to the ttZ(Z → l + l − ) channel. The findings indicate that significant statistical power to increase the sensitivity is achieved in the tail of missing transverse momentum distribution of the ttν lνl process.