Searches for anomalous $tqZ$ couplings from the trilepton signal of $tZ$ associated production at the 14 TeV LHC

We investigate the observability of the top anomalous $tqZ$ couplings via the trilepton signatures at the Large Hadron Collider~(LHC) with the center-of-mass energy of 14 TeV. We focus on signals of the $tZ$ associated production with the decay mode $t\to W^{+}b\to b\ell^{+}\nu_{\ell}$, $Z\to \ell^{+}\ell^{-}$, and $t\bar{t}$ production with the decay mode $\bar{t}\to Z(\to \ell^{+}\ell^{-})\bar{q}$ and $t\to b\ell^{+}\nu_{\ell}$, where $\ell=e, \mu$ and $q$ reflects up and charm quarks. It is shown that at $3\sigma$ level, the FCNC top quark decay branching ratios can be probed at, respectively, about $Br(t\to uZ) \leq 1.3\times 10^{-4}$ and $Br(t\to cZ) \leq 4.2\times 10^{-4}$ with the integrated luminosity of 100 fb$^{-1}$, and probed down to $Br(t\to uZ) \leq 2.2\times 10^{-5}$ and $Br(t\to cZ) \leq 8\times 10^{-5}$ for the high-luminosity LHC with 3000 fb$^{-1}$.


I. INTRODUCTION
As the most massive particle in the standard model (SM), the top quark is generally considered as an appropriate probe for the new physics (NP) beyond the SM [1]. In particular, its flavor-changing neutral current (FCNC) interactions are extremely weak in the SM due to the Glashow-Iliopoulos-Maiani (GIM) mechanism [2]. For instance, the branching ratios of t → Zu(c) are predicted at the order of 10 −17 (10 −14 ) in the SM [3]. However, several extensions of the SM such as the SUSY models [4,5], two-Higgs-doublet models [6], extra dimensions [7], and the other miscellaneous models [8] predict much higher branching ratios up to 10 8 − 10 10 order of magnitude larger than SM predictions. Therefore, any signal for these rare FCNC processes at a measurable rate would be a robust evidence for NP beyond the SM.
Over the years, the top quark FCNC interactions has been studied intensively via the tt production processes with the anomalous decays of top quarks or anomalous production of single top quark [9][10][11]. Furthermore, the anomalous top quark interactions affect b quark FCNC decays through loop diagrams as mentioned in Ref. [12]. Very recently, both the ATLAS and the CMS experiments have obtained the limits on the branching ratios of the top anomalous decays through different channels (for an updated review, see [13]). The current upper limits for Br(t → Zq) at 95% confidence level (CL) have been found to be [14,15]: The most stringent bounds on the strengths of anomalous couplings tqZ come from the CMS experiment with √ s = 8 TeV, using the recent combination with anomalous tZ production [14].
It is notable to mention here that, even at the future facilities, these bounds resulting from tt production would not be improved considerably. The organization of this paper is as follows. In Sec. II, we present the theoretical framework which describes the FCNC tZq couplings. In Sec. III, we discuss the signals of tZ associated production with the decay mode t → W + b → ℓ + νb and Z → ℓ + ℓ − , and tt production with the decay modet → Z(→ ℓ + ℓ − )q and t → bℓ + ν ℓ . Then we analyze the sensitivity of 14 TeV LHC to anomalous tqZ couplings in detail. Finally, we conclude in Sec. IV.

II. CALCULATION FRAMEWORK
In general, the effective Lagrangian describing the interactions between the top quark and a light up-type quark (u or c) and the Z boson can be written as [17] − where g is the SU(2) L gauge coupling constant, C W = cos θ W and θ W is the Weinberg angle, , and Λ is the new physics scale, which is related to the cutoff mass scale above which the effective theory breaks down. The effects of new physics contributions are quantified through the dimensionless parameters κ tqZ and λ tqZ together with the complex chiral parameters κ L,R and λ L,R , which are normalized as The above effective Lagrangian can be used to calculate both production cross sections and the branching ratios of the t → qZ decays. Note that we do not consider the FCNC tqg couplings because the sensitivity is poor in comparison to other channels [18]. On the other hand, the λ tqZ couplings lead to very small cross sections [19]. We thus only consider the cases where κ tqZ /Λ = 0, and no specific chirality is assumed for the FCNC interaction vertices, i.e.
At the leading order (LO) and the next-to-leading order (NLO), the decay widths of the dominant top quark decay mode t → W b could be found in Ref. [20]. The partial decay widths of t → qZ with flavor-violating interactions are given by After neglecting all the light quark masses and assuming the dominant top decay width t → bW , the branching ratio of t → qZ can be approximately given by: Here the NLO QCD correction to the top quark decay via model-independent FCNC couplings is also included and the k-factor is taken as 1.02 [21]. The SM input parameters relevant in our study are taken as follows [22]:

III. SIGNAL AND DISCOVERY POTENTIALITY
In this section, we perform the Monte Carlo simulation and explore the sensitivity of 14 TeV LHC to the tqZ FCNC couplings through the tZ-FCNC and tt-FCNC processes. The representative Feynman diagrams for the signal processes are shown in Fig. 1.
Obviously, the signal is taken as the trilepton plus one b-jet and missing energy. The main backgrounds which yield the identical final states to the signal are tt, ttV (V = W, Z), W Z+ jets and the irreducible tZj, where j denotes non-bottom-quark jets. In the tt case (both top quarks decay semi-leptonically), a third lepton comes from a semi-leptonic B-hadron decay in the b-jet. Here we do not consider multijet backgrounds where jets can be faked as electrons, since they are very negligible in multilepton analyses [23]. On the other hand, the SM tth and tri-boson events can also be the sources of backgrounds for our signal. We have not included these backgrounds in the analysis due to very small cross sections after applying the cuts. The high order corrections for the dominant backgrounds are considered by including a k-factor, which is 2.07 for W Z+ jets [24], 1.27 for ttV [25] and 1.7 for tZj [26], respectively. The LO tt samples are normalized to the theoretical cross-section value for the inclusive tt process of 953.6 pb performed at next-to-next-to-leading order (NNLO) in QCD and including resummation of next-to-next-to-leading logarithmic (NNLL) soft gluon terms [27]. On the other hand, the MLM matching scheme is used, where we included up to three extra jets for W Z + jets and tZj in the simulations [28]. Here it should be mentioned that the k-factor for the LO cross section of σ tZ is chosen as about 1.4 at the 14 TeV LHC [29,30].
In order to simulate and generate the signal events, the κ Lagrangian terms presented in Eq.
(2) are implemented in MadGraph5-aMC@NLO [31] by means of the FeynRules package [32]. All of these signal and backgrounds events are generated at LO with the CTEQ6L parton distribution function (PDF) [33], and the renormalization and factorization scales are set dynamically by default. The events are then passed to Pythia 6 [34] for parton showering and hadronization, and the fast detector simulation in Delphes [35] with CMS detector card is used to include the detector effects. Finally, events are analyzed by using the program of MadAnalysis5 [36].
Further, we apply some general preselections as follows.
Since the third lepton, ℓ 3 , is assumed to originate from the leptonically decaying top quark, the top quark transverse cluster mass could be defined as [37] where p T,ℓ 3 and p T,b are the transverse momentums of the third charged leptons and b-quark, respectively, and / p T is the missing transverse momentum determined by the negative sum of visible momenta in the transverse direction. In Fig. 3 In Fig. 4, we present the normalized spectrum of the rapidity of the reconstructed resonances for the signal and backgrounds. It can be seen the Z boson from the ug → tZ process concentrates in the forwards and backwards regions. This is because the momentum of initial up quark is generally larger than that of gluon, the partonic center-of-mass frame is highly boosted along the direction of the up quark. This case is similar with the top-Higgs associated production process [38]. Thus we impose rapidity cut on reconstructed Z boson for the signal of ug → tZ process as • Cut-4: |y Z | > 1.0.
The cross sections of the signal and backgrounds after imposing the cuts are summarized in Table I, the anomalous couplings are chosen to be κ uZ (1TeV)/Λ = κ cZ (1TeV)/Λ = 0.1. One can see that all the backgrounds are suppressed very efficiently after imposing the selections. However, the cross section of the process pp → tt → tZc is about two times larger than that of cg → tZ process after cuts. As stated before, we should include these two processes when discussing the tcZ couplings. On the other hand, since the momentum of initial charm quark is much smaller than that of the initial up quark, the Z boson from cg initial states is not boosted as from ug initial states. Therefore, we do not apply the cut-4 when it comes to the cg → tZ process.   The statistical significance is calculated after final cut by using [39]: where σ S and σ B are the signal and background cross sections and £ int is the integrated luminosity. Here we define the discovery significance as SS = 5, the possible evidence as SS = 3 and the exclusion limits as SS = 2.  In Fig. 5, the 2σ, 3σ and 5σ lines are drawn as a function of the integrated luminosity and the branching ratios t → qZ. We do not consider the theoretical and systematic uncertainties for simplicity. One can see that the 5σ CL discovery sensitivity of Br ( It is remarkable that even with the high-luminosity of 3000 fb −1 , the branching ratios would not be measured better than 10 −5 . The recent phenomenological studies in Ref. [40] have shown that the 95% CL upper limits on the branching ratios Br(t → qZ) probed down to Br(t → uZ) ≤ 4.1 × 10 −5 and Br(t → cZ) ≤ 1.6 × 10 −3 . Thus our results are comparable with those for the HL-LHC, but they are below the sensitivity limits of the future 100 TeV pp circular collider (FCC-hh) [41].

IV. CONCLUSION
In this letter, we have investigated the signal of the tZ associated production via the FCNC tqZ couplings at the LHC with √ s = 14 TeV. We focus on trilepton final signals of the pp → tZ process with the decay mode t → W + b → bℓ + ν ℓ , Z → ℓ + ℓ − , and tt production process with the decay modet → Z(→ ℓ + ℓ − )q and t → bℓ + ν ℓ , where ℓ = e, µ and q reflects up and charm quarks. It is shown that the branching ratios Br(t → uZ) and Br(t → cZ) are, respectively, about Br(t → uZ) ≤ 1.3 × 10 −4 and Br(t → cZ) ≤ 4.2 × 10 −4 at 3σ level with the integrated luminosity 100 fb −1 , and probed down to Br(t → uZ) ≤ 2.2 × 10 −5 and Br(t → cZ) ≤ 8 × 10 −5 for the future HL-LHC, which are significantly better than the current experimental results.