Top quark flavor changing neutral currents and dipole moments through three and four top-quark productions at the LHC

In this paper, the top quark flavor changing neutral current (FCNC) interaction is studied through the process of the three-top quark production at the LHC for center-of-mass energy of 14 TeV. We also investigate the anomalous top quark chromoelectric and chromomagnetic dipole moments through the four top-quarks production signal at the center-of-mass energy of 13 TeV. We demonstrate that these processes are powerful tools to constrain the top quark FCNC couplings as well as the top dipole moments.


Introduction
The top quark with its unique features like large mass and extremely short lifetime, provides a great opportunity to test the standard model (SM) of particle physics as well as probing new physics (NP) beyond the SM (BSM) [1,2]. Besides the dominant production of top quark pairs with a small contribution of single top quark production, it is also possible to have three or four top-quark production at the large center-of-mass energy in proton-proton (pp) collisions at the LHC [3,4]. The top quark is expected to decay to a W boson and a b-quark in the SM [5]. In flavour changing neutral current (FCNC) interactions, the top quark decays to a neutral boson and an up or charm quark. In the SM, FCNC transitions are not only forbidden at tree level but also suppressed at higher orders due to the Glashow-Iliopoulos-Maiani (GIM) mechanism [6]. In some NP models, a significant enhancement of top quark FCNC couplings are predicted [7,8]. We explore the top quark FCNC interactions through processes with only three top-quark in the final state. In the second part of this analysis, the strong and electroweak dipole moments of the top quark are studied. Even though dipole interactions do not exist at the leading order in the SM, we explore the sensitivity of the four top-quark production at the leading order (LO) to the strong and weak top quark dipole moments.

Theoretical framework and assumptions
The new physics effects may be described in a model-independent way using an effective Lagrangian with the following form [9,10,11,12], 2 where c i are a set of dimensionless coefficients and the NP effects are parameterized with dimension-six operators O i which satisfy the SM symmetries and Λ in Eq. 1 is the scale of NP. In this analysis, our aim is to probe the sensitivity of dimension-six operators which contain FCNC (tqg; tqZ; tqγ; tqH) vertices as well as those which contribute to gtt and Ztt vertices in the four top-quark production at the LHC. The most general effective Lagrangian describing the FCNC interactions, has the following form [6,7]: where ζ qt , η qt , X qt , κ qt and λ qt are the real parameters indicating the strength of FCNC interactions with the gluon, Higgs, Z and photon, respectively.
In the SM, all the above coefficients vanish at tree-level. The effective Lagrangian considering dimension-six operators for gtt and Ztt can be parameterized as [9,13]: and The couplings d

Sensitivity of three-top quark production to FCNC couplings
In this section, we examine the sensitivity of the three top-quark production cross section to the FCNC couplings of tqg, tqγ, tqZ, and tqH. All FCNC couplings of tqg, tqγ, tqZ, and tqH (q = u, c) are studied independently. We mainly focus on a clean signature with two same-sign leptons, where the lepton could be an electron or a muon. So, the signal events are specified by the presence of two isolated same-sign charged leptons, large missing transverse energy, and several jets from which three come from b-quarks. Furthermore, we consider ttW , ttZ, SM four top, ttW W , ttZZ and W W Z as the background processes. The analysis is performed for 300 and 3000 fb −1 of the LHC at the center-of-mass energy of 14 TeV. For generation of both the signal and the background processes, the MadGraph5 aMC@NLO package [14] is used. Figure 1 illustrates the lowest-order Feynman diagram for the three top-quark production from tqg FCNC coupling with the leptonic decay of the W boson from top quark and hadronic decay of the W boson from anti-top quark. For separating signal from background events, the following simple criteria are applied, (I) Two same-sign charged lepton with p T > 10 GeV, |η| < 2.5, m ℓℓ > 10 GeV,  As can be seen, the FCNC signals peak is at three while the backgrounds peak is at two. The invariant mass distribution of dilepton is illustrated on the right side of Figure 2. Since the tqg FCNC interactions are momentum dependent, there is a shift in the tqg signal with respect to the background and the tqH signals. The upper limits on signal rates calculated in terms of the upper bounds on the FCNC branching fractions B(t → qX) are summarized in Table 1 for two scenarios of integrated luminosities 300 and 3000 fb −1 of data. The results from a recent ATLAS experiment analysis based on the tt process in which one of the top quark decays via FCNC and another one decays in the normal way are also presented for comparison.
As the comparison with the ATLAS limits shows, the three top-quark signal can reach similar sensitivity to ATLAS in the tqH FCNC coupling. TeV based on the integrated luminosities of 300 and 3000 fb −1 . The HL-LHC results from a recent ATLAS experiment study which uses tt process are presented for comparison [15].

Sensitivity of four-top quark production to the top quark weak and strong dipole moments
In the following section, we investigate the sensitivity of four top-quark production in protonproton collisions at the center-of-mass energy of 13 TeV to the strong (d g A,V ) and weak (d Z A,V ) top quark electric and magnetic dipole moments. Figure 3 presents leading order Feynman diagrams including the contributions of strong dipole moments. By assuming at most one effective vertex in each diagram, the total four top cross section becomes at most a quadratic function of dipole moments, where σ SM is the SM four top cross section and the linear terms present the interference between the SM and NP and its contribution is at Λ −2 order. The quadratic terms in the ) dipole moments using the recent CMS experiment measurement [4] are presented in Table 2.
The resulting bounds are compatible with the ones obtained from top quark pair cross sections at the Tevatron as well as the LHC.

Summary and conclusions
In this paper, we have explored the FCNC couplings via a model-independent way in threetop quark production. Upper limits on the FCNC branching fractions are calculated. We demonstrate that the three top-quark production is more sensitive to the FCNC couplings of tqH. Moreover, we investigate the sensitivity of the four-top cross section to the strong and weak top quark dipole moments. Upper limits are set on the top quark dipole moments which are compatible with other bounds extracted from different processes at the LHC.