Top quark anomalous FCNC production via $tqg$ couplings at FCC-hh

We investigate the top quark anomalous Flavor Changing Neutral Current (FCNC) $tqg$ interactions to probe limits on the couplings $\zeta_c$ and $\zeta_u$ through the $pp \to l\nu b+X$ signal process at FCC-hh collider with center of mass energy of 100 TeV. To separate signal from relevant Standard Model background processes, selection criteria based on Boosted Decision Trees (BDT) is used with a set of useful kinematic variables. The sensitivities on the anomalous top FCNC couplings ($\zeta_u$, $\zeta_c$) are found to be ($9.77\times10^{-5}$, $1.40\times10^{-4}$ ) for FCC-hh with $L_{int}$=10 ab$^{-1}$ at 95 \% C.L. including realistic detector effects of the FCC-hh baseline detector. The branchings $BR (t \to ug)$ and $BR (t \to c g)$ converted from obtained limits for FCNC couplings are at the order of $10^{-7}$ which is at least one order of magnitude better than the projected limits of HL-LHC with $L_{int}$= 3 ab$^{-1}$.


I. INTRODUCTION
The top quark being the most massive elementary particle in the Standard Model (SM) is an excellent probe not only to search the dynamics of electroweak symmetry breaking but also to test SM and Beyond the Standard Model (BSM) physics. The Flavour Changing Neutral Current (FCNC) interactions involving a top quark, other up type quarks (u, c) and neutral gauge bosons are forbidden at tree level and suppressed in loop level according to the Glashow-Illopoulos-Maiani (GIM) mechanism in the SM [1]. Since predictions for SM branching ratios of the top quark FCNC decay to gluon, photon, Z or Higgs boson and up-type quarks are out of range for current experimental sensitivities, the top quark FCNC interactions can have an important role to test new physics. In the BSM scenarios such as two-Higgs doublet model [2], supersymmetry [3], technicolor [4] and minimal supersymmetric standard model [5], the branching ratios of top quark FCNC decays are predicted promisingly at the order of 10 −6 -10 −5 due to enhancement on the production rate.
One can even expect to improve these limits at higher center of mass energies. The Future Circular Collider (FCC) project [9] has great potential with an option of proton-proton (FCC-hh) collisions at 100 TeV center of mass energy with peak luminosity 5 × 10 34 cm −2 s −1 [10].
In this study, we investigate anomalous FCNC tqg interactions to probe limits on couplings ζ c and ζ u couplings through the pp → lνb + X signal process at FCC-hh collider. Realistic detector effects are included in the production of signal and background processes. In the search of anomalous FCNC tqg interactions at hadron colliders, the effective Lagrangian approach [11,12] has been comprehensively studied in literature for hadron colliders . In this approach, FCNC interactions are described by higher-dimensional effective operators and added to four-dimensional SM Lagrangian. The FCNC Lagrangian of the tqg interactions can be written as where g s is the strong coupling constant, λ a are the Gell-Mann matrices with a = 1, ..., 8 and ζ is the strength of anomalous FCNC couplings for tqg vertices; P L(R) denotes the left (right) handed projection operators. For the FCNC interactions, the tensor σ µν is defined as σ µν = i 2 [γ µ , γ ν ]. In this study, we assumed no specific chirality for the FCNC interaction vertices, i.e. ζ L qt = ζ R qt = ζ q where q denotes up or charm quark.
Within the SM, top quarks are produced either pair via the strong interaction or the singly via weak interaction: i) the t-channel process, ii) the s-channel process and iii) the W t associated production at hadron colliders. With these production modes, the FCNC top-quark decays of t → qX mode with X = H, Z, γ, g can be investigated through the final states of subsequent decays of particles. While the final states including H, Z, γ can be searched promptly, the decay mode t → qg is almost indistinguishable from overwhelming backgrounds such as multijet-production via quantum chromodynamic (QCD) processes. To obtain better sensitivities for FCNC tqg interactions, one can search direct top production, qg → t, which originates from an up (u) or a charm (c) quark and gluon from in the initial state colliding hadrons and through subprocess combining immediately to form an s-channel top quark which then mostly decays to W b. The Feynman diagrams of subprocess qg → lνb including the anomalous FCNC tqg interactions and relevant SM background at tree level are shown in Fig.1.

III. SIGNAL AND BACKGROUND SIMULATION
The effective Lagrangian in Eq.1 is defined in the FeynRules package as a Universal FeynRules Output (UFO) module [49] and embedded into MadGraph2.5.3_aMC@NLO [50]. The cross sections for pp → lνb + X process at 100 TeV center of mass energy have been evaluated as a function of ζ c and ζ u couplings, which include signal and interference between FCNC and SM as shown in Fig.2.
As seen in Fig.2, noticeable deviations for the anomalous contributions starts around a coupling value 3 × 10 −4 . Moreover, the contribution of ζ u coupling is larger than the ζ c coupling because of the dominant up quark parton distribution function at 100 TeV center of mass energy.
Since we study the FCNC tqg couplings via pp → lνb process at FCC-hh, the final state topology of signal process consists of a charged lepton, missing energy and a b-tagged jet. The following relevant SM background processes having the same or similar final state topology are considered as backgrounds; • SM : pp → lνb σ = 4.060 × 10 1 pb Here, the SM refers to SM background of the same final state with the signal process. The W j is considered as background candidate due to any misidentification of light quark as a mis-tagged b-jet in detector when W boson decays leptonically.
The Zj process is considered to another relevant background in this study. The tt and tW , tj processes are added as backgrounds, since they have more jets than one b-tagged jet in final state. The di-boson backgrounds, W W , W Z and ZZ are also included as a background to see the effect of multijets in the final state. Mass reconstruction of W -boson depends on accuracy of hadronic calorimeter of detector and it can not be easily distinguishable from Z-boson. The 10 6 events are generated by using MadGraph2.6.3.2aMC@NLO for each signal and background processes.
The PYTHIA8.2 [51] is utilized in parton showering and hadronization of generated signal and background events. Produced jets inside the events are clustered using FastJet3.2.1 [52] with antikt algorithm [53] where a cone radius is set R = 0.4. FCC-hh detector card embedded into Delphes 3.4.1 [54] is used to include realistic detector effects of the FCC-hh baseline detector.

IV. EVENT SELECTION
Characteristic signature of the pp → lνb + X signal process suggests to work with events having at least one lepton, missing transverse energy and one b-jet for the analysis. Distributions of Pre-selection N l 1 and N b 1 where the E l , p T,l and p z,l are the energy, transverse and longitudinal momentum components of the leading lepton, respectively. The solution that gives the smallest absolute value chosen and other solutions are discarded in our study as in Ref. [55]. The reconstructed m top T and m top distributions are presented in Fig. 4. As shown in Fig. 4, signal peaks in the actual mass region of the top quark.
The distance between leading lepton and b-tagged jet is ∆R(l, b) = (∆φ l,b ) 2 + (∆η l,b ) 2 where φ l,b and η l,b are azimuthal angle and the pseudorapidity difference between leading lepton and b-tagged jet. Similarly, one can obtain the distance between reconstructed top and leading lepton ∆R(t, l),   Therefore one can determine optimal cut on reconstructed BDT distributions considering signal efficiency. In our study, 70% signal efficiency has been taken into account in the determination of optimal BDT cut which varies for each signal scenarios with different values of couplings ζ c and ζ u . Applying the optimal BDT cut value to signal and background events, transverse mass (on the left) and invariant mass (on the right) distributions of reconstructed top quark are shown in Fig.7.
These distributions are normalized to the integrated luminosity of 100 fb −1 and the range between 135 GeV and 195 GeV is used to calculate Statistical Significance (SS). Using Poisson formula for SS as where S and B T are the signal and total background events at a particular luminosity. The SS as a function of couplings ζ u (on the left) and ζ c (on the right) for L int =3 ab −1 and L int =10 ab −1 are shown in Fig.8. In this figure, only one coupling at a time is varied from its SM value. For integrated luminosity of 3 ab −1 , upper limit for ζ u (ζ c ) reaches to 1.614 × 10 −4 (2.162 × 10 −4 ) at 3σ SS value while 2.242 × 10 −4 (2.847 × 10 −4 ) at 5σ. Increasing integrated luminosity to 10 ab −1 lower the upper limit but not drastically.
The predictions for SM branching ratios of the top quark FCNC decay to gluon, photon, Z or Higgs boson and up-type quarks are at the order of 10 −14 . Thus, the precise measurements of these branching can have an important role to test new physics in the top quark sector. One can express results in terms of branching ratios which can be comparable with the results of other studies as in [58]. In Fig.9, the current observed [6,7]  and ζ c are converted to branching ratios BR(t → ug) and BR(t → cg) at FCC-hh. It is found that a sensitivity of the order of 10 −7 for branching ratios at high integrated luminosity would be achievable.   Only one coupling (ζ u or ζ c ) at a time is varied from its SM value.