Analyzing the anomalous dipole moment type couplings of heavy quarks with FCNC interactions at the CLIC

In this study we examine both anomalous magnetic and dipole moment type couplings of a heavy quark via its single production with subsequent dominant Standard Model decay modes at the Compact Linear Collider (CLIC). The signal and background cross sections are analyzed for heavy quark masses 600 and 700 GeV. We make the analysis to delimitate these couplings as well as to find the attainable integrated luminosities or 3$\sigma$ observation limit.


Introduction
Discovery of new particles performs a crucial role for physics beyond the standard model (SM) and may play a milestone role in the discovery of some open questions like the electroweak symmetry breaking [1][2][3][4][5], fermion mass spectrum hierarchies and mixing angle in quark/lepton sectors [6][7][8][9][10], CP violation, and flavor structure of standard theory [11][12][13][14][15][16][17]. The precise determination of heavy quark properties may present the existence of new physics. A heavy down-type quark ( ) with mass less than 645 GeV and an up-type quark ( ) with mass less than 585 GeV [18] are excluded at 95% confidence level from proton-proton collisions at √ = 8 TeV ATLAS detector at the CERN large hadron collider.
Serious contributions can be expected for the production of the heavy fermions, due to the anomalous magnetic moment type interactions. Phenomenological studies with these anomalous effects of these quarks have been performed on hadron colliders [26][27][28][29][30][31], on electron proton colliders [32,33], and on linear colliders [34]. In this work, we study the production of single heavy quark at compact linear collider (CLIC) [35] via both anomalous magnetic and dipole moment type interactions. CLIC, a most popular proposed linear collider on TeV scale, would complete the LHC results by performing precision measurements to provide necessary information about some parameters of heavy quarks. The aim of this study is to delimitate the anomalous magnetic    and dipole moment type couplings of quark from a detailed signal and background analysis including Monte Carlo simulation with the effects of initial state radiation (ISR) and beamstrahlung (BS) in the + − collisions.

Single Production and Decay of Quark
The interaction Lagrangian for quark within the SM is given by where , , 0 , and + are the vector fields for photon, gluon, boson, and boson, respectively. is the electroweak coupling constant and is the strong coupling constant.
are the Gell-Mann matrices; is the electric charge of heavy quark . and are the vector and axial-vector type couplings of the neutral weak current with Advances in High Energy Physics   = 600 and 700 GeV separately, in [36]. In our calculations we use this parameterization for values of the 4 × 4 CKM matrix elements and we assume > with a mass splitting of − ≈ 50 GeV. We implement the related interaction vertices, given in the effective Lagrangian, into the tree level event generator CompHEP package [37] for numerical calculations. In Figure 1, branching ratios (BR) dependence oñ/Λ for SM decay channels ( ( , )) and anomalous decay channels ( ( , )) of quark which are calculated by using Lagrangians (1) and (2)  The contributing tree level Feynman Diagram for the anomalous single production of quark in + − collision is shown in Figure 3. In Figure 4, the total cross sections for single production of quark are plotted at collision center of mass energy of 3 TeV with respect tõ/Λ for = 600 and 700 GeV with /Λ = 0 and 0.1 TeV −1 . Initial state radiation (ISR) and beamstrahlung (BS) are specific features of the linear colliders. We take the beam parameters for the CLIC given in Table 1, when calculating the ISR and BS effects. Hereafter, in all our numerical calculations we take into account ISR + BS effects.

Signal and Background Analysis
The signal process of single production of quark including the dominant SM decay mode over anomalous decay is + − →̄→ +̄, wherē=,. The dominant source of SM background process is + − +̄f or the corresponding signal processes.
In the transverse momentum, rapidity, and invariant mass distributions analysis, we assumẽ/Λ = /Λ = 0.1 TeV −1 . In Figure 5, the transverse momentum ( ) distributions of the final state quark for signal and background are shown for CLIC energy. We applied a cut of > 50 GeV to reduce the background, comparing the signal distribution of quark with that of the corresponding background.
Advances in High Energy Physics 5 Table 2: The signal and background cross sections and signal statistical significance (SS) by taking /Λ = 0 TeV −1 for the CLIC at √ = 3 TeV with integrated luminosity of 5.9 × 10 5 pb −1 .
(GeV)̃/ Λ = 0. In Figure 6, we plot the rapidity distributions of final state quark in signal and background processes. According to these figures, the cut | | < 2.5 can be applied to suppress the background while the signal remains almost unchanged.
In Figure 7, the invariant mass distributions for the + system in the final state are plotted. From these figures, we can see that the signal has a peak around mass of quark over the background.
In Table 2, we calculate cross sections of the signal and background and the statistical significance (SS) to discuss the observability of 600 and 700 GeV quark for̃/Λ = 0.1 and 0.01 TeV −1 by taking /Λ = 0 TeV −1 at CLIC. The SS of the signal is obtained by using the following formula: where is the signal and is the background cross sections for the + − →̄→ +̄p rocess, respectively, and = , . We take into account finite energy resolution of the detectors for realistic analysis. In our numerical calculations we use the mass bin width Δ = max(2Γ, ) to count signal and background events with the mass resolution . The mentioned and cuts are applied assuming the integrated luminosity given in Table 1.
After this point, we will focus on limiting the anomalous magnetic and dipole moment type couplings. Firstly, in Figure 8, we present the 3 contour plot for̃/Λ-/Λ plane at √ = 3 TeV with = 600 GeV. According to these figures, the lower limits of /Λ and̃/Λ are about 0.033 TeV −1 at the CLIC energy.
We plot the lowest necessary luminosities with 3 observation limits for (a) = 600 GeV and (b) = 700 GeV at √ = 3 TeV depending on anomalous couplings in Figure 10. In the case of /Λ =̃/Λ = 0.1 TeV −1 , it is seen that from these figures, quarks with masses 600 and 700 GeV can be observed at 3 observation limit with lowest integrated luminosity at the order of 10 4 pb −1 at CLIC.

Conclusion
The anomalous FCNC interactions of heavy quarks could be important for some parameter regions due to the expected large masses. The sensitivity to the anomalous couplings ( , ) and (̃,̃) can be obtained for = 600 GeV about (0.033, 0.033) and (0.035, 0.038) for = 0.01, and for = 700 GeV (̃,̃) values can be obtained about (0.019, 0.0195) for = 0.01 with Λ = 1 TeV. We also find the lowest necessary luminosity limit values at the order of 10 4 pb −1 for CLIC.