Sensitivity analysis for the anomalous $tqγ$ couplings via $ γ q {\rightarrow} t γ$ subprocess in photon-proton collisions at the FCC-$μ$p

Abstract: In this study, we investigate anomalous flavour-changing neutral current (FCNC) interactions related to the top quark, particularly the $t\rightarrow q\gamma$ transition, within the Standard Model Effective Field Theory (SMEFT) framework. These rare processes are largely suppressed in the Standard Model (SM) and are strong indicators for new physics scenarios beyond the SM. In our study, we have analyzed the cross sections of the $ \gamma q {\rightarrow} t {\gamma}$ subprocess for two different center-of-mass energies, 17.3 TeV and 24.5 TeV, at the Future Circular Collider (FCC-${\mu}$p) collider. Our results derived from simulations show that the branching ratios for these processes can be reduced to the order of $10^{-5} $. These values provide significantly tighter limits than the current experimental limits. In light of these findings, it can be stated that the FCC-${\mu}$p collider offers significant potential for discovering new physics which represents a sensitivity improvement over the current experimental limits from CMS, enhancing sensitivity by approximately 30\%.Moreover, it has been demonstrated that higher centre-of-mass energies and integrated luminosity values significantly enhance the discovery potential of these rare processes. Accordingly, the results indicate that-energy colliders such as FCC-${\mu}$p are of critical importance in the search for new physics and in the study of the role of the top quark in the context of flavour physics. As a result, by providing a comprehensive theoretical analysis, this study contributes to the importance of FCNC processes in the search for new physics beyond the Standard Model and will shed light on future experimental and phenomenological studies.