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As the heaviest known fundamental particle, the top quark ensures testing ofthe Standard Model and occupies a significant role in a lot of theories of newphysics beyond the Standard Model. Up to now, the top quark has been onlygenerated at the Tevatron and the Large Hadron Collider. However, one of themost important tasks of the physics program at the Large Hadron Collider is theinvestigation of the anomalous top quark interactions. In addition, theproduction of single top quarks, though rarer than production in pairs,presents us a different way to study the top quark produced via the electroweakinteraction. This makes single top quark production an important signature forstudying the properties of the top quark. Hence, we examine the anomalous$t\bar{t}\gamma$ interactions to investigate limits on the anomalous $a_A$ and$a_V$ couplings through single top quark production of the process$pp\rightarrow p \gamma^{*} p \rightarrow p t W X$ at the Large HadronCollider, the High Luminosity Large Hadron Collider and High Energy LargeHadron Collider. The best limits obtained on the anomalous $a_A$ and $a_V$couplings through the subprocess $\gamma^{*} b \rightarrow W t$ at the HighEnergy Large Hadron Collider with $L_{int}=15$ ab$^{-1}$ at $68\%$ ConfidenceLevel are found to be $|a_{A}|=0.0590$ and $a_{V}=[-0.3202;0.0108]$. Therefore,we understand that $\gamma^{*} p$ collisions at the High Energy Large HadronCollider improves the sensitivity limits of the anomalous coupling parametersaccording to previous studies.

Model-independent sensitivity estimates for the electromagnetic dipole moments of the top quark at the Large Hadron Collider and beyond