As the heaviest known fundamental particle, the top quark ensures testing of the Standard Model and occupies a significant role in a lot of theories of new physics beyond the Standard Model. Up to now, the top quark has been only generated at the Tevatron and the Large Hadron Collider. However, one of the most important tasks of the physics program at the Large Hadron Collider is the investigation of the anomalous top quark interactions. In addition, the production of single top quarks, though rarer than production in pairs, presents us a different way to study the top quark produced via the electroweak interaction. This makes single top quark production an important signature for studying the properties of the top quark. Hence, we examine the anomalous $t\overline{t}\gamma$ interactions to investigate limits on the anomalous $a_A$ and $a_V$ couplings through single top quark production of the process $pp\to p{\gamma }^{⁎}p\to ptWX$ at the Large Hadron Collider, the High Luminosity Large Hadron Collider and High Energy Large Hadron Collider. The best limits obtained on the anomalous $a_A$ and $a_V$ couplings through the subprocess ${\gamma }^{⁎}b\to Wt$ at the High Energy Large Hadron Collider with $L_{int}=15$ ab⁻¹ at 68% Confidence Level are found to be $|a_A|=0.0509$ and $a_V=[-0.3171;0.0077]$. Therefore, we understand that ${\gamma }^{⁎}p$ collisions at the High Energy Large Hadron Collider improves the sensitivity limits of the anomalous coupling parameters according to previous studies.

作为已知最重的基本粒子，顶夸克可确保对标准模型进行测试，并且在标准模型之外的许多新物理理论中均扮演着重要角色。到目前为止，仅在Tevatron和“大型强子对撞机”上才产生顶夸克。然而，大型强子对撞机物理学程序最重要的任务之一就是对异常夸克相互作用的研究。此外，单顶夸克的生产虽然比成对生产少，但它为我们提供了一种通过电弱相互作用研究顶夸克的不同方法。这使得单个顶夸克生产成为研究顶夸克性质的重要标志。因此，我们检查异常$Ť\overline{Ť}\gamma$ 互动以研究异常的限制 ${\mathrm{一种}}_{\mathrm{一种}}$ 和 ${\mathrm{一种}}_V$ 通过单顶夸克生产过程进行耦合 $pp\to p{\gamma }^{⁎}p\to pŤ\mathrm{w\; ^}X$在大型强子对撞机，高光度大型强子对撞机和高能大型强子对撞机上。在异常情况下获得的最佳限制${\mathrm{一种}}_{\mathrm{一种}}$ 和 ${\mathrm{一种}}_V$ 通过子过程的耦合 ${\gamma }^{⁎}b\to \mathrm{w\; ^}Ť$ 在高能大型强子对撞机上 ${\mathrm{大号}}_{\mathrm{一世}ñŤ}=15$发现68％置信水平下的ab ^-1为$|{\mathrm{一种}}_{\mathrm{一种}}|=0.0509$ 和 ${\mathrm{一种}}_V=[-0.3171;0.0077]$。因此，我们了解${\gamma }^{⁎}p$ 根据先前的研究，高能大型强子对撞机的碰撞提高了异常耦合参数的灵敏度极限。