Resonance Production of Excited u-quark at the FCC Based $\gamma$ $p$ Colliders

Several Beyond the Standard Model theories are proposed that fermions might have composite substructure. The existence of excited quarks is going to be the noticeable proof for the compositeness of Standard Model fermions. For this reason, excited quarks have been investigated by phenomenological and experimental high energy physicists at various collider options for the last few decades. The Future Circular Collider (FCC) has been recently planned as particle accelerator to be established at CERN. Beside the $\sqrt{s}$ = 100 TeV proton-proton collisions, the FCC includes electron-positron and electron-proton collision options. Construction of linear $e^- e^+$ colliders (or dedicated e-linac) tangential to the FCC will afford an opportunity to handle multi-TeV $ep$ and $\gamma p$ collisions. In this respect, we executed a simulation of the resonance production of the excited $u$ quark at the FCC based $\gamma p$ colliders with choosing both the polarized and unpolarized photon beams. The findings revealed that the chirality structure of the $q^*$-$q$-$\gamma$ vertex can be determined by the photon beam polarization. The attainable mass limits of the excited $u$ quark reached the highest values when the polarized photon beam was chosen. In addition, the ultimate compositeness scale values can be handled by appropriate choice of the photon beam polarization.