Excited Quarks Production at FCC and S$pp$C $pp$ Colliders

Potential discovery, observation and exclusion limits of excited $u$ and $d$ quarks with gamma+jet final state are researched at the multi-TeV scale colliders, FCC and S$pp$C in this work. Both colliders, FCC and S$pp$C, show that excited $u$ and $d$ quarks could be discovered up to 42.1 TeV and 55.2 TeV for $u^\star$, 30.3 TeV and 39.4 TeV for $d^\star$ and 42.3 TeV and 55.5 TeV mass values for degenerate case (m$_{u^\star}$ = m$_{d^\star}$), respectively. Determination of excited quarks compositeness scale is examined, which will be up to multi-PeV level. Beside these analysis, free parameters ($f_s,\;f\;\text{and}\; f^\prime$) are scanned from around 0.1 up to 1 that show excited quark could be discovered at dozens of TeV with even coupling constants under 0.1.