Photoproduction of C-even quarkonia at EIC and EicC

The $\eta_c$ photoproduction in $ep$ collision has long been proposed as an ideal process to probe the existence of odderon. In the current work, we systematically investigate the photoproduction of various $C$-even heavy quarkonia (exemplified by $\eta_{c(b)}$, and $\chi_{c(b)J}$ with $J=0,1,2$) via one-photon exchange channel, at the lowest order in $\alpha_s$ and heavy quark velocity in the context of NRQCD factorization. We find that the photoproduction rates of the $C$-even quarkonia through this mechanism are comparable in magnitude with that through the odderon-initiated mechanism, even in the Regge limit ($s\gg -t$), though the latter types of predictions suffers from considerable theoretical uncertainties. The future measurements of these types of quarkonium photoproduction processes in \texttt{EIC} and \texttt{EicC} are crucial to ascertain which mechanism plays the dominant role.