Opportunities for studying $\mathit C$-even resonances at 3-12 GeV photon collider

Recently, a $\gamma\gamma$ collider based on the existing 17.5 GeV linac of the European XFEL has been proposed. High-energy photons will be generated by Compton scattering of laser photons with a wavelength of 0.5-1 $\mu$m on electrons. Such a photon collider covers the range of invariant masses $W_{\gamma\gamma} <12$ GeV. The physics program includes spectroscopy of $\mathit C$-even resonances ($c$-, $b$-quarkonia, 4-quark states, glueballs) in various $J^P$ states. Variable circular and linear polarizations will help in determining the quantum numbers. In this paper, we present a summary of measured and predicted two-photon widths of various resonances in the mass region 3-12 GeV and investigate the experimental possibility of observing these heavy two-photon resonances under the conditions of a large multi-hadron background. Registration of all final particles is assumed. The minimum values of $\Gamma_{\gamma\gamma}(W)$ are obtained at which resonances can be detected at a $5\sigma$ confidence level in one year of operation.