Recently, a $$\gamma \gamma $$
γ
γ
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$${\,\upmu \mathrm m}$$
μ
m
on electrons. Such a photon collider covers the range of invariant masses $$W_{\gamma \gamma } <12$$
W
γ
γ
<
12
$${\mathrm {\,Ge V\!/}c^2}$$
Ge
V
/
c
2
. The physics program includes spectroscopy of $$ C $$
C
-even resonances (c-, b-quarkonia, 4-quark states, glueballs) in various $$J^P$$
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 $${\mathrm {\,Ge V\!/}c^2}$$
Ge
V
/
c
2
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 $$\varGamma _{\gamma \gamma }(W)$$
Γ
γ
γ
(
W
)
are obtained at which resonances can be detected at a $$5\sigma $$
5
σ
confidence level in 1 year of operation.