Possible probe of the QCD odderon singularity through the quasidiffractive eta_c production in gamma-gamma collisions

The reactions gamma-gamma to eta_c eta_c and gamma gamma to eta_c + X are discussed within the three gluon exchange model. We give predictions for the differential cross-sections and discuss feasibility of measuring these processes at LEP2 and TESLA. The total cross-sections were estimated to be approximately equal to 40 fb and 120 fb for gamma-gamma to eta_c eta_c and gamma-gamma to eta_c + X respectively assuming exchange of elementary gluons that corresponds to the odderon with intercept equal to unity. These values can be enhanced by a factor equal to 1.9 and 2.1 for LEP2 and TESLA energies if the odderon intercept is equal to 1.07. The estimate of cross-sections sigma(e^+ e^- to e^+ e^- eta_c eta_c) and sigma (e^+ e^- to e^+ e^- eta_c + X) for untagged e^+ and e^- is also given.