Exclusive $η_c$ photo- and electroproduction at HERA as a possible probe of the odderon singularity in QCD

Theory and phenomenology of the $\eta_c$ photo- and electroproduction is developed from the point of view of probing the odderon singularity in QCD which corresponds to the three gluon exchange mechanism. This mechanism leads to the cross-sections which are independent of $W^2$ for the exchange of three non-interacting gluons or exhibit increase with increasing $W^2$ (or $1/x$) for the odderon intercept above unity. The $\eta_c$ electroproduction in the three gluon exchange mechanism is shown to be entirely controlled by the transversely polarised virtual photons. The magnitude of the $\eta_c$ photoproduction cross-section is estimated to be around 100-400 pb. The t-dependence of the differential cross-section is also discussed.