Probing the Odderon in coherent hadron - hadron interactions at CERN LHC

One of the open questions of the strong interaction theory is the existence of the Odderon, which is an unambiguous prediction of Quantum Chromodynamics, but still not confirmed in the experiment. In this paper we propose the study of the diffractive $\eta_c$ photoproduction in coherent interactions as a new alternative to probe the Odderon in $pp$ and $PbPb$ collisions at CERN - LHC. As the Pomeron exchange cannot contribute to this process, its observation would indicate the existence of the Odderon. We predict total cross sections of order of $pb \, (\mu b)$ for $pp \, (PbPb)$ collisions and large values for the event rates/year, which makes, in principle, the experimental analysis of this process feasible at LHC.