Isolating the Odderon in central production in high energy $pA$ and $AA$ collisions

We study the rapidity dependence of the cross section on the rapidity of the central exclusive production cross sections of C-even mesons in $pA$ and $AA$ collisions, where $A$ is a heavy ion. We observe qualitatively different behaviour of the contributions arising from $\gamma$-Odderon and Pomeron-Pomeron fusion mechanisms. This can be used to extract the Odderon signal from the events of $f_2$ mesons exclusively produced in the forward region. Estimates, obtained using expected values of the Odderon cross section, indicate that the $\gamma$-Odderon contribution may exceed by a few times the Pomeron-induced background in Pb-Pb collisions. Moreover, the Odderon effect can be clearly seen in terms of the asymmetry in $pA$ and $AA$ collisions with the beam and target reversed. It is particularly interesting to note that the asymmetry for $\gamma$-Odderon fusion reaches its maximum value close to 1 in the forward direction, whereas the asymmetry for the Pomeron-Pomeron fusion contribution is small. The role of additional interactions of the $f_2$ meson with nucleons in the heavy ion, and also the contributions from secondary Reggeons, are estimated. The photon-Odderon contribution has a large normalisation uncertainty but the enhances cross-section in the forward region combined with a large asymmetry increases the chance of experimentally detecting the Odderon.