Exclusive chi_c production in DIS is sensitive to the C-odd colorless tri-gluon correlation in the t-channel - the long sought Odderon. While the non-perturbative C-odd compound has been recently discovered in hadronic collisions [1], however, so far it escaped direct detections at HERA. In [2] we performed a computation of the chi_cJ (J = 0, 1, 2) exclusive production that takes into account the interference with the Primakoff (photon exchange). Our results reveal that the (spin independent) Odderon interferes constructively with the photon exchange and dominates the moderate to high momentum transfer region. The high luminosity of the EIC counteracts the feeble Odderon amplitude and we find a dozen of events per month. The excess above the Primakoff background as well as the characeristically slow falling t-distribution would serve as a direct signature of the Odderon at the EIC.
In the low-t region a contribution from the spin dependent Odderon is revealed that is closely related to the gluon Sivers function [3]: one of the main targets at the future EIC. Focusing on axial vector chi_c1, where the Coulomb tail (~1/|t|) of the Primakoff process is screened (Landau-Yang theorem), the spin dependent Odderon can be directly probed in unpolarized gammma+p collisions. The two contributions (spin dependent Odderon and photon) can be disentangled by accesing the chi_c1 polarization via the angular distribution of its decay products.
[1] TOTEM, Eur. Phys. J. C 80, 91 (2020); D0, Phys. Rev. D 86, 012009 (2012)
[2] S. Benic, A. Dumitru, A. Kaushik, L. Motyka, T. Stebel, 2402.19134v1 (PRD in press)
[3] R. Boussarie, Y. Hatta, L. Szymanowski, S. Wallon, Phys. Rev. Lett. 124, 172501 (2020).
[4] S. Benic, A. Dumitru, L. Motyka, T. Stebel, 2407.04968