Constraints on the odderon amplitude in the CGC framework

In this manuscript we analyzed the elastic $pp$ and $p\bar{p}$ cross-section in the Color Glass Condensate framework, treating them as a dilute-dense system, and derived the phenomenological constraints (upper bounds) on the odderon-mediated part of the dipole scattering amplitude $\mathcal{O}(Y,\,\boldsymbol{r},\,\boldsymbol{b})$. For our analysis we used the experimental data available from TOTEM-D0 and ISR collaborations and construct an observable defined as a combination of the cross-sections which allows us to suppress possible uncertainties associated with charge-parity even part of the amplitude. We analyzed two phenomenological parametrizations of odderons and demonstrated that after minor adjustments to the global normalization, they can describe the experimental data reasonably well, although due to large experimental uncertainties the odderon amplitude remains loosely constrained. Our results indicate that existing data provide limited sensitivity to the odderon and emphasize the need for improved precision and complementary observables.