Gluon Sivers function from forward exclusive χc1 photoproduction on unpolarized protons

Exclusive production of a χc1 axial vector quarkonia in photon-proton scattering at high energies requires a C-odd t-channel exchange. In the limit of vanishing momentum transfer this occurs either via the exchange of a photon, the Primakoff process, where the spin of the proton does not change. For axial-vector meson production, as a consequence of the Landau-Yang theorem, the Primakoff cross section is finite as t → 0. Alternatively, a C-odd spin dependent Odderon can be exchanged, which involves a spin flip of the proton. The resulting cross section is related to the square of the gluon Sivers function or its k_⊥²-moment. Using two models for the gluon Sivers function from the literature we compute the ratio of Sivers to Primakoff cross sections and the angular coefficient λ_θ governing the angular distribution of the χc1 → J/ψ + γ decay as functions of x. We point out that these observables constrain the magnitude of the gluon Sivers function at small x which could be accessed in electron-proton scattering and ultraperipheral proton-proton and nucleus-proton collisions.