Accessing the real part of the forward J /ψ -p scattering amplitude from J /ψ photoproduction on protons around threshold

We provide an updated analysis of the forward J /ψ -p scattering amplitude, relating its imaginary part to γ p →J /ψ p and γ p →c c ¯X cross section data, and calculating its real part through a once-subtracted dispersion relation. From a global fit to both differential and total cross section data, we extract a value for the spin-averaged J /ψ -p s-wave scattering length a_{ψ p}=0.046 ±0.005 fm , which can be translated into a J /ψ binding energy in nuclear matter of B_ψ=2.7 ±0.3 MeV . We estimate the forward-backward asymmetry to the γ p →e^-e⁺p process around the J /ψ resonance, which results from interchanging the leptons in the interference between the J /ψ production and the Bethe-Heitler mechanisms. We show that to good approximation this asymmetry depends linearly on a_{ψ p}, and can reach values around -25 % for forthcoming J /ψ threshold production experiments at Jefferson Lab. Its measurement can thus provide a very sensitive observable for a refined extraction of a_{ψ p}.