Accessing the real part of the forward elastic J/Psi-p and Phi-p threshold scattering amplitudes

We provide an updated analysis of the forward $J/\psi$-p scattering amplitude, relating its imaginary part to $\gamma p\to J/\psi p$ and $\gamma p\to c\bar cX$ 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 $J/\psi$-p s-wave scattering length $a_{\psi p}=0.046\pm0.005$~fm, which can be translated into a $J/\psi$ binding energy in nuclear matter $B_\psi=2.7\pm0.3$~MeV. We estimate the forward-backward asymmetry to the $\gamma p\to e^-e^+p$ process around the $J/\psi$ resonance, which results from interchanging the leptons in the interference between the $J/\psi$ production and the Bethe-Heitler mechanisms. We show that this asymmetry can reach values around -25\%. Its measurement can thus provide a very sensitive observable for a refined extraction of $a_{\psi p}$. A preliminary analysis of the $\phi$-p forward scattering led to the estimated forward-backward asymmetry reaching values of about -20\% for the beam energies $E=2.2,4.4$ GeV. The suitable kinematics were investigated for the specific setup of HMS and SHMS detectors of Hall C at JLab. Studies for the other JLab experiments (e.g. GlueX, SOLID) are ongoing.