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$Υ$ photo-production on the proton at the Electron-Ion Collider

We present a dispersive analysis with the aim to extract the $Υ$-p scattering length from $γp \to Υp$ experiments. In this framework, the imaginary part of the $Υ$-p forward scattering amplitude is obtained from $γp \to Υp$ cross section measurements, and is constrained at high energies from existing HERA and LHC data. Its real part is calculated through a once-subtracted dispersion relation, and the subtraction constant is proportional to the $Υ$-p scattering length. We perform a feasibility study for $Υ$ photo-production experiments at an Electron-Ion Collider and discuss the sensitivity and precision that can be reached in the extraction of the $Υ$-p scattering length.