A QCD interpretation of the scaling observed in the LHC proton-proton elastic cross-sections at moderate transfer momentum

Abstract: A phenomenological scaling property of the LHC proton-proton elastic scattering cross sections at moderate transfer momentum has been recently observed. The theoretical QCD saturation framework for hard elastic scattering on the proton, which we recall, predicts a strikingly similar scaling property in the same configuration of energy and momentum transfer. This similarity favors a theoretical interpretation where the hard amplitude is the building block of the $pp$ amplitude via unitarization. The values of the scaling exponents favor two QCD saturation approaches where the saturation scale exponent is of order one half of that which is found for hard elastic scattering and deep inelastic processes on the proton.