Scaling properties of elastic proton-proton scattering at LHC energies

Abstract

The TOTEM Collaboration has measured the differential cross section of elastic proton-proton scattering $\mathrm{d}\sigma /\mathrm{d}|t|$ at $\sqrt{s}=2.76$, 7, 8, and 13 TeV. It is observed that all $\mathrm{d}\sigma /\mathrm{d}|t|$ data points vary in the same way as a function of the center-of-mass energy in the so-called "dip" and "bump" regions. These features hint at possible universal properties of elastic scattering. Based on these empirical observations, and taking inspiration from saturation models, we propose a simple scaling law for proton-proton elastic scattering at LHC energies. We find that the $\mathrm{d}\sigma /\mathrm{d}|t|$ at LHC energies fall onto a universal curve when they are mapped to the scaling variables $\mathrm{d}\sigma /\mathrm{d}|t|\times (s/{\text{TeV}}^2{)}^{-0.305}$ versus $(s/{\text{TeV}}^2{)}^{0.065}(|t|/{\text{GeV}}^2{)}^{0.72}$. Some implications of this scaling law in the impact parameter picture of the scattering amplitudes are explored.