Scaling properties of elastic proton-proton scattering at LHC energies

The TOTEM Collaboration has measured the differential cross section of elastic proton-proton scattering dσ/d|t| at s=2.76, 7, 8, and 13 TeV. It is observed that all dσ/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 dσ/d|t| at LHC energies fall onto a universal curve when they are mapped to the scaling variables dσ/d|t|×(s/TeV²)^−0.305 versus (s/TeV²)^0.065(|t|/GeV²)^0.72. Some implications of this scaling law in the impact parameter picture of the scattering amplitudes are explored.