Scaling Laws of Elastic Proton-Proton Scattering Differential Cross Sections

We show that elastic scattering pp → pp differential cross sections asfunction of the four-momentum transfer square |t| have a universal property,such that the ratio of bump-to-dip positions is constant from the energies ofthe ISR to the LHC, from tens of GeV and up to the TeV scale. We explore thisproperty to compare the geometrical scaling observed at the ISR with therecently proposed scaling law at the LHC. We argue that, at the LHC, withinpresent experimental uncertainties, there is in fact a family of scaling laws.We discuss the constraints that the scaling laws impose on the parametrizationof the elastic pp→ pp scattering amplitude.