Universal fit to p−p elastic diffraction scattering from the Lorentz-contracted geometrical model

We examine the prediction of the Lorentz-contracted geometrical model for proton-proton elastic scattering at small angles. The model assumes that when two high-energy particles collide, each behaves as a geometrical object which has a Gaussian density and is spherically symmetric except for the Lorentz contraction in the incident direction. It predicted that dσdt should be independent of energy when plotted against the variable β²P_⊥²σₜₒₜ(s)(38.3 mb). Thus the energy dependence of the diffraction-peak slope (b in an e^-b|t| plot) is given by b(s)=A²β²σₜₒₜ(s)(38.3 mb), where β is the proton's c.m. velocity and A is its radius. We used recently measured values of σₜₒₜ(s), and obtained an excellent fit to the elastic slope in both t regions [-t<0.1 (GeV/c)² and 0.1<-t<0.4 (GeV/c)²] at all energies from s=6 to 4000 (GeV)².