Lorentz contracted geometrical model

Abstract

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. Folding the two spatial distribution together we obtain the slope ( b) of the elastic diffraction peak in terms of the c.m. velocities ( β i and β j ) and the sizes ( A i and A j ) of the two incident particles. These sizes are assumed to have the experimental s-dependence of σ tot ∝ πA 2 for each reaction. The combined s-dependence of the σ tot 's and the β's gives the s-dependence of the elastic slope b ij(s) = 1 2 (A i 2β i 2 + A j 2β j 2) σ ij tot (s) σ ij tot (∞) . This formula agrees with the experimental slope for p-p, p -p, K +-p, K −-p and π ±-p elastic scattering from 3 to 1500 GeV/ c, with only 3 parameters: A π 2 = 6.1, A K 2 = 3.3 and A p 2 = 10.5 (GeV/ c) −2.