Comprehensive fits to high energy data for $\sigma$, $\rho$, and $B$ and the asymptotic black-disk limit

Abstract

We demonstrate that the entirety of the data on proton--proton and antiproton--proton forward scattering between 6 GeV and 57 TeV center-of-mass energy is sufficient to show that ${\sigma }_{\mathrm{elas}}/{\sigma }_{\mathrm{tot}}\to 1/2$, and that $8\pi B/{\sigma }_{\mathrm{tot}}\to 1$ at very high energies, where $B$ the forward slope parameter for the differential elastic scattering cross sections. The relations demonstrate convincingly that the asymptotic $pp$ and $\bar{p}p$ scattering amplitudes approach those of scattering from a black disk. This result obviously has implications for any new physics that modifies the forward scattering amplitudes.

Comments: 13 pages, 5 figures; accepted for publication in Physical Review D