Comprehensive fits to high energy data for $σ$, $ρ$, and $B$ and the asymptotic black-disk limit

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 $σ_{\rm elas}/σ_{\rm tot} \rightarrow 1/2$, and that $8πB/σ_{\rm tot}\rightarrow 1$ 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.

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