Energy dependence of proton-proton elastic scattering at large momentum transfer

TL;DR

This paper analyzes proton-proton elastic scattering at high energies, revealing a consistent power-law behavior with energy-dependent magnitude, and predicts significant cross section reduction at 13 TeV, informing future experiments.

Contribution

It introduces a detailed analysis of energy dependence in proton-proton elastic scattering, linking the tail magnitude decrease to a power of the strong coupling, and provides predictions for high-energy experiments.

Findings

The differential cross section follows a |t|^{-8} behavior with no energy dependence in shape.

The tail magnitude decreases with energy, scaling as a power of the strong coupling.

At 13 TeV, the cross section reduces by a factor of 5.71.

Abstract

The measurements of proton-proton elastic scattering for large momentum transfer at energies in the range $\approx$ 20 to 60 GeV show a simple behaviour of form $d \sigma/dt \approx {\rm const}~|t|^{-8}$, apparently with no energy dependence. In the present work detailed analysis of the data shows a decrease of the magnitude of the tail with the energy, still with preservation of the power $|t|^{-8}$. The analysis allows the definition of a band for the energy dependence with the form of a power of the strong coupling $\alpha_S^{1.57}$. The rate of decrease describes very well the data at the distant energy $\sqrt{s}$ = 13 TeV, with reduction of the cross section by a factor 5.71. This result gives prediction for new experiments at high energies, and opens important question for theoretical investigation.