Determination of the forward slope in $p~p$ and $\bar p~p$ elastic scattering up to LHC energy

TL;DR

This paper investigates the variation of the forward slope parameter in elastic proton-proton and antiproton-proton scattering, revealing it is not constant and providing methods to extract this information from experimental data, with implications for future LHC measurements.

Contribution

It demonstrates that the forward slope is not constant and introduces a model-independent method to analyze its variation in elastic scattering data.

Findings

The slope parameter varies with momentum transfer.

The slope is not a simple constant, contrary to common assumptions.

Extension of analysis to LHC energies for future experiments.

Abstract

In the analysis of experimental data on $p p$ (or $\bar p p$) elastic differential cross section it is customary to define an average forward slope $b$ in the form $\exp{(-b|t|)}$, where $t$ is the momentum transfer. Taking as working example the results of experiments at Tevatron and SPS, we will show with the help of the impact picture approach, that this simplifying assumption hides interesting information on the complex non-flip scattering amplitude, and that the slope $b$ is not a constant. We investigate the variation of this slope parameter, including a model-independent way to extract this information from an accurate measurement of the elastic differential cross section. An extension of our results to the LHC energy domain is presented in view of future experiments.