The slope, curvature, and higher parameters in $pp$ and $\bar{p}p$ scattering, and the extrapolation of measurements of $d\sigma(s,t)/dt$ to $t=0$

TL;DR

This paper investigates how curvature in the differential elastic scattering cross section near t=0 affects the extrapolation of measurements, revealing that curvature parameters significantly influence the forward slope and cross sections, thus requiring their consideration in data analysis.

Contribution

It introduces a detailed analysis of curvature effects in the expansion of the differential cross section near t=0 within an eikonal model, highlighting their importance for accurate extrapolation.

Findings

Curvature parameters C and D cause significant changes in the forward slope.

Curvature effects impact the extrapolation of total and elastic cross sections.

Ignoring curvature can lead to inaccuracies in scattering data analysis.

Abstract

We study the effects of curvature in the expansion of the logarithm of the differential elastic scattering cross section near $t=0$ as $d\sigma(s,t)/dt=d\sigma(s,0)/dt\,\times\exp(Bt+Ct^2+Dt^3\cdots)$ in an eikonal model for $pp$ and $\bar{p}p$ scattering, and use the results to discuss the extrapolation of measured differential cross sections and the slope parameters $B$ to $t=-q^2=0$. We find that the curvature effects represented by the parameters $C$ and $D$, while small, lead to significant changes in the forward slope parameter relative to that determined in a purely exponential fit, and to smaller but still significant changes in the forward elastic scattering and total cross sections. Curvature effects should therefore be considered in future analyses or reanalyses of the elastic scattering data.