Energy Dependence of Profile Functions in $\rm{p\bar p}$ and $\rm pp$ Scattering

TL;DR

This paper develops analytical impact parameter space models for proton-proton and proton-antiproton elastic scattering, accurately fitting data across a wide energy range and revealing the significance of the real amplitude component.

Contribution

It introduces new analytical forms for scattering amplitudes in impact parameter space that fit experimental data precisely and explore their energy dependence and structural properties.

Findings

Accurate modeling of scattering amplitudes across 20 GeV to 7 TeV.

Identification of the real part's influence on differential cross-section at intermediate and large |t|.

Extrapolation of scattering parameters to 14 TeV and beyond.

Abstract

We construct analytical forms in the impact parameter $b$-space for the real and imaginary amplitudes describing elastic pp and $\rm p \bar p $ scattering. The amplitudes converted analytically to the momentum transfer $t$-space have magnitudes, slopes, curvatures, zeros, signs, obeying phenomenological and theoretical expectations, and describe with high precision all details of the data, in the full-t range, and for energies from 20 GeV to 7 TeV. The connection of forward with large-$|t|$ behavior allows precise determination of total cross-sections, slopes and other scattering parameters. We study the properties and the energy dependence of the $b$-space profile functions, observing that the real part has fundamental influence in the structure of $d\sigma/dt$ at intermediate and large $|t|$ values. We discuss the 540/546 GeV and 1.8/1.96 TeV data from CERN SPS and Fermilab TEVATRON and the 7 TeV results from TOTEM measurements at LHC, and investigate the extrapolation to 14 TeV and higher energies.