Amplitudes in the Coulomb interference region of pp and ppbar scattering

TL;DR

This paper analyzes proton-proton and proton-antiproton scattering data in the Coulomb interference region, exploring how different exponential slopes in real and imaginary amplitudes affect parameter determination and phase treatment.

Contribution

It introduces a more general Coulomb phase treatment and examines the impact of separate slopes B_R and B_I on scattering amplitude analysis.

Findings

Cannot uniquely determine all parameters from data

Identifies parameter correlations and optimal ranges for chi2 minimization

Determines normalization factor for low |t| event rate measurements

Abstract

We discuss the determination of the parameters of the pp and ppbar amplitudes for the description of scattering in the Coulomb interference region. We put enphasis on the possibility that the effective slope observed in the differential cross section is formed by different exponential slopes in the real and imaginary amplitudes (called B_R and B_I). For this purpose we develop a more general treatment of the Coulomb phase. We analyse the differential cross section data in the range from 19 to 1800 GeV with four parameters (sigma , rho, B_I, B_R), and observe that we cannot obtain from the data a unique determination of the parameters. We investigate correlations in pairs of the four quantities, showing ranges leading to the smaller chi2 values. In the specific case of p-pbar scattering at 541 GeV, we investigate the measurements of event rate dN/dt at low |t| in terms of the Coulomb interference with exponentially decreasing nuclear amplitudes. The analysis allows a determination of the normalization factor connecting the event rate with the absolute cross section.