Elastic $\rm{p\bar p}$ Scattering Amplitude at 1.8 TeV and Determination of Total Cross Section

TL;DR

This paper analyzes proton-antiproton elastic scattering data at 1.8 and 1.96 TeV, accurately modeling amplitudes to determine total cross sections and predict a dip in differential cross section due to three-gluon exchange.

Contribution

Introduces a high-accuracy method for analyzing scattering amplitudes, determining total cross sections, and predicting features like a dip caused by three-gluon exchange.

Findings

Determined total cross sections consistent with experimental data.

Predicted a dip in differential cross section at 3-5 GeV^2 due to three-gluon exchange.

Established the importance of separate slopes for real and imaginary amplitudes.

Abstract

The data on p$\mathrm{\bar p}$ elastic scattering at 1.8 and 1.96 TeV are analysed in terms of real and imaginary amplitudes, in a treatment with high accuracy, covering the whole t-range and satisfying the expectation of dispersion relation for amplitudes and for slopes. A method is introduced for determination of the total cross section and the other forward scattering parameters and to check compatibility of E-710, CDF and the recent D0 data. Slopes $B_R$ and $ B_I$ of the real and imaginary amplitudes, treated as independent quantities, influence the amplitudes in the whole t-range and are important for the determination of the total cross section. The amplitudes are fully constructed, and a prediction is made of a marked dip in $ d\sigma/dt$ in the $|t|$ range 3 - 5 GeV$^2$ due to the universal contribution of the process of three gluon exchange.