High-energy asymptotic behavior of the Bourrely-Soffer-Wu model for elastic scattering

TL;DR

This paper derives a high-energy asymptotic formula for the BSW model's scattering amplitude in elastic proton-proton and antiproton-proton scattering, revealing oscillatory behavior and comparing it with unitarity bounds.

Contribution

It provides the first high-energy asymptotic representation of the BSW model's scattering amplitude, simplifying analysis at very high energies.

Findings

Asymptotic formula accurately describes oscillations in differential cross section.

Comparison shows the asymptotic behavior approaches the Singh-Roy unitarity bound.

Asymptotic approximation is valid for energies much higher than current experiments.

Abstract

Some time ago, an accurate phenomenological approach, the BSW model, was developed for proton-proton and antiproton-proton elastic scattering cross sections at center-of-mass energies above 10 GeV. This model has been used to give successful theoretical predictions for these processes, at successive collider energies. The BSW model involves a combination of integrals that, while computable numerically at fairly high energies, require some mathematical analysis to reveal the high-energy asymptotic behavior. In this paper we present a high-energy asymptotic representation of the scattering amplitude at moderate momentum transfer, for the leading order in an expansion parameter closely related to the logarithm of the center-of-mass energy. The fact that the expansion parameter goes as the logarithm of the energy means that the asymptotic behavior is accurate only for energies greatly beyond any foreseeable experiment. However, we compare the asymptotic representation against the numerically calculated model for energies in a less extreme region of energy. The asymptotic representation is given by a simple formula which, in particular, exhibits the oscillations of the differential cross section with momentum transfer. We also compare the BSW asymptotic behavior with the Singh-Roy unitarity upper bound for the diffraction peak.