Fixed-Angle Elastic Hadron Scattering

TL;DR

This paper analyzes the asymptotic behavior of the scattering amplitude in a dual model with Mandelstam analyticity at fixed angles, deriving a series decomposition using the saddle point method.

Contribution

It provides a new explicit series decomposition of the scattering amplitude in the dual model with Mandelstam analyticity at high energies and fixed angles.

Findings

Derived the leading and sub-leading terms of the amplitude.

Established the asymptotic form of the scattering amplitude.

Applied the saddle point method for the analysis.

Abstract

The scattering amplitude in the dual model with Mandelstam analyticity and trajectory $\alpha (s)=\alpha_{0}-\gamma \ln [ (1+\beta \sqrt{s_{0} -s})/(1+ \beta \sqrt{s_{0}})]$ is studied in the limit $s,|t|\to \infty, s/t=const.$ By using the saddle point method, a series decomposition for the scattering amplitude is obtained, with the leading and two sub-leading terms calculated explicitly.