Diagrammatic derivation of the eikonal formula for high-energy scattering in Yang-Mills theory

Abstract

A new calculational scheme for unitarizing $S$-matrix amplitudes in the high-energy limit is applied to a Yang-Mills theory with SU(2) symmetry.The The vector-meson-vector-meson elastic scattering amplitude is calculated through the tenth order in the coupling constant and the result agrees with the expansion of an eikonal formula in the impactdistance space, $S=\mathrm{exp}(\mathrm{iV})$. The potential $V$ is an infinite-dimensional matrix whose entry for a given process is related to the sum of the lowest-order amplitudes for that process, with the exchanged vector mesons Reggeized. This result is explicitly unitary.