High-energy scattering amplitudes of Yang-Mills theories in generalized leading-term approximation and eikonal formulas

Abstract

In this paper, we study the apparent discrepancy between Feynman diagrams and the eikonal formulas, and the apparent paradox between the eikonal formulas and the $s\ensuremath{-}u$ crossing symmetry. We analyze the generalized leadingterm approximation (GLA), which generates the terms of the eikonal formulas from Feynman diagrams. This analysis is done through using the techniques of decomposing diagrammatically the isospin factors (or group-theoretical weights in general) of Feynman diagrams. As a result, we modify the GLA into a generalized complex leading-term approximation. We calculate, with this new formalism, the high-energy limit ($s\ensuremath{\rightarrow}\ensuremath{\infty}$ with $t$ fixed) of the vector-meson-vector-meson elastic amplitude of a Yang-Mills theory with SU(2) symmetry through tenth perturbative order. With this new method, we resolve the apparent discrepancy and paradox mentioned above. This method is generalizable to other non-Abelian gauge theories.