Eikonal Approximation in Pseudoscalar Theory

Abstract

In an effort to extend the semiclassical intuitions developed in infrared-dominated field theories (quantum electrodynamics, ${\ensuremath{\varphi}}^{3}$, etc.) to field theories more likely characteristic of strong interactions, we have considered the high-energy-small-momentum-transfer limit of the ordinary linearly coupled fermion-pseudoscalar (nucleon-pion) interaction. In contrast with the infrared theories, we find (without using a cutoff) dominance of "hard" exchanged pions, but with a dynamically forced pairwise correlation resulting in an $s$-dependent effective potential appearing in the eikonal phase. The correspondence of the nonfixed-pole "soft" two-pion structure thus developed to a nonlocal generalization of Wentzel-pair theory is made, and the qualifications on the quantum field theory necessary to produce this semiclassical picture are explored. The role played by internal structure such as spin, isospin, and chiral symmetry is particularly interesting. The asymptotic behavior of the theory is extracted and we find that the dominant $N\ensuremath{-}N$ amplitude is $s$-channel helicity nonflip.