Non-Abelian eikonals

A functional formulation and partial solution is given of the non-Abelian eikonal problem associated with the exchange of noninteracting, charged or colored bosons between a pair of fermions, in the large {ital s} small {ital t} limit. A simple, functional {open_quotes}contiguity{close_quotes} prescription is devised for extracting those terms which exponentiate, and appear to generate the leading, high-energy behavior of each perturbative order of this simplest non-Abelian eikonal function; the lowest nontrivial order agrees with the corresponding SU({ital N}) perturbative amplitude, while higher-order contributions to this eikonal generate an {open_quotes}effective Reggeization{close_quotes} of the exchanged bosons, resembling previous results for the perturbative amplitude. One exact and several approximate examples are given, including an application to self-energy radiative corrections. In particular, for this class of graphs and to all orders in the coupling, we calculate the leading-log eikonal for SU(2). Based on this result, we conjecture the form of the eikonal scattering amplitude for SU({ital N}). {copyright} {ital 1997} {ital The American Physical Society}