  In the presence of a large parameter, such as mass or energy, leading
behavior of individual Feynman diagrams often get cancelled in the sum. This is
known to happen in large-$N_c$ QCD in the presence of a baryon, and also in the
case of high-energy electron-electron as well as quark-quark scatterings. We
present an exact combinatorial formula, involving multiple commutators of the
vertices, which can be used to compute such cancellations. It is a non-abelian
generalization of the eikonal formula, and will be applied in subsequent
publications to study the consistency of large-$N_c$ QCD involving baryons, as
well as high-energy quark-quark scattering in ordinary QCD.
