ar X iv : h ep - p h / 96 06 37 4 v 1 1 9 Ju n 19 96 McGill / 96 - 23 Nonabelian Cut Diagrams and Their Applications ∗

A new kind of cut diagram is introduced to sum Feynman diagrams with non-abelian vertices. Unlike the Cutkosky diagrams which compute the discontinuity of single Feynman diagrams, the nonabelian cut diagrams represent a resummation of both the real and the imaginary parts of Feynman diagrams related by permutations. Several applications of the technique are reported, including a resolution of the apparent inconsistency of the baryon problem in large-N c QCD, a simplified calculation of high-energy low-order QCD diagrams, and progress made with this technique on the unitarization of the BFKL equation. 1 Nonabelian cut diagrams This note serves to introduce the recently developed nonabelian cut diagrams [1, 2] and to summarize their applications to date [2, 3, 4]. A tree diagram of the type shown in Fig. 1, with bosons of relatively small momenta q i absorbed or emitted from a particle of large momentum p, has an amplitude given approximately by − 2πiδ   n j=1 ω j   n−1 i=1 1 i j=1 ω j + iǫ ·t 1 t 2 · · · t n ·V ≡ a[12 · · · n]·t[12 · · · n]·V , (1.1) where ω j = 2p·q j , t[12 · · · n] ≡ t 1 t 2 · · · t n , with t i being some nonabelian vertices. V contains other objects such as coupling constants, etc., independent of the ordering of the bosons. For easy reference we shall assume p to be the momentum of a fermion, though the kinematical and combinatorial formulas discussed below remain unaltered whatever that particle is. The momenta q i have been assumed in (1.1) to be much smaller than the momentum p, so that the approximation (p + j q j) 2 − M 2 ≃ 2p · j q j can be used to compute the denominators of propagators. This would be so in the presence of a very large fermion mass, as is the case for baryons in large-N c QCD. It is also valid when the fermion is taken from the incoming beam of a high energy process like quark-quark scattering. These two applications will be discussed separately in the next two sections.