Nonperturbative multiparticle tree graphs in the standard electroweak theory.

Abstract

I present a lower bound for the cross section at the tree level for {ital f}{sub {ital R}{bar f}{ital L}}{r arrow}{ital NZ} to lowest order in the hypercharge coupling {ital g}{prime}. It is seen that the cross section grows like {ital g}{sup 2{ital N}N} , and hence violates {ital J}=1 unitarity for large enough {ital N}{approx gt}(const/{ital g}{sup 2}). This phenomenon occurs in the kinematic region where coherence among {similar to}{ital N} graphs is possible: the vector mesons are nonrelativistic and they all have the same or a small fixed number of polarization vectors. The argument is then extended to the process {ital f}{sub {ital R}{bar f}{ital L}}{r arrow}(({ital N}/3){ital W}{sup +},({ital N}/3){ital W}{sup {minus}},({ital N}/3){ital Z}), and finally to the general case of an arbitrary initial state, and a final state containing a large number of nonrelativistic {ital W}{sup {plus minus}}'s and {ital Z}'s. The result involves only the gauge couplings, and is independent of the size of the quartic scalar coupling. There is qualitative similarity with the result found previously for tree graphs in {lambda}{phi}{sup 4} theory.