Nonperturbative multiparticle tree graphs in the standard electroweak theory

I present a lower bound for the cross section at the tree level for fRbarfL→NZ to lowest order in the hypercharge coupling g'. It is seen that the cross section grows like g2NN exclamation point, and hence violates J=1 unitarity for large enough N approx-gt(const/g2). This phenomenon occurs in the kinematic region where coherence among ∼N exclamation point 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 fRbarfL→((N/3)W+,(N/3)W-,(N/3)Z), and finally to the general case of an arbitrary initial state, and a final state containing a large number of nonrelativistic W±'s and 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 λφ4 theory