INSTANTON INDUCED CROSS-SECTIONS BELOW THE SPHALERON

We study the S-matrix and the total cross section of high-energy collision in the one-instanton sector of purely bosonic theories with instantons. Making use of the coherent state formalism, we develop the perturbation theory around the instanton. We find that in the limit g2 --> 0, E/E(sph) fixed, the leading behaviour of the total cross section is sigma-tot approximately exp[g-2(-2S0 + F(E/E(sph)))], where S0 is the instanton action. In the electroweak theory at E/E(sph) << 1, the function F(E/E(sph)) is determined by the gauge boson part of the instanton configuration and its explicit form is found. Our results suggest that there may exist a semiclassical type of procedure for evaluating the leading behaviour of the one-instanton total cross section at E greater-than-or-similar-to E(sph) and g2 --> 0.