NONPERTURBATIVE VALLEY CONTRIBUTION TO THE TOTAL TRANSITION-PROBABILITY IN THE O(3) SIGMA MODEL

We construct a valley in the two-dimensional O(3) sigma-model with explicit conformal symmetry breaking, using its reduction to the static sine-Gordon model. We then study the inclusive transition probability P(tot)(2 --> any) for boson scattering by means of the optical theorem. The corresponding forward elastic scattering amplitude is computed in a semiclassical expansion of the path integral, using the valley as its stationary point. We recover the well-known behavior of P(tot), approximately exp[-(4-pi/g2)F(E)] and find F in leading order in an expansion in E/E(s), where E(s) is the sphaleron mass. Our results open the possibility of a determination of F(E) in the O(3) sigma-model valid for all energies.