BREAKDOWN OF THE SEMICLASSICAL EXPANSION IN THE INSTANTON SECTOR AT HIGH-ENERGIES

We study the instanton contribution to 2n-particle cross section σ(2 → 2n) and to the inclusive cross section σ(2 → ny) to the leading and next-to-leading orders in the semiclassical expansion, in the two-dimensional O(3) sigma model with explicit conformal symmetry breaking. The leading order instanton inclusive cross section increases exponentially with the c.m. energy √s and violates the unitary bound at √s ∼ Esph, where Esph is the energy of the sphaleron in this model. The first correction becomes of the order of the leading term at lower energies √s ∼ gEsph, where g is the dimensionless coupling constant. Our results suggest that the semiclassical expansion for the inclusive baryon number violating cross section in the standard electroweak theory breaks down, due to the vector field pertubations around the instanton, at √s of order of the Higgs vacuum expectation value, where the instanton cross section is still exponentially small. However, we present some arguments implying that the corrections to the leading order semiclassical result may sum up in such a way that the exponential growth of the cross section is not destroyed up to energies of order Esph. © 1990.