Multi-instantons do not stop the cross-section at half the 't Hooft suppression

Abstract Using the (1+1)-dimensional abelian Higgs model as a toy model we study the non-perturbative semiclassical behaviour of the total cross-section in the limit of large Higgs mass m h as compared to the vector boson mass m w . In the single-instanton approximation the total cross-section rises steeply with energy. The leading-order exponential suppression by the 't Hooft factor (twice the instanton action) disappears at energies near the sphaleron energy. Above the sphaleron energy semiclassical methods based on the instanton/anti-instanton valley break down. The influence of multi-instanton contributions is found to be completely negligible up to energies of the order of the sphaleron energy.