Classical corrections to instanton-induced interactions

Abstract

We consider instanton-induced production of vector particles at high energies. In the leading-order approximation for n-particle cross sections the total cross section grows exponentially with energy and hits the unitarity bound at energy s of order ϱ −2 g −2, where ϱ is the instanton size. The approximation implies in fact that smearing of the classical solution at short distances due to ϱ ≠ 0 is neglected, and we look for the effect of finite ϱ. We argue that the smearing of the classical solution can be reproduced in terms of quantum exchanges by combining instanton-induced vertices with ordinary perturbation theory. The first correction to the total cross section becomes of order unity at energy s of order ϱ −2 and does not have any extra factor g. Moreover, an exponential form factor can be derived under some conditions. However the form factor can stop the cross section growing only at energies of order ϱ −2 g −2, where the approximations made are no longer valid.