Strong instanton-induced amplitudes in a weakly coupled theory

We address the recently suggested possibility that nonperturbative effects in the electroweak theory produce, at an energy above $\sim \frac{m_W}{{\alpha }_W}$, strong amplitudes for multiple production of gauge and Higgs bosons both in the baryon-number-violating and in the baryon-number-conserving sectors. We find such an occurrence of strong instanton-induced amplitudes for multiple production of light scalars in a weakly coupled supersymmetric SU(2) gauge theory with a so-called "flat direction" in the scalar field potential. In this model the self-interaction of the light scalars can be neglected, which simplifies our analysis of the amplitudes beyond the leading WKB approximation where we find an exponential growth of the cross section for multiple production of the scalar quanta up to the unitarity bound. This result seems to clearly demonstrate the possibility for a theory with a weak coupling to develop strong nonperturbative amplitudes at high energy.