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Non-Perturbative Isotropic Multi-Particle Production in Yang--Mills Theory

We use singular Euclidean solutions to find multi-particle production cross sections in field theories. We investigate a family of time-dependent O(3) symmetrical solutions of the Yang--Mills equations, which govern the isotropic high-energy gauge boson production. At low energies our approach reproduces the instanton-induced cross sections. For higher energies we get new results. In particular, we show that the cross section for isotropic multiparticle production remains exponentially small in the running gauge coupling constant. The result applies both to the baryon number violation in the electro-weak theory and to the QCD jet production. We find that the isotropic multi-gluon production cross section falls off approximately as a ninth power of energy but possibly might be observable