VALLEY BIFURCATION IN AN O(3) SIGMA-MODEL - IMPLICATIONS FOR HIGH-ENERGY BARYON NUMBER VIOLATION

The valley method for computing the total high-energy anomalous cross section sigma(anom) is the extension of the optical theorem to the cas e of instanton-antiinstanton backgrounds. As a toy model for baryon nu mber violation in Electroweak theory, we consider a version of the O(3 ) sigma model in which the conformal invariance is broken perturbative ly. We show that at a critical energy the saddle-point values of the i nstanton size and instanton-antiinstanton separation bifurcate into co mplex conjugate pairs. This nonanalytic behavior signals the breakdown of the valley method at an energy where sigma(anom) is still exponent ially suppressed.