Abstract
The valley method for computing the total high-energy anomalous cross section σ anom is the extension of the optical theorem to the case of instanton-antiinnstanton backgrounds. As a toy model for baryon number violation in Electroweak theory, we consider a version of the O(3) σ model in which the conformal invariance is broken perturbatively. We show that at a critical energy the saddle-point values of the instanton size and instanton-antiinstanton separation bifurcate into complex conjugate pairs. This nonanalytic behavior signals the breakdown of the valley method at an energy where σ anom is still exponentially suppressed.
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