Valley Bifurcation in an $O(3)$ $σ$ Model: Implications for High-Energy Baryon Number Violation

Jeffrey M. Grandy; Michael P. Mattis

doi:10.1016/0370-2693(93)90203-t

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arXiv · hep-ph/9303218

Valley Bifurcation in an $O(3)$ $σ$ Model: Implications for High-Energy Baryon Number Violation

Jeffrey M. Grandy·Michael P. Mattis

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Abstract

The valley method for computing the total high-energy anomalous cross section $S_{anom}$ is the extension of the optical theorem to the case of instanton-antiinstanton 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 $S_{anom}$ is still exponentially suppressed. (Figures replaced 5/3/93).

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Jeffrey M. Grandy, Michael P. Mattis. 1993-05-03. Valley Bifurcation in an $O(3)$ $σ$ Model: Implications for High-Energy Baryon Number Violation. https://doi.org/10.1016/0370-2693(93)90203-t

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