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

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

1993-03-04

arxiv.org/abs/hep-ph/9303218v2

Phys.Lett. B307 (1993) 140-146

Physics

High Energy Physics

High Energy Physics - Phenomenology

(14 pages, Los Alamos Preprint LA-UR-93-811). 3 uuencoded figures included

Scientific paper

10.1016/0370-2693(93)90203-T

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 $O(3)$ $\sigma$ 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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