Baryon Number Violating Process and Sphaleron

点击翻译按钮获取中文摘要

A formalism to treat tunneling process in quantum field theory is developed. Even in quantum field theory, the process is known to be reduced to an one dimensional problem with respect to a parameter along the tunneling. The bounce solution in the reduced version of the theory is made full use of to obtain tunneling probability.The formalism was applied to evaluating high energy cross section with baryon number violation due to anomaly of quantum electroweak dynamics. Sphaleron is a saddle point solution at the top of the tunneling barrier that connects topologically inequivalent vacua.The evaluated cross section is by orders of magnitude smaller than the unitarity bound. The reasons are as follows: (i) Since the sphaleron is an extended configuration of the nonperturbative character, its overlap with the incident (outgoing) plane wave at the entrance (exit) of the tunneling damps rapidly for high momentum particles. (ii) The number of the produced particles are finite (about 100), so that an easy approximation usually adpoted such as exponentiation is misleading.The alove result forms a sharp contrast to earlier works by Ringwald and Espinosa that the cross section with baryon number violation brows as largely as to reach the unitarity bound. It should be added, however, that many of recent works support our conclusion.