Baryon Number Violating Process and Sphaleron

发展了一种处理量子场论中隧穿过程的形式。即使在量子场论中，我们也知道这个过程可以归结为一个关于隧道传输参数的一维问题。该理论充分利用了简化版理论中的反弹解来获得隧道几率，并将其应用于计算由于量子电弱动力学反常而导致重子数破缺的高能截面。球翼是连接拓扑不等价真空的隧道势垒顶部的鞍点解。计算的截面比单位边界小一个数量级。原因如下：(1)由于翼面是非微扰性质的扩展构型，对于高动量粒子，它与隧穿入口(出口)的入射(出射)平面波的重叠迅速衰减。(Ii)产生的粒子数目是有限的(约100个)，因此通常采用的简单近似(如求幂)具有误导性。此外，与Ringwald和Espinosa早期的工作形成鲜明对比的是，具有重子数破坏的截面很大程度上达到了么正界限。然而，应该补充的是，最近的许多著作支持我们的结论。

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.