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arXiv 1208.3572hep-phquant-ph
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中性K介子系统的一致概率描述

Consistent Probabilistic Description of the Neutral Kaon System

J. Bernabeu, N. E. Mavromatos, P. Villanueva-Perez

备注：
10 pages latex, non-trivial observations and clarifications made compared to previous version, concerning interpretation of results (relevant parametrization) which leads to agreement of time-dependent rates with those of WWA. References added. Matches version to appear in Phys. Lett. B
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摘要：

中性K介子系统在质量矩阵中存在CP破坏，在宽度矩阵中存在非零寿命差。这导致了一个有效的哈密顿量，它不是一个正常的运营商，不兼容（非交换）的质量和宽度。在Weisskopf-Wigner方法（WWA）中，通过对角化整个哈密顿量，得到非物理的非正交“定态”$K_{L,S}$。这些状态具有复数本征值，其实部（虚部）与质量（宽度）矩阵的本征值不一致。在这项工作中，我们描述的系统作为一个开放的Lindblad型量子力学系统由于K介子衰变。这种方法，在密度矩阵的初始和最终状态，提供了一个一致的概率描述，避免了标准的问题，因为宽度矩阵成为一个复合算子不包括在哈密顿量。我们考虑了两个π介子的主导衰变通道，使得其中一个有确定寿命的K介子态成为稳定态。这种新的方法提供的结果与WWA的时间相关的衰减率。

英文摘要：

The neutral Kaon system has both CP violation in the mass matrix and a non-vanishing lifetime difference in the width matrix. This leads to an effective Hamiltonian which is not a normal operator, with incompatible (non-commuting) masses and widths. In the Weisskopf-Wigner Approach (WWA), by diagonalizing the entire Hamiltonian, the unphysical non-orthogonal "stationary" states $K_{L,S}$ are obtained. These states have complex eigenvalues whose real (imaginary) part does not coincide with the eigenvalues of the mass (width) matrix. In this work we describe the system as an open Lindblad-type quantum mechanical system due to Kaon decays. This approach, in terms of density matrices for initial and final states, provides a consistent probabilistic description, avoiding the standard problems because the width matrix becomes a composite operator not included in the Hamiltonian. We consider the dominant-decay channel to two pions, so that one of the Kaon states with definite lifetime becomes stable. This new approach provides results for the time dependent decay rates in agreement with those of the WWA.

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