Non-Orthogonality of Residues in the Wigner-Weisskopf Model for Neutral K Meson Decay

Abstract

We review the application of the Wigner-Weisskopf model for the neutral K meson system in the resolvent formalism. The Wigner-Weisskopf model is not equivalent to the Lee-Oehme-Yang-Wu formulation (which provides an accurate representation of the data). The residues in the pole approximation in the Wigner-Weisskopf model are not orthogonal, leading to additional interference terms in the $K_S-K_L 2\pi$ channel. We show that these terms would be detectable experimentally in the decay pattern of the beam emitted from a regenerator if the Wigner-Weisskopf theory were correct. The consistency of the data with the Lee-Oehme-Yang-Wu formulation appears to rule out the applicability of the Wigner-Weisskopf theory to the problem of neutral K meson decay.