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

TL;DR

This paper critically examines the Wigner-Weisskopf model's application to neutral K meson decay, highlighting its non-orthogonality issues and contrasting it with the more accurate Lee-Oehme-Yang-Wu formulation, which aligns better with experimental data.

Contribution

It demonstrates that the residues in the Wigner-Weisskopf model are non-orthogonal, leading to detectable interference effects, and shows that the model is inconsistent with experimental observations.

Findings

Residues in the Wigner-Weisskopf model are non-orthogonal.

Interference terms predicted by the model are experimentally detectable.

Data supports the Lee-Oehme-Yang-Wu formulation over Wigner-Weisskopf.

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.