Irreversible Quantum Mechanics in the Neutral K-System

TL;DR

This paper explores the quantum mechanics of the neutral Kaon system, deriving a complex Hamiltonian model that captures resonance decay phenomena and predicts long-time decay behaviors even under CP conservation.

Contribution

It introduces a truncated Lee-Oehme-Yang theory within Rigged Hilbert space for the neutral Kaon system, highlighting the effects of Hamiltonian commutation properties on decay predictions.

Findings

Derivation of a two-dimensional complex Hamiltonian model

Prediction of long-time 2 pion decays with CP-conserving Hamiltonian

Analysis of the impact of Hamiltonian commutation on decay phenomena

Abstract

The neutral Kaon system is used to test the quantum theory of resonance scattering and decay phenomena. The two dimensional Lee-Oehme-Yang theory with complex Hamiltonian is obtained by truncating the complex basis vector expansion of the exact theory in Rigged Hilbert space. This can be done for K_1 and K_2 as well as for K_S and K_L, depending upon whether one chooses the (self-adjoint, semi-bounded) Hamiltonian as commuting or non-commuting with CP. As an unexpected curiosity one can show that the exact theory (without truncation) predicts long-time 2 pion decays of the neutral Kaon system even if the Hamiltonian conserves CP.