Consistent Probabilistic Description of the Neutral Kaon System

Abstract

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.

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

References in corpus (2)

• Perturbative Non-Equilibrium Thermal Field Theory
• Unstable particles as open quantum systems

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