A fresh look at neutral meson mixing

TL;DR

This paper investigates the mathematical conditions for diagonalizing the effective Hamiltonian in neutral meson systems and proposes a method to test CPT invariance through cascade decay observations.

Contribution

It establishes the necessity of a biorthonormal eigenvector set for Hamiltonian diagonalization and introduces a way to measure CPT violation via decay time analysis.

Findings

Complete biorthonormal eigenvector set is necessary for Hamiltonian diagonalization.

Method to determine CPT violation parameter from cascade decay time dependence.

Provides a framework for testing CPT invariance in neutral meson systems.

Abstract

In this work we show that the existence of a complete biorthonormal set of eigenvectors of the effective Hamiltonian governing the time evolution of neutral meson system is a necessary condition for diagonalizability of such a Hamiltonian. We also study the possibility of probing the $CPT$ invariance by observing the time dependence of cascade decays of type $P^{\circ}(\bar{P^{\circ}})\to \{M_a,M_b\}X\to fX$ by employing such basis and exactly determine the $CPT$ violation parameter by comparing the time dependence of the cascade decays of tagged $P^{\circ}$ and tagged $\bar{P^{\circ}}$.