Quantum Field Theory of Meson Mixing

TL;DR

This paper develops a quantum field theoretic framework for meson mixing and oscillations, revealing a condensate structure and providing formulas applicable to systems like eta-eta' and kaons, with potential applications in meson lasers.

Contribution

It introduces a novel quantum field theory approach to meson mixing, highlighting the role of vacuum condensates and deriving formulas for boson oscillations in arbitrary occupation states.

Findings

Proves the unitary inequivalence of Fock spaces for mixed and unmixed states.

Derives formulas for two-flavor boson oscillations with arbitrary occupation numbers.

Analyzes meson mixing phenomena such as eta-eta' and comments on kaon systems.

Abstract

We have developed a quantum field theoretic framework for scalar and pseudoscalar meson mixing and oscillations in time. The unitary inequivalence of the Fock space of base (unmixed) eigenstates and the physical mixed eigenstates is proven and shown to lead to a rich condensate structure. This is exploited to develop formulas for two flavor boson oscillations in systems of arbitrary boson occupation number. The mixing and oscillation can be understood in terms of vacuum condensate which interacts with the bare particles to induce non-trivial effects. We apply these formulas to analyze the mixing of $\eta$ with $\eta'$ and comment on the $K_L K_S$ system. In addition, we consider the mixing of boson coherent states, which may have future applications in the construction of meson lasers.