Nonperturbative vacuum effect in the quantum field theory of meson mixing

Abstract

Replacing the perturbative vacuum by the nonperturbative vacuum, we extend a recent development of a quantum field theoretic framework for scalar and pseudoscalar meson mixing. The unitary inequivalence of the Fock space of base (unmixed) eigenstates and the physical mixed eigenstates is investigated and the flavor vacuum state structure is explicitly found. This is exploited to develop formulas for two flavor boson oscillations in systems of arbitrary boson occupation number. We apply these formulas to analyze the mixing of $\ensuremath{\eta}$ with ${\ensuremath{\eta}}^{\ensuremath{'}}$ and comment on the other meson-mixing systems. In addition, we consider the mixing of boson coherent states, which may have future applications in the construction of meson lasers.