Title: Effective field theory of particle mixing

Abstract: We introduce an effective field theory to study \emph{indirect} mixing of two fields induced by their couplings to a common decay channel in a medium. The extension of the method of Lee, Oehme and Yang, the cornerstone of analysis of CP violation in flavored mesons, to include mixing of particles with different masses provides a guide to and benchmark for the effective field theory. The analysis reveals subtle caveats in the description of mixing in terms of the widely used non-Hermitian effective Hamiltonian, more acute in the non-degenerate case. The effective field theory describes the dynamics of field mixing where the common intermediate states populate a bath in thermal equilibrium, as an \emph{open quantum system}. We obtain the effective action up to second order in the couplings, where indirect mixing is a consequence of off-diagonal self-energy components. We find that if only one of the mixing fields features an initial expectation value, indirect mixing induces an expectation value of the other field. The equal time two point correlation functions exhibit asymptotic approach to a stationary thermal state, and the emergence of long-lived \emph{bath induced} coherence which display quantum beats as a consequence of interference of quasinormal modes in the medium. The amplitudes of the quantum beats are resonantly enhanced in the nearly degenerate case with potential observational consequences.