Non equilibrium dynamics of mixing, oscillations and equilibration: a model study

Abstract

The non-equilibrium dynamics of mixing, oscillations and equilibration is studied in a field theory of flavored neutral mesons that effectively models two flavors of mixed neutrinos, in interaction with other mesons that represent a thermal bath of hadrons or quarks and charged leptons. This model describes the general features of neutrino mixing and relaxation via charged currents in a medium. The reduced density matrix and the non-equilibrium effective action that describes the propagation of neutrinos is obtained by integrating out the bath degrees of freedom. We obtain the dispersion relations, mixing angles and relaxation rates of ``neutrino'' quasiparticles. The dispersion relations and mixing angles are of the same form as those of neutrinos in the medium, and the relaxation rates are given by $Γ_1(k) = Γ_{ee}(k) \cos^2θ_m(k)+Γ_{μμ}(k)\sin^2θ_m(k) ; Γ_2(k)= Γ_{μμ}(k) \cos^2θ_m(k)+Γ_{ee}(k)\sin^2θ_m(k) $ where $Γ_{αα}(k)$ are the relaxation rates of the flavor fields in \emph{absence} of mixing, and $θ_m(k)$ is the mixing angle in the medium. A Weisskopf-Wigner approximation that describes the asymptotic time evolution in terms of a non-hermitian Hamiltonian is derived. At long time $>>Γ^{-1}_{1,2}$ ``neutrinos'' equilibrate with the bath. The equilibrium density matrix is nearly diagonal in the basis of eigenstates of an \emph{effective Hamiltonian that includes self-energy corrections in the medium}. The equilibration of ``sterile neutrinos'' via active-sterile mixing is discussed.