Sterile neutrino production via active-sterile oscillations: the quantum Zeno effect

We study several aspects of the kinetic approach to sterile neutrino production via active-sterile mixing. We obtain the neutrino propagator in the medium including self-energy corrections up to O(G2F), from which we extract the dispersion relations and damping rates of the propagating modes. The dispersion relations are the usual ones in terms of the index of refraction in the medium, and the damping rates are Γ1(k) Γaa(k)cos2 θm(k); Γ2(k) = Γaa(k)sin2 θm(k) where Γaa(k) ∝ G2F kT4 is the active neutrino scattering rate and θm(k) is the mixing angle in the medium. We provide a generalization of the transition probability in the medium from expectation values in the density matrix: Pa→s(t) = [(sin2 2θm)/4][e-Γ1t+e-Γ2t-2e- 1/2 (Γ1+Γ2)t cos(ΔEt)] and study the conditions for its quantum Zeno suppression directly in real time. We find the general conditions for quantum Zeno suppression, which for ms ∼ keV sterile neutrinos with sin 2θ ∼< 10-3 may only be fulfilled near an MSW resonance. We discuss the implications for sterile neutrino production and argue that in the early Universe the wide separation of relaxation scales far away from MSW resonances suggests the breakdown of the current kinetic approach