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

We study several aspects of the kinetic approach to sterile neutrinoproduction via active-sterile mixing. We obtain the neutrino propagator in themedium including self-energy corrections up to $\mathcal{O}(G^2_F)$, from whichwe extract the dispersion relations and damping rates of the propagating modes.The dispersion relations are the usual ones in terms of the index of refractionin the medium, and the damping rates are $\Gamma_1(k) = \Gamma_{aa}(k)\cos^2\theta_m(k); \Gamma_2(k) = \Gamma_{aa}(k) \sin^2\theta_m(k)$ where$\Gamma_{aa}(k)\propto G^2_F k T^4$ is the active neutrino scattering rate and$\theta_m(k)$ is the mixing angle in the medium. We provide a generalization ofthe transition probability in the \emph{medium from expectation values in thedensity matrix}: $ P_{a\to s}(t) = \frac{\sin^22\theta_m}{4}[e^{-\Gamma_1t} +e^{-\Gamma_2 t}-2e^{-{1/2}(\Gamma_1+\Gamma_2)t} \cos\big(\Delta E t\big)] $ andstudy the conditions for its quantum Zeno suppression directly in real time. Wefind the general conditions for quantum Zeno suppression, which for $m_s\sim\textrm{keV}$ sterile neutrinos with $\sin2\theta \lesssim 10^{-3}$ \emph{mayonly be} fulfilled near an MSW resonance. We discuss the implications forsterile neutrino production and argue that in the early Universe the wideseparation of relaxation scales far away from MSW resonances suggests thebreakdown of the current kinetic approach.Comment: version to appear in JHE