Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
2006-12-07
JHEP 0707:030,2007
Physics
High Energy Physics
High Energy Physics - Phenomenology
version to appear in JHEP
Scientific paper
10.1088/1126-6708/2007/07/030
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 $\mathcal{O}(G^2_F)$, 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 $\Gamma_1(k) = \Gamma_{aa}(k) \cos^2\theta_m(k); \Gamma_2(k) = \Gamma_{aa}(k) \sin^2\theta_m(k)$ 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 of the transition probability in the \emph{medium from expectation values in the density 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)] $ and study the conditions for its quantum Zeno suppression directly in real time. We find the general conditions for quantum Zeno suppression, which for $m_s\sim \textrm{keV}$ sterile neutrinos with $\sin2\theta \lesssim 10^{-3}$ \emph{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.
Boyanovsky Daniel
Ho Chang-Ming
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