Decaying neutrinos: The long way to isotropy

Abstract

We investigate a scenario in which neutrinos are coupled to a pseudoscalar degree of freedom $\text{ph}$ and where decays ${\nu }_1\to {\nu }_2+\text{ph}$ and inverse decays are the responsible mechanism for obtaining equilibrium. In this context we discuss the implication of the invisible neutrino decay on the neutrino-pseudoscalar coupling constant and the neutrino lifetime. Assuming the realistic scenario of a thermal background of neutrinos and pseudoscalar we update the bound on the (off-diagonal) neutrino-pseudoscalar coupling constant to $g<2.6\times 10^{-13}$ and the bound on the neutrino lifetime to $\tau <1\times 10^{13}\mathrm{s}$. Furthermore we confirm analytically that kinetic equilibrium is delayed by two Lorentz $\text{ga}$--factors -- one for time dilation of the (decaying) neutrino lifetime and one from the opening angle. We have also confirmed this behavior numerically.

Comments: Updated to match published version in Phys. Rev. D