Relic Neutrino Helicity Evolution in Galactic Magnetic Field and Its Implications

Abstract

We simulate the evolution of the helicity of relic neutrinos as they propagate to Earth through a realistic model of the Galactic magnetic field, improving upon the rough estimates in the literature. For magnetic moments consistent with experimental bounds and several orders of magnitude smaller, we confirm that the helicity of relic neutrinos and anti-neutrinos rotates so much that the spin projection changes by $\mathcal{O}$(1). However, as we show, the total event rate in an inverse tritium beta decay (ITBD) experiment changes by less than a few percent, unless the lightest neutrino has mass of order 0.001 eV or less. Such a tiny reduction in the absolute rate relative to the standard model value would be very difficult to establish, even if detecting relic neutrinos were routine. However as we show, the \emph{directional anisotropy} of the rate in a \emph{polarized} ITBD detector is $\gtrsim \mathcal{O}$(10\%) as long as the lightest neutrino mass is $\gtrsim \mathcal{O}$(0.01 eV). Thus with percent-level error bars on the absolute neutrino flux and its directional anisotropy, both the mass and magnetic moment of the relic neutrinos can in principle be probed if they are within a few orders of magnitude of current bounds.