Pathways and impediments towards a detection of the relic neutrino wind

Abstract

A direct detection of the cosmic neutrino background (CNB) in laboratories on Earth has been called the ``holy grail'' of experimental neutrino physics, but a still more glorious prize awaits. Beyond simply detecting the presence of relic neutrinos and measuring their flux, one may aspire to measure their energy distribution, polarization, anisotropies, temporal variation, and other properties. In this work we focus on the CNB wind, which is the approximately dipolar anisotropy in the CNB flux resulting from the relative velocity of the CNB rest frame and the lab frame. We consider a CNB detection strategy based on measuring the angular distribution of recoiling electrons at the tritium $\beta$-decay endpoint. In order to quantify the difficulty of detecting the CNB wind, we calculate the required exposure (detector mass times observation duration) for a $3\sigma$ discovery. We find that detecting the CNB wind would require an exposure that is at least $10^{5}$ times larger than what's required for detecting the CNB flux alone. Additionally if the experimental energy resolution were to exceed the neutrino mass scale, then an exceptionally good control of systematic uncertainties would also be required. For nonrelativistic neutrinos, the Majorana wind signal is suppressed relative to the Dirac case by the cancellation of the leading helicity-odd angular-correlation term, leading parametrically to an exposure penalty of order $(m_\nu/T_\nu)^2$.