Cosmic neutrino background on the surface of the Earth

Abstract

We argue that the reflection of relic neutrinos from the surface of the Earth results in a significant local $\ensuremath{\nu}\ensuremath{-}\overline{\ensuremath{\nu}}$ asymmetry, far exceeding the expected primordial lepton asymmetry. The net fractional electron neutrino number $\frac{{n}_{{\ensuremath{\nu}}_{e}}\ensuremath{-}{n}_{{\overline{\ensuremath{\nu}}}_{e}}}{{n}_{{\ensuremath{\nu}}_{e}}}$ is up to $\mathcal{O}({10}^{5})\sqrt{\frac{{m}_{\ensuremath{\nu}}}{0.1\text{ }\text{ }\mathrm{eV}}}$ larger than that implied by the baryon asymmetry. This enhancement is due to the weak 4-Fermi repulsion of the ${\ensuremath{\nu}}_{e}$ from ordinary matter which slows down the ${\ensuremath{\nu}}_{e}$ near the Earth's surface, and to the resulting evanescent neutrino wave that penetrates below the surface. This repulsion thus creates a net ${\ensuremath{\nu}}_{e}$ overdensity in a shell $\ensuremath{\sim}7\text{ }\text{ }\text{meters}\sqrt{\frac{0.1\text{ }\text{ }\mathrm{eV}}{{m}_{\ensuremath{\nu}}}}$ thick around the Earth's surface. Similarly the repulsion between ${\overline{\ensuremath{\nu}}}_{\ensuremath{\mu}}$ or ${\overline{\ensuremath{\nu}}}_{\ensuremath{\tau}}$ and ordinary matter creates an overdensity of ${\overline{\ensuremath{\nu}}}_{\ensuremath{\mu},\ensuremath{\tau}}$ of similar size. These local enhancements increase the size of $\mathcal{O}({G}_{F})$ torques of the $C\ensuremath{\nu}B$ on spin-polarized matter by a factor of order ${10}^{5}$. In addition, they create a gradient of the net neutrino density which naturally provides a way out of the forty-year-old ``no-go'' theorems on the vanishing of $\mathcal{O}({G}_{F})$ forces. The torque resulting from such a gradient force can be ${10}^{8}$ times larger than that of earlier proposals. Although the size of these effects is still far from current reach, they may point to new directions for $C\ensuremath{\nu}B$ detection.

Topics & Concepts