The 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 $\nu -\bar{\nu }$ asymmetry, far exceeding the expected primordial lepton asymmetry. The net fractional electron neutrino number $\frac{n_{{\nu }_e}-n_{{\bar{\nu }}_e}}{n_{{\nu }_e}}$ is up to $\mathcal{O}(10^5)\sqrt{\frac{m_{\nu }}{0.1\text{eV}}}$ larger than that implied by the baryon asymmetry. This enhancement is due to the weak 4-Fermi repulsion of the ${\nu }_e$ from ordinary matter which slows down the ${\nu }_e$ near the Earth's surface, and to the resulting evanescent neutrino wave that penetrates below the surface. This repulsion thus creates a net ${\nu }_e$ overdensity in a shell $\sim 7\text{meters}\sqrt{\frac{0.1\text{eV}}{m_{\nu }}}$ thick around the Earth's surface. Similarly the repulsion between ${\bar{\nu }}_{\mu }$ or ${\bar{\nu }}_{\tau }$ and ordinary matter creates an overdensity of ${\bar{\nu }}_{\mu ,\tau }$ of similar size. These local enhancements increase the size of $\mathcal{O}(G_F)$ torques of the $C\nu B$ 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 $C\nu B$ detection.

Comments: 14 pages, 6 figures, references updated