Neutrino-antineutrino Asymmetry of C$\nu$B on the Surface of the Round Earth

Understand

It has been claimed that the coherent scattering of relic neutrinos with the Earth will result in a neutrino-antineutrino asymmetry of $\mathcal{O}(10^{-4})$ on the Earth surface, which is five orders of magnitude larger than the naive model expectation.

• In this work we show that this overdensity was overestimated for the perfectly round Earth by solving the exact solution with partial waves.
• The maximal asymmetry after summing over all the angular modes is only around $10^{-8}$ above the ground.
• To achieve the proposed asymmetry of $\mathcal{O}(10^{-4})$, a special geography may be needed as the experimental site.