Neutrino-antineutrino asymmetry of CνB on the surface of the round Earth

It has been claimed that the coherent scattering of relic neutrinos with the Earth will result in a neutrino-antineutrino asymmetry of O\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathcal{O} $$\end{document}(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. After summing over all the angular modes, the maximal asymmetry is only around 10-8 above the ground. To achieve the proposed asymmetry of O\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathcal{O} $$\end{document}(10-4), a special geography may be needed as the experimental site. The code for a fast evaluation of Bessel functions with large orders through asymptotic expansions has been attached along with this work as supplementary material.