High-energy neutrino conversion into an electron-<i>W</i>pair in a magnetic field and its contribution to neutrino absorption

Abstract

We calculate the conversion rate of high-energy neutrinos propagating in a constant magnetic field into an electron-$W$ pair $(\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\nu}}W+e)$ from the imaginary part of the neutrino self-energy. Using the exact propagators in a constant magnetic field, the neutrino self-energy has been calculated to all orders in the field within the Weinberg-Salam model. We obtain a compact formula in the limit of $B\ensuremath{\ll}{B}_{\mathrm{cr}}\ensuremath{\equiv}{m}^{2}/e.$ We find that above the process threshold ${E}^{(\mathrm{th})}\ensuremath{\approx}2.2\ifmmode\times\else\texttimes\fi{}{10}^{16}\mathrm{eV}\ifmmode\times\else\texttimes\fi{}{(B}_{\mathrm{cr}}/B)$ this contribution to the absorption of neutrinos yields an asymptotic absorption length $\ensuremath{\approx}1.1\mathrm{m}\mathrm{}\ifmmode\times\else\texttimes\fi{}{(B}_{\mathrm{cr}}{/B)}^{2}\ifmmode\times\else\texttimes\fi{}{(10}^{16}\mathrm{eV}/E).$