Radiative corrections to neutrino indices of refraction

Abstract

Quantum loop corrections to coherent forward neutrino scattering and , l=e,\ensuremath{\mu},\ensuremath{\tau} are examined in the standard SU(2${)}_{L}$\ifmmode\times\else\texttimes\fi{}U(1) model. For a neutral unpolarized medium with particle densities ${N}_{e}$=${N}_{p}$,${N}_{n}$ we find ${\mathit{p}}_{\mathit{v}}$(${\mathit{n}}_{\mathit{v}\mathit{e}}$-${\mathit{n}}_{{\mathit{v}}_{\mathit{e}}}$-${\mathit{n}}_{{\mathit{v}}_{\mathrm{\ensuremath{\mu}}}}$) =-\ensuremath{\surd}2\ifmmode\bar\else\textasciimacron\fi{}${\mathit{G}}_{\mathrm{\ensuremath{\mu}}}$${\mathit{N}}_{\mathit{e}}$[1+O(\ensuremath{\alpha}${\mathit{m}}_{\mathrm{\ensuremath{\mu}}}^{2}$/${\mathit{m}}_{\mathit{w}}^{2}$)] and and .sp.5 ${p}_{\ensuremath{\nu}}$( )= ${G}_{\ensuremath{\mu}}$ / \ensuremath{\surd}2 3\ensuremath{\alpha} / 2\ensuremath{\pi} ${\mathrm{sin}}^{2}$${\mathrm{theta}}_{\mathrm{W}}$ ${\mathrm{m}}_{\mathrm{\ensuremath{\tau}}}$${\mathrm{}}^{2}$ / ${\mathrm{m}}_{\mathrm{W}}$${\mathrm{}}^{2}$ [(${\mathit{N}}_{\mathit{p}}$+${\mathit{N}}_{\mathit{n}}$)ln(${\mathit{m}}_{\mathrm{\ensuremath{\tau}}}^{2}$/${\mathit{m}}_{\mathit{w}}^{2}$)+(${\mathit{N}}_{\mathit{p}}$${+}^{2}$${/}_{3}$${\mathit{N}}_{\mathit{n}}$)]. Implications of our results for neutrino matter oscillations and elastic scattering are briefly discussed.