Radiative corrections to neutrino indices of refraction

Quantum loop corrections to coherent forward neutrino scattering and &, l=e,μ,τ are examined in the standard SU(2${)}_L$×U(1) model. For a neutral unpolarized medium with particle densities $N_e$=$N_p$,$N_n$ we find ${\mathit{p}}_{\mathit{v}}$(${\mathit{n}}_{\mathit{v}\mathit{e}}$-${\mathit{n}}_{{\mathit{v}}_{\mathit{e}}}$-${\mathit{n}}_{{\mathit{v}}_{\mathrm{\mu }}}$) =-√2¯${\mathit{G}}_{\mathrm{\mu }}$ ${\mathit{N}}_{\mathit{e}}$[1+O(α${\mathit{m}}_{\mathrm{\mu }}^2$/${\mathit{m}}_{\mathit{w}}^2$)] and and .sp.5 $p_{\nu }$( &)= $G_{\mu }$ / √2 3α / 2π ${\sin }^2$ ${\mathrm{theta}}_{\mathrm{W}}$ ${\mathrm{m}}_{\mathrm{\tau }}$ ${\mathrm{}}^2$ / ${\mathrm{m}}_{\mathrm{W}}$ ${\mathrm{}}^2$ [(${\mathit{N}}_{\mathit{p}}$+${\mathit{N}}_{\mathit{n}}$)ln(${\mathit{m}}_{\mathrm{\tau }}^2$/${\mathit{m}}_{\mathit{w}}^2$)+(${\mathit{N}}_{\mathit{p}}$ ${+}^2$ ${/}_3$ ${\mathit{N}}_{\mathit{n}}$)]. Implications of our results for neutrino matter oscillations and elastic scattering are briefly discussed.