Induced Neutrino Charge in a Magnetized Medium

In this paper we estimate the contribution to neutrino effective charge from the vector type (coupling constant \(g_{V}\) ) vertex \(e^{\nu _{V}}_{eff}\) coming from the polarization tensor \(\Pi _{\mu \nu }\) in a magnetized medium. For electron type neutrinos \(g_\textrm{V} = 1 - (1 - 4 \sin ^2 \theta _\textrm{W})/2\) , and for tau and mu type neutrino \(g_\textrm{V} = -(1 - 4 \sin ^2 \theta _\textrm{W})/2 \) . We note that keeping PCT symmetry in view, the leading powers of B and \(\mu \) that appears in the expression of \(e^{\nu _{V}}_{eff}\) is of order \((eB)^{2}\) and \(\mu ^{2}\) . We further elucidate on the direction dependence of this charge that’s a manifestation of loss of isotropy due to the presence of an external field. We conclude this work by inferring on astrophysical and cosmological consequences of the same.