Neutrino-Induced Polarization Rotation in Active Galactic Nuclei Plasmas

We study parity-violating birefringence induced by an asymmetric neutrino background in plasmas associated with active galactic nuclei (AGN). We derive a directionality factor arising from the relative bulk motion between the neutrino medium and plasma, and show that it can produce an anomalous frequency dependence of the polarization-rotation angle, distinct from the $\omega^{-2}$ scaling of Faraday rotation. This anomalous scaling can occur either at the resonance plasma frequency condition $\omega \simeq \omega_p$, or when $E_\nu^{0}\simeq m_\nu \omega/\omega_p$ lies within the range of the neutrino energy spectrum. We estimate the effect for three scenarios: jets propagating through the cosmic neutrino background (C$\nu$B), jets with an internal flux of high-energy neutrinos, and accretion-disk plasma permeated by the C$\nu$B. Of the three scenarios, the latter gives the largest rotation angle $\phi_{\rm d} \sim 10^{-35}\,\mathrm{rad}$, at X-ray frequencies. Although the predicted rotation angles are below current polarimetric sensitivity, the identified spectral signatures provide a theoretical framework for probing neutrino asymmetries and AGN plasma properties independent of magnetic field models.