Magnetic field induced neutrino chiral transport near equilibrium

Based on the recently formulated chiral radiation transport theory for left-handed neutrinos, we study the chiral transport of neutrinos near thermal equilibrium in core-collapse supernovae. We first compute the near-equilibrium solution of the chiral radiation transport equation under the relaxation time approximation, where the relaxation time is directly derived from the effective field theory of the weak interaction. By using such a solution, we systematically derive analytic expressions for the nonequilibrium corrections of the neutrino energy-momentum tensor and neutrino number current induced by magnetic fields via the neutrino absorption on nucleons. In particular, we find the nonequilibrium neutrino energy current proportional to the magnetic field. We also discuss its phenomenological consequences such as the possible relation to pulsar kicks.