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Impact of magnetic field on neutrino-matter interactions in core-collapse supernova

We explore the impact of magnetic field on neutrino-matter interactions in core-collapse supernova. We first derive the modified source terms for neutrino-nucleon scattering and neutrino absorption and emission processes in the moment formalism. Then we perform full relativistic three-dimensional, magnetorotational core-collapse supernova simulations of a 20 $M_\odot$ star with spectral neutrino transport. Our simulations treat self-consistently the parity violation effects of weak interaction in the presence of external magnetic field. The result shows a significant global asymmetry, mostly confined in the proto-neutron star, with clearly reflecting the magnetic field structure. The asymmetric property arises from two factors: the angle between the neutrino flux and magnetic field, and the term, which is parallel to the magnetic field and is also proportional to the deviation of distribution function of neutrinos from thermal equilibrium. The typical correction value amounts to $\sim1$ % relative to the total neutrino-matter interaction rate for the magnetic field strength of $\sim 10^{15-16}$~G. Although these asymmetric properties do not immediately affect the explosion dynamics, our results imply that they would be significant once the neutrinos diffuse out the proto-neutron star core carrying those asymmetries away. We also show that, during our simulation time of $\sim370$ ms after bounce, our results indicate that the correction value due to the modified inelastic scattering process dominates over that of the modified neutrino absorption and emission process.