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Abstract

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.