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We revisit the rates of neutrino pair emission and absorption fromnucleon-nucleon bremsstrahlung in supernova matter using the $T$-matrixformalism in the long-wavelength limit. Based on two-body potentials of chiraleffective field theory ($\chi$EFT), we solve the Lippmann-Schwinger equationfor the $T$-matrix including non-diagonal contributions. We considerfinal-state Pauli blocking and hence our calculations are valid for nucleonswith an arbitrary degree of degeneracy. We also explore the in-medium effectson the $T$-matrix and find that they are relatively small for supernova matter.We compare our results with one-pion exchange rates, commonly used in supernovasimulations, and calculations using an effective on-shell diagonal $T$-matrixfrom measured phase shifts. We estimate that multiple-scattering effects andcorrelations due to the random phase approximation introduce small correctionson top of the $T$-matrix results at subsaturation densities. A numerical tableof the structure function is provided that can be used in supernovasimulations.

Chiral effective field theory description of neutrino nucleon-nucleon Bremsstrahlung in supernova matter