Chiral Effective Field Theory Description of Neutrino Nucleon-Nucleon Bremsstrahlung in Supernova Matter

We revisit the rates of neutrino pair emission and absorption from nucleon-nucleon bremsstrahlung in supernova matter using the T-matrix formalism in the long-wavelength limit. Based on two-body potentials of chiral effective field theory (χEFT), we solve the Lippmann-Schwinger equation for the T-matrix including non-diagonal contributions. We consider final-state Pauli blocking and hence our calculations are valid for nucleons with an arbitrary degree of degeneracy. We also explore the in-medium effects on 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 supernova simulations, and calculations using an effective on-shell diagonal T-matrix from measured phase shifts. We estimate that multiple-scattering effects and correlations due to the random phase approximation introduce small corrections on top of the T-matrix results at subsaturation densities. A numerical table of the structure function is provided that can be used in supernova simulations.