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

Abstract

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 ( χ EFT), 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.