Soft electroweak bremsstrahlung: Theorems and astrophysical relevance

Abstract

We analyze the structure of the amplitudes for electroweak bremsstrahlung in nucleon-nucleon collisions, for the charged $(N+\stackrel{\ensuremath{\rightarrow}}{N}{N+N+e}^{\ensuremath{-}}+{\overline{\ensuremath{\nu}}}_{e})$ and neutral $(N+\stackrel{\ensuremath{\rightarrow}}{N}N+N+{\ensuremath{\nu}}_{f}+{\overline{\ensuremath{\nu}}}_{f})$ weak current. Theorems are derived for the matrix elements of the vector and axial-vector currents in the soft regime. A comparison is made with previous work, usually performed in the nonrelativistic limit and by using a one-pion exchange two-nucleon interaction in Born approximation. Such approaches are argued to be unrealistic. This is explicitly shown for the neutrino-pair emission process in neutron-neutron scattering. Our results are relevant for calculations of neutrino emissivities in supernovae and in cooling scenarios of neutron stars.