Neutrino-pair bremsstrahlung from nucleon-nucleon scattering

Background: Neutrino-pair bremsstrahlung processes from nucleon-nucleon scattering NN nu(nu) over bar (nn nu(nu) over bar, pp nu(nu) over bar, and np nu(nu) over bar) have recently attracted attention in studies of neutrino emission in neutron stars, because of the implications for the neutron star cooling. The calculated NN nu(nu) over bar emissivities within the neutron star environment are relatively insensitive to the two-nucleon dynamical model used in the calculations, but differ significantly from those obtained using an one-pion-exchange (OPE) model. Purpose: We investigate the free NN nu(nu) over bar cross sections using a realistic nucleon-nucleon scattering amplitude, comparing the relative sizes of the cross sections for the three processes nn nu(nu) over bar, pp nu(nu) over bar, and np nu(nu) over bar. Method: We employ a realistic one-boson-exchange (ROBE) model for NN scattering and combine those strong scattering amplitudes with the well-known nucleon weak interaction vertices to construct weak bremsstrahlung amplitudes. Using the resulting NN nu(nu) over bar amplitudes we investigate the relative importance of the vector (Gamma(mu)(V)), axial vector (Gamma(mu)(A)), and tensor (Gamma(mu)(T)) terms. The ROBE model bremsstrahlung amplitudes are also used as a two-nucleon dynamical model with which we calculate the cross sections d sigma/d omega for nn nu(nu) over bar, pp nu(nu) over bar, and np nu(nu) over bar. Results: The three free NN nu(nu) over bar cross sections d sigma/d omega are of similar order of magnitude. Each increases with increasing neutrino-pair energy omega. For the neutrino-pair energy of omega = 1MeV our nn nu(nu) over bar results are in quantitative agreement with those previously reported by Timmermans et al. [Phys. Rev. C65, 064007 (2002)], who used the leading-order term of the soft-neutrino-pair bremsstrahlung amplitude to calculate the cross sections. Differences between the nn nu(nu) over bar and pp nu(nu) over bar cross section are not discernible over the nucleon-nucleon incident energy region considered, due to the complete dominance of the axial vector component of the weak interaction nucleon vertex function Gamma(mu) as demonstrated analytically in Appendix A. The np nu(nu) over bar cross section is smaller than either the nn nu(nu) over bar or the pp nu(nu) over bar cross section for low to moderate values of omega; this characteristic only changes at larger neutrino-pair energies around omega similar to 50 MeV, which is above the low energy region characterized in Appendix B. Conclusions: The free NN nu(nu) over bar cross sections, calculated using a realistic nucleon-nucleon amplitude model, are new except for the nn nu(nu) over bar cross section at omega = 1MeV that was first reported by Timmermans et al., and at. = 0.5,1,2 MeV by Li et al. [Phys. Rev. C 80, 035505 (2009)]. The nn nu(nu) over bar and pp nu(nu) over bar cross sections are virtually identical in magnitude. All three NN nu(nu) over bar processes are dominated by the axial vector component of the vertex function Gamma(mu), with only slight deviations from this behavior being seen in the np nu(nu) over bar process at large neutrino-pair energies.