Elastic and Inelastic Neutrino–Deuteron Scattering in Effective Field Theory

The differential cross-sections for elastic and inelastic neutrino–deuteron scattering are calculated analytically using nucleon-nucleon effective field theory. For elastic scattering, the deuteron axial form factor and the deuteron strange magnetic moment form factor are computed to next-to-leading order, including two-body currents. For inelastic scattering, two neutral current processes νd → νnp, νd → νnp and one charged current process νd → e+nn are computed to next-to-leading order. These depend on an isovector axial two-body matrix element whose value is yet to be fixed by experiment. Potential model calculations by Kubodera et al. and Ying et al. are reproduced for different values of the two-body matrix element. The charged current to neutral current νd cross-section ratio is confirmed to be insensitive to short distance physics and the same ratio is obtained by potential models and the calculation presented here, for incident energies above 6 MeV. The two-body matrix element could be fixed using the parity violating process −→e d → enp.