Parity-Violating Electron-Deuteron Scattering

The longitudinal asymmetry due to $Z^0$ exchange is calculated in quasi-elastic electron-deuteron scattering at momentum transfers $|Q^2| \simeq 0.1$ GeV$^2$ relevant for the SAMPLE experiment. The deuteron and $pn$ scattering-state wave functions are obtained from solutions of a Schr\"odinger equation with the Argonne $v_{18}$ potential. Electromagnetic and weak neutral one- and two-nucleon currents are included in the calculation. The two-nucleon currents of pion range are shown to be identical to those derived in Chiral Perturbation Theory. The results indicate that two-body contributions to the asymmetry are small ($\simeq$ 0.2%) around the quasi-elastic peak, but become relatively more significant ($\simeq$ 3%) in the high-energy wing of the quasi-elastic peak.