  The parity-violating (PV) asymmetry of inclusive $\pi^-$ production in
electron scattering from a liquid deuterium target was measured at backward
angles. The measurement was conducted as a part of the G0 experiment, at a beam
energy of 360 MeV. The physics process dominating pion production for these
kinematics is quasi-free photoproduction off the neutron via the $\Delta^0$
resonance. In the context of heavy-baryon chiral perturbation theory
(HB$\chi$PT), this asymmetry is related to a low energy constant $d_\Delta^-$
that characterizes the parity-violating $\gamma$N$\Delta$ coupling. Zhu et al.
calculated $d_\Delta^-$ in a model benchmarked by the large asymmetries seen in
hyperon weak radiative decays, and predicted potentially large asymmetries for
this process, ranging from $A_\gamma^-=-5.2$ to $+5.2$ ppm. The measurement
performed in this work leads to $A_\gamma^-=-0.36\pm 1.06\pm 0.37\pm 0.03$ ppm
(where sources of statistical, systematic and theoretical uncertainties are
included), which would disfavor enchancements considered by Zhu et al.
proportional to $V_{ud}/V_{us}$. The measurement is part of a program of
inelastic scattering measurements that were conducted by the G0 experiment,
seeking to determine the $N-\Delta$ axial transition form-factors using PV
electron scattering.
