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 $A_gamma^-=-0.36pm 1.06pm 0.37pm 0.03$ 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.
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