Parity-Violating Asymmetry in the N $\to\Delta$ Transition

The primary focus of the recently completed $Q_{\mathrm{weak}}$ experiment at Jefferson Lab is the determination of the proton's weak charge. To properly make corrections to the measured asymmetry, dedicated measurements were made of the parity-violating asymmetry at low $Q^2$ in inelastic $\vec{e}$-p scattering at the N $\to\Delta$ transition for two different beam energies. The asymmetries are used to extract an additional physics result, the low energy constant d$_\Delta$, which is responsible for the Siegert term that causes the asymmetry to be non-zero even at the photon point ($Q^2$=0). The d$_\Delta$ term is a measure of the hadronic parity violation in this transition. It has been shown to be related to some puzzles in radiative hyperon decays. These analyses suggest potential values of d$_\Delta$ much larger than its natural scale. The measurements described here were done at beam energies of 877 MeV ($Q^2$ = 0.011 GeV$^2$) and 1165 MeV ($Q^2$= 0.021 GeV$^2$) using the $Q_{\mathrm{weak}}$ apparatus. An overview of the motivations for the measurement, the experimental approach, and the status of the analysis will be presented.