Measurement of the parity-violating asymmetry in inclusive electroproduction of $\pi^-$ near the $\Delta^0$ resonance

TL;DR

This paper reports a measurement of the parity-violating asymmetry in inclusive $ ext{π}^-$ electroproduction near the $ ext{Δ}^0$ resonance, providing insights into weak interactions and constraining theoretical models of parity violation.

Contribution

The study provides the first experimental measurement of the PV asymmetry in this process, testing predictions of heavy-baryon chiral perturbation theory and models of weak couplings.

Findings

Measured asymmetry: $A_ ext{γ}^- = -0.36 ext{ ppm}$ with uncertainties.

Results disfavor certain theoretical enhancements proportional to $V_{ud}/V_{us}$.

Supports the use of PV electron scattering to probe $N- ext{Δ}$ axial transition form-factors.

Abstract

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.