Parity-violating inelastic electron-proton scattering at low $Q^2$ above the resonance region

We report the measurement of the parity-violating asymmetry for the inelastic scattering of electrons from the proton, at $Q^2=0.082{\mathrm{GeV}}^2$ and $W=2.23$ GeV, above the resonance region. The result $A_{\mathrm{Inel}}=-13.5\pm 2.0\left(\mathrm{stat}\right)\pm 3.9\left(\mathrm{syst}\right)$ ppm agrees with theoretical calculations, and helps to validate the modeling of the $\gamma Z$ interference structure functions $F_1^{\gamma Z}$ and $F_2^{\gamma Z}$ used in those calculations, which are also used for determination of the two-boson exchange $\gamma \text{−}Z$ box diagram (${\square }_{\gamma Z}$) contribution to parity-violating elastic scattering measurements. A positive parity-violating asymmetry for inclusive ${\pi }^{-}$ production was observed, as well as positive beam-normal single-spin asymmetry for scattered electrons and a negative beam-normal single-spin asymmetry for inclusive ${\pi }^{-}$ production.

Figure 1

Typical photoelectron spectrum, after subtraction of the electronic pedestal, for an unblocked main detector (MD4). Two distinct peaks can be seen. The narrow peak on the left, centered near 20 photoelectrons, is due to pions. The broader peak on the right, centered near 100 photoelectrons, is due to electrons.

Figure 2

Typical fit to the photoelectron spectrum from an unblocked main detector (MD4). The black histogram is the data, and the simulated spectra from pions (magenta), electrons (blue), and the sum of the electrons and pions (red) are superimposed.

Figure 3

The fraction of the detector yield due to pions, $f_{\pi }^i$, is shown for each main detector, except MD3 and MD7 (see text). The statistical uncertainties from the fitting routine are smaller than the plotting symbols. Also shown is the average value (black line) and the RMS deviation (hatched area), which we adopt as the uncertainty on the average.

Figure 4

Photoelectron spectrum from the blocked main detector (MD7). Only the peak due to pions ($\approx 20$ photoelectrons) is visible; cf. Fig. 1.

Figure 5

Measured asymmetry from the mixed data set, averaged over the unblocked detectors, vs data subset, where each data subset corresponds to a particular state of the insertable half-wave plate used to reverse the sign of the electron-beam helicity. Each data subset represents roughly 4 hours of data-taking. The “OUT” subsets reveal the unreversed sign of the asymmetry.

Figure 6

Measured and fitted asymmetries vs detector number, for both (a) the mixed data set and (b) the transverse data set. The fitted data points are connected via a line to guide the eye; detector 7 is the “blocked detector” with enhanced sensitivity to pions.

Figure 7

$A_{\mathrm{Al}}$, the asymmetry measured from the aluminum alloy target, plotted vs detector number. Errors shown are statistical only. The horizontal solid line and hatched region represent the average value and its uncertainty, respectively.

Figure 8

Simulated energy $E^{\prime }$ spectrum for elastically scattered electrons for those events that generated signals in the main detectors (log scale). Note the two distinct peaks. The peak near 1100 MeV represents highly radiated scattered electrons that pass through the collimators and the apertures of the concrete shield hut, to directly impinge on the main detector. The peak at the right is due to elastically scattered “punch-through” electrons (see text) which had radiated little energy, but which struck the shield-hut wall, creating a shower that generated signal in the main detectors.

Figure 9

Model calculations for $A_{\mathrm{Inel}}$ vs $W$, at $Q^2=0.082{\mathrm{GeV}}^2$, and the present measured datum (solid circle). The central values (solid curve) are from the AJM group [32] and the dashed lines represent the theoretical uncertainty from that calculation. The dotted lines are the larger theoretical uncertainties using the approach of the model by Gorchtein et al. [28] (adapted from Fig. 16 of Ref. [32]). The statistical (inner) and total (outer) error bars for the present measurement are indicated.