Measurement of Strange-Quark Contributions to the Nucleon's Form Factors at $Q^2=0.230(\mathrm{G}\mathrm{e}\mathrm{V}/c{)}^2$

We report on a measurement of the parity-violating asymmetry in the scattering of longitudinally polarized electrons on unpolarized protons at a $Q^2$ of $0.230(\mathrm{G}\mathrm{e}\mathrm{V}/c{)}^2$ and a scattering angle of ${\theta }_e=30°–40°$. Using a large acceptance fast ${\mathrm{P}\mathrm{b}\mathrm{F}}_2$ calorimeter with a solid angle of $\Delta \Omega =0.62\mathrm{s}\mathrm{r}$, the A4 experiment is the first parity violation experiment to count individual scattering events. The measured asymmetry is $A_{\mathrm{p}\mathrm{h}\mathrm{y}\mathrm{s}}=(-5.44\pm {0.54}_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}}\pm {0.26}_{\mathrm{s}\mathrm{y}\mathrm{s}})\times {10}^{-6}$. The standard model expectation assuming no strangeness contributions to the vector form factors is $A_0=(-6.30\pm 0.43)\times {10}^{-6}$. The difference is a direct measurement of the strangeness contribution to the vector form factors of the proton. The extracted value is $G_E^s+0.225G_M^s=0.039\pm 0.034$ or $F_1^s+0.130F_2^s=0.032\pm 0.028$.

Figure 1

The dashed histogram shows a raw energy spectrum of accepted particles from the hydrogen target as read directly from the hardware memory of the readout electronics of the lead fluoride calorimeter. For the solid black curve, this raw spectrum has been corrected for the differential nonlinearity of the ADC, i.e., for measured variations of the ADC channel width. The position of the elastic scattering peak, the threshold for ${\pi }^0$ production, and the position of the $\Delta$ resonance is indicated as well as the lower and the upper cut positions for the extraction of $N_e^R$ and $N_e^L$ as described in the text.

Figure 2

The extracted experimental asymmetries are shown with the $\lambda /2$ plate in or out, respectively, as a function of the data sample. The dashed line represents the value of $A_0$ as described in the text.

Figure 3

The solid line represents all possible combinations of $G_E^s+0.225G_M^s$ as extracted from the work presented here at a $Q^2$ of $0.230(\mathrm{G}\mathrm{e}\mathrm{V}/c{)}^2$. The densely hatched region represents the uncertainty. The recalculated result from the HAPPEX published asymmetry at $Q^2$ of $0.477(\mathrm{G}\mathrm{e}\mathrm{V}/c{)}^2$ is indicated by the dashed line; the less densely hatched area represents the associated error of the HAPPEX result.