First Determination of the Weak Charge of the Proton

The $Q_{\mathrm{weak}}$ experiment has measured the parity-violating asymmetry in $\overrightarrow{e}p$ elastic scattering at $Q^2=0.025(\mathrm{GeV}/c{)}^2$, employing $145\mu \mathrm{A}$ of 89% longitudinally polarized electrons on a 34.4 cm long liquid hydrogen target at Jefferson Lab. The results of the experiment’s commissioning run, constituting approximately 4% of the data collected in the experiment, are reported here. From these initial results, the measured asymmetry is $A_{ep}=-279\pm 35$ (stat) $\pm 31$ (syst) ppb, which is the smallest and most precise asymmetry ever measured in $\overrightarrow{e}p$ scattering. The small $Q^2$ of this experiment has made possible the first determination of the weak charge of the proton $Q_W^p$ by incorporating earlier parity-violating electron scattering (PVES) data at higher $Q^2$ to constrain hadronic corrections. The value of $Q_W^p$ obtained in this way is $Q_W^p(\mathrm{PVES})=0.064\pm 0.012$, which is in good agreement with the standard model prediction of $Q_W^p(\mathrm{SM})=0.0710\pm 0.0007$. When this result is further combined with the Cs atomic parity violation (APV) measurement, significant constraints on the weak charges of the up and down quarks can also be extracted. That $\mathrm{PVES}+\mathrm{APV}$ analysis reveals the neutron’s weak charge to be $Q_W^n(\mathrm{PVES}+\mathrm{APV})=-0.975\pm 0.010$.

Figure 1

The basic experimental design showing the target, collimation, magnet coils, electron trajectories, and detectors. Elastically scattered electrons (red tracks) focus at the detectors while inelastically scattered electrons (not shown), are swept away from the detectors (to larger radii). The distance along the beam line from the target center to the center of the quartz bar detector array is 12.2 m.

Figure 2

Global fit result (solid line) presented in the forward angle limit as reduced asymmetries derived from this measurement as well as other PVES experiments up to $Q^2=0.63(\mathrm{GeV}/c{)}^2$, including proton, helium, and deuterium data. The additional uncertainty arising from this rotation is indicated by outer error bars on each point. The yellow shaded region indicates the uncertainty in the fit. $Q_W^p$ is the intercept of the fit. The SM prediction [34] is also shown (arrow).

Figure 3

The constraints on the neutral-weak quark coupling constants $C_{1u}-C_{1d}$ (isovector) and $C_{1u}+C_{1d}$ (isoscalar). The more horizontal (green) APV band (shown at $\Delta {\chi }^2=2.3$) provides a tight constraint on the isoscalar combination from ${}^{133}\mathrm{Cs}$ data. The more vertical (blue) ellipse represents the global fit of the existing $Q^2<0.63$ PVES data including the new result reported here at $Q^2=0.025(\mathrm{GeV}/c{)}^2$. The smaller (red) ellipse near the center of the figure shows the result obtained by combining the APV and PVES information. The SM prediction [34] as a function of ${sin}^2{\theta }_W$ in the $\overline{MS}$ scheme is plotted (diagonal black line) with the SM best fit value indicated by the (black) point at ${sin}^2{\theta }_W=0.23116$.