$\gamma Z$ corrections to forward-angle parity-violating $ep$ scattering

We use dispersion relations to evaluate the $\gamma Z$ box contribution to parity-violating electron scattering in the forward limit arising from the axial-vector coupling at the electron vertex. The calculation makes full use of the critical constraints from recent JLab data on electroproduction in the resonance region as well as high-energy data from HERA. At the kinematics of the $Q_{\mathrm{weak}}$ experiment, this gives a correction of ${0.0047}_{-0.0004}^{+0.0011}$ to the standard model value 0.0713(8) of the proton weak charge. While the magnitude of the correction is highly significant, the uncertainty is within the anticipated experimental uncertainty of $\pm 0.003$.

Figure 1

Proton $F_2$ structure function versus $W$ in the resonance region for fixed $Q^2$. The data are from JLab (circles) [16] and SLAC (triangles) [15]. The shaded (yellow) band between the solid lines represents the uncertainty on our fit, while the dashed lines are obtained by summing the resonance fit from Ref. 19 and the nonresonant contributions from Ref. 20.

Figure 2

As in Fig. 1 but for higher values of $W$. The data are from SLAC (triangles) [15], NMC (circles) [25], and H1 (squares) [26]. The solid lines show the fit [21, 22] used in this analysis, with the (yellow) bands representing the uncertainty. The dashed lines are the results of the generalized vector dominance color dipole model [20], while the dotted lines represent the MRST leading twist fit [24].

Figure 3

As in Fig. 2 but for $Q^2=5$, 10, 25, and $60{\mathrm{GeV}}^2$.

Figure 4

$\gamma Z$ box correction ${\square }_{\gamma Z}^V(E)$ to $Q_W^p$ as a function of electron energy $E$, showing the resonant (dashed line) and nonresonant (dotted line) contributions, as well as the sum (solid line) and the overall (asymmetric) uncertainty (shaded area). The vertical arrow at $E=1.165\mathrm{GeV}$ indicates the energy of the $Q_{\mathrm{weak}}$ experiment.