Measurement of neutral current $e^{\pm }p$ cross sections at high Bjorken $x$ with the ZEUS detector

The neutral current $e^{\pm }p$ cross section has been measured up to values of Bjorken $x\cong 1$ with the ZEUS detector at HERA using an integrated luminosity of $187{\mathrm{pb}}^{-1}$ of $e^{-}p$ and $142{\mathrm{pb}}^{-1}$ of $e^{+}p$ collisions at $\sqrt{s}=318\mathrm{GeV}$. Differential cross sections in $x$ and $Q^2$, the exchanged boson virtuality, are presented for $Q^2\ge 725{\mathrm{GeV}}^2$. An improved reconstruction method and greatly increased amount of data allows a finer binning in the high-$x$ region of the neutral current cross section and leads to a measurement with much improved precision compared to a similar earlier analysis. The measurements are compared to Standard Model expectations based on a variety of recent parton distribution functions.

Figure 1

For $e^{-}p$ and $e^{+}p$ event samples with $Q^2>550{\mathrm{GeV}}^2$, distributions of (a), (b) the ratio of the measured electron energy, $E_e^{\prime }$, to the expected energy, $E_{\mathrm{KP}}$, for $y<0.1$, (c), (d) of the transverse energy of the electron, $E_T^e$, to the transverse energy of the jet, $E_T^{\text{jet}}$, in one-jet events with $y<0.8$ for jets in the FCAL and (e), (f) similarly for jets in the BCAL. In all upper panels, data samples are represented by dots while MC samples, normalized to the number of data events, are represented by histograms. The lower panels show the ratio of data to MC distributions.

Figure 2

Distribution of the pulls obtained from the kinematic fit for (a) the electron energy, $E_e^{\prime }$ , (b) jet energy, $E_{\text{jet}}$, (c) electron scattering angle, ${\theta }_e$, and (d) jet angle, ${\theta }_{\text{jet}}$, in data (dots) compared to the corresponding distribution in MC (histogram) for the $e^{+}p$ events with measured $Q^2>550{\mathrm{GeV}}^2$ and $y<0.8$. The MC distributions are normalized to the number of events in the data.

Figure 3

Distributions of (a) electron energy, $E_e^{\prime }$, (b) electron scattering angle, ${\theta }_e$, (c) transverse energy of all jets, $E_T^{\text{jet}}$, and (d) jet production angle, ${\theta }_{\text{jet}}$, for $e^{-}p$ events with $Q^2>550{\mathrm{GeV}}^2$ and $y<0.8$ in data (dots) compared to the corresponding distributions in MC (histograms). The MC distributions are normalized to the number of events in the data.

Figure 4

Distributions of (a) electron energy, $E_e^{\prime }$, (b) electron scattering angle, ${\theta }_e$, (c) transverse energy of all jets, $E_T^{\text{jet}}$, and (d) jet production angle, ${\theta }_{\text{jet}}$, for $e^{+}p$ events with $Q^2>550{\mathrm{GeV}}^2$ and $y<0.8$ in data (dots) compared to the corresponding distributions in MC (histograms). The MC distributions are normalized to the number of events in the data.

Figure 5

Distribution of (a), (b) $Q^2$, (c), (d) the jet multiplicity, $N_{\text{jet}}$, and (e), (f) $x$ for events with at least one jet for the $e^{-}p$ and $e^{+}p$ data samples (dots) for $Q^2>550{\mathrm{GeV}}^2$ and $y<0.8$. The distributions are compared to MC expectations (histograms) normalized to the number of events in the data.

Figure 6

The double-differential cross section for NC $e^{-}p$ scattering at $\sqrt{s}=318\mathrm{GeV}$ (dots) as a function of $x$ and the double-differential cross section integrated over $x$ divided by the bin width and placed at the center of the bin (triangles) for different values of $Q^2$ as shown, compared to the Standard Model expectations evaluated using HERAPDF1.5 PDFs (line). The error bars show the statistical and systematic uncertainties added in quadrature.

Figure 7

The double-differential cross section for NC $e^{+}p$ scattering at $\sqrt{s}=318\mathrm{GeV}$ (dots) as a function of $x$ and the double-differential cross section integrated over $x$ divided by the bin width and placed at the center of the bin (triangles) for different values of $Q^2$ as shown, compared to the Standard Model expectations evaluated using HERAPDF1.5 PDFs (line). The error bars show the statistical and systematic uncertainties added in quadrature. For bins with zero measured events, a 68% probability limit is given.

Figure 8

Ratio of the double-differential cross section for NC $e^{-}p$ scattering and of the double-differential cross section integrated over $x$ to the Standard Model expectation evaluated using the HERAPDF1.5 PDFs as a function of $x$ at different $Q^2$ values as described in the legend. For HERAPDF1.5, the uncertainty is given as a band. The expectation for the integrated bin is also shown as a hatched box. The error bars show the statistical and systematic uncertainties added in quadrature. The expectations of other commonly used PDF sets normalized to HERAPDF1.5 PDFs are also shown, as listed in the legend. Note that the scale on the $y$ axis changes with $Q^2$.

Figure 9

Ratio of the double-differential cross section for NC $e^{+}p$ scattering and of the double-differential cross section integrated over $x$ to the Standard Model expectation evaluated using the HERPDF1.5 PDFs as a function of $x$ at different $Q^2$ values as described in the legend. For HERAPDF1.5, the uncertainty is given as a band. The expectation for the integrated bin is also shown as a hatched box. The error bars show the statistical and systematic uncertainties added in quadrature. For bins with zero measured events, a 68% probability limit is given. The expectations of other commonly used PDF sets normalized to HERAPDF1.5 PDFs are also shown, as listed in the legend. Note that the scale on the $y$ axis changes with $Q^2$.