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Measurement of neutral current cross sections at high Bjorken-x with the ZEUS detector at HERA

A new method is employed to measure the neutral current cross section up to Bjorken-x values of one with the ZEUS detector at HERA using an integrated luminosity of 65.1 pb-1 for e+p collisions and 16.7 pb-1 for e-p collisions at sqrt{s}=318 GeV and 38.6 pb-1 for e+p collisions at sqrt{s}=300 GeV. Cross sections have been extracted for Q2>= 648 GeV2 and are compared to predictions using different parton density functions. For the highest x bins, the data have a tendency to lie above the expectations using recent parton density function parametrizations.


Introduction
Only limited information is available on structure functions at high Bjorken-x in the deep inelastic scattering (DIS) regime. This is largely due to limitations in beam energies, in measurement techniques and the small cross section at high x. In this paper, a new method is described and used to measure the neutral current (NC) cross section in electron-proton scattering up to x = 1 with data from the ZEUS detector at HERA.
At HERA, proton beams of 920 GeV (820 GeV prior to 1998), collide with either electron or positron beams of 27.5 GeV. The electron 1 interacts with the proton via the exchange of a gauge boson. The description of DIS is usually given in terms of three Lorentz-invariant quantities, Q 2 , x and y, which are related by Q 2 = sxy, where the masses of the electron and proton are neglected, s is the square of the center-of-mass energy, Q 2 is the negative of the square of the transferred four-momentum, x is the Bjorken variable [1] and y is the inelasticity. The NC electron-proton differential scattering cross section is typically written in terms of the proton structure functions as where Y ± ≡ 1 ± (1 − y) 2 and α denotes the fine-structure constant. At leading order (LO) in QCD, the longitudinal structure function, F L , is zero and the structure functions F 2 and xF 3 can be expressed as products of electroweak couplings and parton density functions (PDFs).
The form of the PDFs is typically parametrized as q(x) = Ax −λ f (x)(1 − x) η , where f (x) interpolates between the low-x and high-x domains. Such a form allows for an accurate description of the data at low x [2][3][4][5][6]. For x ≥ 0.3, the PDFs are found to decrease very quickly. However, a direct confrontation with data has not been possible to date for x → 1. The highest measured points in the DIS regime are for x = 0.75 [7]. Data at higher x exist [8,9] but these are in the resonance production region and cannot be easily interpreted in terms of parton distributions. The highest x value for HERA structure function data reported to date is x = 0.65 [4,5]. The differences between different PDF sets increase rapidly as x increases, even though they use similar data and have common parametrization for x → 1. The uncertainties for x > 0.75 are large and hard to quantify.
This paper presents a reanalysis of previously published ZEUS data [4,10,11] with a new reconstruction technique designed to extract cross sections extending up to x = 1 at high Q 2 . The data correspond to an integrated luminosity of 38.6 pb −1 for e + p collisions at √ s = 300 GeV recorded in 96-97, 16.7 pb −1 for e − p collisions at √ s = 318 GeV recorded in 98-99 and 65.1 pb −1 for e + p collisions at √ s = 318 GeV recorded in 99-00. 2 The ZEUS experiment at HERA ZEUS is a multipurpose detector described elsewhere [12]. A schematic depiction of the ZEUS detector is given in Fig. 1. A brief outline of the components that are most relevant for this analysis is given below.
The high-resolution uranium-scintillator calorimeter (CAL) [13] consists of three parts: the forward (FCAL), the barrel (BCAL) and the rear (RCAL) calorimeters. Each part is divided into modules and further subdivided into towers; each tower is longitudinally segmented into one electromagnetic section (EMC) and either one (in RCAL) or two (in BCAL and FCAL) hadronic sections (HAC). The smallest subdivision of the calorimeter is called a cell. The CAL energy resolutions, measured under test-beam conditions, are σ(E)/E = 0.18/ √ E for electrons and σ(E)/E = 0.35/ √ E for hadrons, with E in GeV. The timing resolution of the CAL is ∼ 1 ns for energy deposits larger than 4.5 GeV.
Charged particles are tracked in the central tracking detector (CTD) [14], which operates in a magnetic field of 1.43 T provided by a thin superconducting solenoid. The CTD consists of 72 cylindrical drift-chamber layers, organized in nine superlayers covering the polar-angle 2 region 15 • < θ < 164 • . The transverse-momentum resolution for full-length tracks is σ(p T )/p T = 0.0058 p T ⊕ 0.0065 ⊕ 0.0014/p T , with p T in GeV.
The luminosity is measured using the Bethe-Heitler reaction ep → eγp [15]. The resulting small-angle photons were measured by the luminosity monitor, a lead-scintillator calorimeter placed in the HERA tunnel 107 m from the interaction point in the electron beam direction. Figure 1 also shows a schematic depiction of a high-Q 2 NC event in the ZEUS detector: a scattered electron and a jet are outlined in the CAL, while the proton remnant largely disappears down the forward beam pipe. The electron is typically scattered at a large angle and is easily recognized in the detector. Such events have been analyzed by a variety of techniques in the past, such as the double-angle method, all of which limited the maximum value of x which could be measured. In the new techniques presented here, the hadronic system can be used to measure x by reconstructing the energy and angle of the jet produced by the scattered quark. Above some x value that depends on Q 2 , the jet is at a small angle and not well reconstructed. An integrated cross section above an x where E p is the proton beam energy. The relative resolution in x varied from 15% to 4% as x increased from 0.06 to 0.7 in events where a jet could be reconstructed. At high x, θ jet is small and x ≈ E jet /E p , where E jet has good resolution. The events with a reconstructed jet were sorted into x bins to allow a measurement of the double differential cross-section d 2 σ Born /dxdQ 2 . Events with no jet reconstructed within the fiducial volume were assumed to come from high x and were collected in a bin with x edge < x < 1. An integrated cross section was calculated from 1 x edge (d 2 σ Born /dxdQ 2 )dx. Due to their poorer x resolution, events with more than one jet were discarded. The correction to the cross section for multi-jet events was taken from the Monte Carlo simulation described below, and ranged from 9% at x = 0.1 to 1% at x = 0.6. The systematic uncertainty associated with this cut is discussed in Section 6.2.2. More details of this reconstruction technique are given elsewhere [21].

Monte Carlo simulations
Monte Carlo (MC) simulations were used to evaluate the efficiency for selecting events, for determining the accuracy of the kinematic reconstruction, and for estimating the background rate. The statistical uncertainties from the MC samples were negligible in comparison to those of the data.
Standard Model (SM) NC DIS events were simulated with DjangoH version 1.1 [22] which includes an interface to the Heracles 4.6.1 [23] program. Heracles includes the corrections for the initial-and final-state electroweak radiation, vertex and propagator corrections, and two-boson exchange. The hadronic final state was simulated using the Meps model of Lepto 6.5 [24], which includes order-α S matrix elements (ME) with a lower and upper cutoff on the soft and collinear divergences. Both the ME cut-offs and the parton evolutions are treated by parton showers based on the DGLAP evolution equations. The fragmentation of the scattered partons into observable hadrons is performed with the Lund string hadronization model by Jetset [25]. The CTEQ6D PDF set [3] was used.
The ZEUS detector response was simulated using a program based on Geant 3.13 [26]. The generated events were passed through the detector simulation, subjected to the same trigger requirements as the data and processed by the same reconstruction programs.
The vertex distribution in data is a crucial input to the MC simulation for the correct evaluation of the event-selection efficiency. Therefore, the Z-vertex distribution used in the MC simulation was determined from a sample of NC DIS events in which the eventselection efficiency was independent of the Z position of the event vertex [4]. 5 Event selection 5.1 Trigger ZEUS operates a three-level trigger system [4,27]. At the first-level, only coarse calorimeter and tracking information are available. Events were selected using criteria based on energy deposits in the CAL consistent with an isolated electron. In addition, events with high E T in coincidence with a CTD track were accepted. At the second level, a cut on δ > 29 GeV was imposed to select NC events, with δ defined as: where the sum runs over all calorimeter energy deposits E i with polar angles θ i . Timing information from the calorimeter was used to reject events inconsistent with the bunchcrossing time. At the third level, events were fully reconstructed and selected according to requirements similar to, but looser than, the offline cuts described below.
The main uncertainty in the trigger efficiency comes from the first level. The efficiency in data and MC simulation agreed to within ∼ 0.5% and the overall efficiency was above 95%.

Offline selection
The following criteria were imposed to select NC DIS events offline: • an electron with E ′ e > 25 GeV was required. An isolation cut was imposed by requiring that less than 4 GeV be deposited in calorimeter cells not associated with the scattered electron in an η-φ cone of radius R cone = 0.8 centered on the candidate cluster. For those electrons in the CTD acceptance, a matched track was required which passed within 10 cm of the cluster center. The matched track was required to traverse at least four of the nine superlayers of the CTD. The momentum of the track, p trk , had to be at least 10 GeV. For electrons outside the forward tracking acceptance of the CTD, the tracking requirement in the electron selection was replaced by a cut on the transverse momentum of the electron, p T,e > 30 GeV; • a fiducial-volume cut was applied to the electron to guarantee that the experimental acceptance was well understood. It excluded the transition regions between the FCAL and the BCAL [28]. It also excluded the regions within 1.5 cm of the module gaps in the BCAL. As the kinematic region considered in this analysis is at high Q 2 , events with electrons in the RCAL were discarded.
The following cuts were used to select an essentially background free and well reconstructed event sample: • either 0 or 1 valid jets. Valid jets were required to have E T,jet > 10 GeV and θ jet > 0.12 rad; • a reconstructed vertex with −50 < Z vtx < 50 cm, a range consistent with ep interactions; • δ > 40 GeV to suppress photoproduction events, in which the scattered electron escaped through the beam hole in the RCAL. This cut value was δ > 47 GeV for events in the highest x bins. This cut also rejected events with large initial-state QED radiation. In addition, δ < 65 GeV was required to remove "overlay" events in which a normal DIS event coincided with additional energy deposits in the RCAL from some other reaction. This requirement had a negligible effect on the efficiency for selecting NC DIS events.
• y e < 0.95 to further reduce background from photoproduction events, where y e was defined as (1 − cos θ e ); • P T / √ E T < 4 √ GeV to remove cosmic rays and beam-related backgrounds. The variables P T and E T were defined by: where the sums run over all calorimeter energy deposits, E i , with polar and azimuthal angles θ i and φ i with respect to the event vertex, respectively; • ≥ 5 HAC cells with energy above 110 MeV to remove elastic Compton scattering events (ep → eγp) and further reduce the size of the QED radiative corrections. The contribution from deeply virtual Compton scattering was found to be negligible; • y JB < 1.3 · Q 2 edge /(s · x edge ) to limit event migration from small x to large x for zero-jet events. The variable y JB was calculated with the Jacquet-Blondel method [29]. The quantities x edge and Q 2 edge are the lower x and upper Q 2 edges of the bins defined for the cross-section measurement (see Section 6.1).
After these selections, 10298 events remained in the 99-00 e + p data, 2664 in the 98-99 e − p data and 5935 in the 96-97 e + p data in the bins used to extract the cross sections. The numbers of events in the zero-jet bins were 1292, 293 and 493, respectively.
Monte Carlo distributions are compared with those from data in Figs. 2-5 for several variables. The MC distributions are normalized to the measured luminosity. Only the comparison to 99-00 e + p data is shown; the comparisons of 98-99 e − p and 96-97 e + p data with MC distributions show similar features. The first set of plots, Fig. 2, shows general properties for the full sample of events. Good agreement between data and MC simulation is observed, with no indication of residual backgrounds. The small disagreement observed in Fig. 2c has been verified to have negligible impact on the results presented in this paper. Figure 3 shows distributions related to the scattered electron. Figure 4 presents a series of control plots for jet quantities. The MC reproduces the data distribution for the number of reconstructed jets to high accuracy. This is important since the MC is used to correct for the inefficiency resulting from the requirement of zero or one jet in the event. The remaining distributions in this figure are for the jet quantities in one jet events. Figure 5 shows distributions for the class of events with zero jets. Overall, 13% more data events for 99-00 e + p, 2% more data events for 98-99 e − p and 5% more data events for 96-97 e + p are observed for zero-jet events than expected in the simulation. An offset in the δ distribution is seen, with the MC distribution slightly lower than the data. This offset can however be explained by shifting the electron energy scale by 1%, which is within its estimated uncertainty.

Binning, acceptance and cross-section determination
The bins in the (x, Q 2 ) kinematic space used in this analysis are shown in Fig. 6. The bin widths in Q 2 were chosen to correspond to three times the resolution of the reconstructed Q 2 . The minimum value of Q 2 corresponds roughly to the acceptance of the BCAL.
The lower x edge of the bin for zero-jet events, x edge , was determined from the condition θ jet > 0.12 rad. For the bins where a jet was reconstructed, the bin widths in x were chosen to correspond to three times the resolution of the reconstructed x.
The MC simulation was used to study the x distribution of the zero-jet events. Figure 7 shows the true x distribution for the 99-00 e + p MC events in different Q 2 bins. Similar distributions are observed in the 98-99 e − p and 96-97 e + p MC. As can be seen in this figure, the zero-jet events originate predominantly from the interval x edge < x < 1. We note that these distributions depend on the particular PDF chosen and that there are uncertainties at large x.
The efficiency, defined as the number of events generated and reconstructed in a bin after all selection cuts divided by the number of events that were generated in that bin, was typically 40%. In some low-Q 2 bins, dominated by events in which the electron is scattered into the RCAL or the B/RCAL transition region and removed by the fiducial cut, the efficiency was lower. The purity, defined as the number of events generated and reconstructed in a bin after all selection cuts divided by the total number of events reconstructed in that bin, was typically 50%. The efficiency and purity in the (x, Q 2 ) bins for the 99-00 e + p simulation are shown in Fig. 8. The 96-97 e + p and 98-99 e − p simulations yielded similar values. The efficiency and purity in zero-jet bins are comparable to those in the mid-x bins.
The double-differential cross section was determined as and the integrated cross section was determined as where N data (∆x, ∆Q 2 ) is the number of data events in a bin (∆x, ∆Q 2 ) and N MC (∆x, ∆Q 2 ) is the number of signal MC events normalized to the luminosity of the data. The SM prediction, d 2 σ SM Born (x, Q 2 )/dxdQ 2 , was evaluated according to Eq. (1) with the same PDF and electroweak (EW) parameters as used in the MC simulation. This procedure implicitly takes the acceptance, bin-centering and leading-order radiative corrections from the MC simulation. The variation of the cross sections resulting from different choices of PDF in the MC are described in the next section. The values of (x, Q 2 ) at which the cross sections are quoted are given in Tables 1-6.
Monte Carlo studies indicated that the radiative corrections have little dependence on x for the kinematic reconstruction method used here. The correction for higher-order radiative effects, δ(Q 2 ), calculated from HECTOR [30] varied from 3% at low Q 2 to 0% at high Q 2 .

Systematic uncertainties
Systematic uncertainties associated with the MC simulations were estimated by re-calculating the cross section after modifying the simulation to account for known uncertainties. Cut values were varied where this method was not applicable.

Uncorrelated systematic uncertainties
The following systematic uncertainties are either small or exhibit no bin-to-bin correlations: • electron energy resolution in the MC simulation. The effect on the cross sections was evaluated by changing the resolution by ±1% in the MC. This resulted in ±1% effects over almost the full kinematic range. The effect increased to ±2% for the doubledifferential cross section in several low Q 2 bins and for several integrated cross section bins; • electron angle. Uncertainties in the electron scattering-angle determination are known to be at most 1 mrad [11]. The resulting systematic effects on the cross-section measurement were at most 2%; • electron-isolation requirement. Variation of the electron-isolation energy by ±2 GeV caused negligible effects in the measured cross section in the low-Q 2 region and 2.5% in the high-Q 2 region; • FCAL alignment. The FCAL jet position was varied by ±0.5 cm in both X and Y directions. The resulting changes in the cross sections were negligible; • reconstructed-vertex uncertainty. The cut on the reconstructed Z vertex was changed by ±2 cm; The uncertainties in the cross sections associated with this variation were negligible over the full kinematic range; • background uncertainty. The estimated background from all sources was less than 1% and gave negligible uncertainty.

Correlated systematic uncertainties
The significant correlated systematic uncertainties are listed below and labeled for further reference. They were determined to result from the following sources: • {δ 1 } electron-energy scale. The systematic uncertainty resulting from uncertainty in the electron energy scale was checked by changing the energy scale by ±1%. This resulted in typically 2% systematic variations in the cross sections; • {δ 2 } jet-energy scale. The uncertainty in the cross sections arising from the measurement of the jet energy was checked by changing the energy scale by ±1%. The effect in the highest-x bins was negligible over the full Q 2 region. The uncertainty in the double-differential cross-section bins was 0 − 7% for 0.1 < x < 0.7; • {δ 3 } FCAL first inner ring (FIR) EMC energy scale. The effect of the FIR EMC energy scale uncertainty on the cross section was checked by changing the energy scale by ±5%, which gave 0 − 3.5% uncertainty as x increased from 0.1 to 0.9; • {δ 4 } different PDFs. The uncertainty in the extracted cross section resulting from uncertainties in the shape of the PDFs at high x was checked by comparing the cross sections calculated from different sets: CTEQ4D, CTEQ6D, MRST99, ZEUS-S and ZEUS-JETS. The effect was less than 1% at low x and increased to 5% at high x; • {δ 5 } simulation of the hadronic final state and jet-selection procedure. The invariant k T jet algorithm was replaced with a cone algorithm [19] with cone radius 0.7, and cross sections were re-evaluated. The uncertainty was found to be ±1.6% in the highest x bins and ±2.5% in the lower x bins. In addition, the analysis was redone under the following conditions: including multijet events for the events with x < x edge ; varying the jet E T and θ jet cuts for the jet selection; and varying the y JB cut. These checks produced small differences consistent with expected statistical variations and were not included in the systematic uncertainty; • {δ 6 } higher order radiative corrections and a possible dependence on x. The uncertainty was estimated to be about 2% at low x, increasing to 12% at x > 0.8; • {δ 7 } uncertainties on the luminosity. The uncertainties for the 96-97 e + p sample, 98-99 e − p sample and 99-00 e + p sample are 1.6%, 1.8% and 2.25%, respectively.

Results
The measured Born level cross sections for 96-97 e + p, 98-99 e − p and 99-00 e + p and their systematic uncertainties are shown in Tables 1-6. The statistical uncertainties on the cross sections correspond to the central 68% probability interval evaluated using a Bayesian approach with flat prior and a Poisson likelihood. For bins with zero measured events, a 68% probability limit, calculated including the uncorrelated systematic uncertainty, is given. The cross sections are shown in Figs. 9, 10 and 11 and compared to SM expectations using the CTEQ6M PDFs [3]. The double differential cross sections are represented by solid points, and generally agree well with the expectations. The cross section in the highest-x bins is plotted as In these bins, the expected cross section is drawn as a horizontal line, while the measured cross section is displayed as the open symbol at the center of the bin. The error bars represent the quadratic sum of the correlated systematic uncertainty and the combined statistical and uncorrelated systematic uncertainty determined from the Bayesian probability analysis.
The ratios of the measured cross sections to the SM expectation using the CTEQ6M PDFs for 96-97 e + p , 98-99 e − p and 99-00 e + p are shown in Figs. 12, 13 and 14 respectively. The ratios of the expectations using the ZEUS-S PDF [31] to that using CTEQ6M and ZEUS-JETS PDF [32] to that using CTEQ6M are also shown. The uncertainty for the CTEQ6M fit is displayed in the figure as a shaded band. The measured double-differential cross sections generally agree well with all three sets of expectations. For the highest x bins, which extend to previously unmeasured kinematic ranges, the data have a tendency to lie above the expectations.
The data presented here, specifically the zero-jet data at high x, extend the kinematic coverage for DIS. These results are expected to have a significant impact on the valencequark distributions at high x, where little data are available to date. It should however be noted that there is overlap with the data presented in previous ZEUS publications, and these new results should therefore not be used simultaneously with the previously published ZEUS data [4,10,11] in fits to extract model parameters. In the kinematic region of overlap of this technique with the previous ZEUS technique, the extracted cross sections are in excellent agreement.

Summary
This paper has presented a reanalysis of previously published ZEUS data with a new technique designed for the reconstruction of large x events, which allows for the extraction of the cross section up to x = 1. In the previously measured kinematic region, the data and simulation based on the CTEQ6M PDF are in good agreement. The Standard Model predictions tend to underestimate the data at the highest values of x. x values at which the cross section is quoted, the third contains the measured cross section d 2 σ/dxdQ 2 corrected to the electroweak Born level or the upper limit in case of zero observed events, the fourth contains the number of events reconstructed in the bin, N, the fifth contains the statistical uncertainty, δ s , and the sixth contains the total systematic uncertainty, δ t . The right part of the table lists the total uncorrelated systematic uncertainty, δ u , followed by the bin-to-bin correlated systematic uncertainties δ 1 -δ 6 defined in the text. The upper (lower) numbers refer to the variation of the cross section, whereas the signs of the numbers reflect the direction of change in the cross sections. Note that the normalization uncertainty, δ 7 is not listed.       x edge d 2 σ/dxdQ 2 corrected to the electroweak Born level or the upper limit in case of zero observed events, the fourth contains the number of events reconstructed in the bin, N, the fifth contains the statistical uncertainty, δ s , and the sixth contains the total systematic uncertainty, δ t . The right part of the table lists the total uncorrelated systematic uncertainty, δ u , followed by the bin-tobin correlated systematic uncertainties δ 1 -δ 6 defined in the text. The upper (lower) numbers refer to the variation of the cross section, whereas the signs of the numbers reflect the direction of change in the cross sections. Note that the normalization uncertainty, δ 7 is not listed.  x values at which the cross section is quoted, the third contains the measured cross section d 2 σ/dxdQ 2 corrected to the electroweak Born level or the upper limit in case of zero observed events, the fourth contains the number of events reconstructed in the bin, N, the fifth contains the statistical uncertainty, δ s , and the sixth contains the total systematic uncertainty, δ t . The right part of the table lists the total uncorrelated systematic uncertainty, δ u , followed by the bin-to-bin correlated systematic uncertainties δ 1 -δ 6 defined in the text. The upper (lower) numbers refer to the variation of the cross section, whereas the signs of the numbers reflect the direction of change in the cross sections. Note that the normalization uncertainty, δ 7 is not listed.        x edge d 2 σ/dxdQ 2 corrected to the electroweak Born level or the upper limit in case of zero observed events, the fourth contains the number of events reconstructed in the bin, N, the fifth contains the statistical uncertainty, δ s , and the sixth contains the total systematic uncertainty, δ t . The right part of the table lists the total uncorrelated systematic uncertainty, δ u , followed by the bin-tobin correlated systematic uncertainties δ 1 -δ 6 defined in the text. The upper (lower) numbers refer to the variation of the cross section, whereas the signs of the numbers reflect the direction of change in the cross sections. Note that the normalization uncertainty, δ 7 is not listed.  x values at which the cross section is quoted, the third contains the measured cross section d 2 σ/dxdQ 2 corrected to the electroweak Born level or the upper limit in case of zero observed events, the fourth contains the number of events reconstructed in the bin, N, the fifth contains the statistical uncertainty, δ s , and the sixth contains the total systematic uncertainty, δ t . The right part of the table lists the total uncorrelated systematic uncertainty, δ u , followed by the bin-to-bin correlated systematic uncertainties δ 1 -δ 6 defined in the text. The upper (lower) numbers refer to the variation of the cross section, whereas the signs of the numbers reflect the direction of change in the cross sections. Note that the normalization uncertainty, δ 7 is not listed.
6966 0.79 < 4.07 · 10 −6 0 x edge d 2 σ/dxdQ 2 corrected to the electroweak Born level or the upper limit in case of zero observed events, the fourth contains the number of events reconstructed in the bin, N, the fifth contains the statistical uncertainty, δ s , and the sixth contains the total systematic uncertainty, δ t . The right part of the table lists the total uncorrelated systematic uncertainty, δ u , followed by the bin-tobin correlated systematic uncertainties δ 1 -δ 6 defined in the text. The upper (lower) numbers refer to the variation of the cross section, whereas the signs of the numbers reflect the direction of change in the cross sections. Note that the normalization uncertainty, δ 7 is not listed.    Figure 6: Definition of the bins as used in this analysis for: (a) 98-00 data with E p = 920 GeV and (b) 96-97 data with E p = 820 GeV . The shaded bins extending to x = 1 are for the zero-jet events. The y = 1 lines shows the kinematic limit. The θ jet = 0.12 rad shows the selection cut for jets.   Figure 9:

96-97
The double-differential cross section for 96-97 e + p NC scattering at √ s = 300 GeV (solid circles) and the integral of the double differential cross section (open circles) compared to the Standard Model expectations evaluated using CTEQ6M PDFs (lines).The error bars show the statistical and systematic uncertainties added in quadrature. For bins with zero measured events, a 68% probability limit, calculated including the uncorrelated systematic uncertainty, is given.  Figure 10: The double-differential cross section for 98-99 e − p NC scattering at √ s = 318 GeV (solid circles) and the integral of the double differential cross section (open circles) compared to the Standard Model expectations evaluated using CTEQ6M PDFs (lines). The error bars show the statistical and systematic uncertainties added in quadrature. For bins with zero measured events, a 68% probability limit, calculated including the uncorrelated systematic uncertainty, is given.  Figure 11: The double-differential cross section for 99-00 e + p NC scattering at √ s = 318 GeV (solid circles) and the integral of the double differential cross section (open circles) compared to the Standard Model expectations evaluated using CTEQ6M PDFs (lines). The error bars show the statistical and systematic uncertainties added in quadrature. For bins with zero measured events, a 68% probability limit, calculated including the uncorrelated systematic uncertainty, is given.