Backgrounds and Systematic Errors

We have learned a great deal from the 4 GeV running about how to improve the measurement, particularly in determining backgrounds. One source of background is the pion contamination of the electron distribution. During E89-008 this contamination was always less than 1% in the HMS when using the calorimeter and Cerenkov information for particle identification. It is estimated that during 6 GeV running this pion contamination will get somewhat worse, but is still expected to be negligible. The front two layers of the HMS calorimeter have been outfitted with phototubes on both ends of each lead glass block since the 4 GeV running was completed. This will improve our ability to distinguish electrons from pions, as will the fact that the $\pi / e$ separation in the calorimeter will be better for the larger scattered electron energies of the 6 GeV kinematics.

There is also a background from secondary electrons produced in the target which was larger than expected for E89-008. The main source likely comes from electro-production and photo-production of neutral pions. These pions then decay into photons which can produce positron-electron pairs. This background is charge-symmetric, and can be measured directly by changing the spectrometer to positive polarity and detecting the produced positrons. For the largest angles measured in E89-008 (55$^{\circ}$ and 74$^{\circ}$), this background was significant and required a fit to our positron measurements and subtraction from our electron data (see Ref. [41] for more details). As a result, we will limit our running with 6 GeV beam to 60$^\circ$, and have included time in our beamtime request to measure this background.

The combined systematic uncertainties from the E89-008 run totaled 3.2 to 4.7% for the HMS data with the primary contributors being knowledge of the acceptance, radiative corrections, target thickness, and bin centering (correcting an integral number of counts within a momentum/angle bin to the measured cross section at the center of the bin). Each of these four items ranged from approximately 1% to 2% depending on the scattering angle. Table 1 below from Ref. [41] summarizes the systematic uncertainties during the 4 GeV running. We expect similar results for the 6 GeV running.

There is an additional uncertainty in the extraction of $F_2$ from the cross section due to the uncertainty in $R = \sigma_L / \sigma_T$. This was generally negligible, except at the largest $x$ and $Q^2$ values measured. We will take a small amount of data with $\sim$ 4 GeV beam, both as a cross calibration with the previous measurement and also to provide a rough determination of $R$. In the E89-008 analysis, a value of $R = 0.32/Q^2$ was assumed, with a 100% uncertainty in this value. At the highest $Q^2$ possible with 6 GeV measurements, it is not clear if this uncertainty is large enough. We expect to be able to measure $R$ at relatively high values of $Q^2$ (where $R$ is quite small) with uncertainties of $50-100$%, which will be sufficient to keep this from being a dominant source of uncertainty in the extracted structure functions.

Table I: Systematic uncertainties in the extraction of the cross section for 4 GeV running. Entries with an asterisk indicate that a correction was made directly to the cross section which had the listed uncertainty. Entries without an asterisk indicate no correction to the cross section, just a contribution to the overall uncertainty.

Systematic	HMS
Acceptance Correction	1.0-2.2%$^*$
Radiative Correction	2.5%$^*$
Target Track Cuts	0.5%
Bin Centering Correction	1.0-2.2%$^*$
PID Efficiency	0.5%$^*$
Charge Measurement	1.0%
Target Thickness	0.5-2.0%
Target/Beam Position Offset	0.25%
Tracking Efficiency	0.5%$^*$
Trigger Efficiency	0.05%$^*$
Normalization	0.0%
COMBINED UNCERTAINTY	3.2-4.7%