Measurements of electron-proton elastic cross sections for $0.4<Q^2<5.5{(\mathrm{GeV}∕c)}^2$

We report on precision measurements of the elastic cross section for electron-proton scattering performed in Hall C at Jefferson Lab. The measurements were made at 28 distinct kinematic settings covering a range in momentum transfer of $0.4<Q^2<5.5{(\mathrm{GeV}∕c)}^2$. These measurements represent a significant contribution to the world’s cross section data set in the $Q^2$ range, where a large discrepancy currently exists between the ratio of electric to magnetic proton form factors extracted from previous cross section measurements and that recently measured via polarization transfer in Hall A at Jefferson Lab. This data set shows good agreement with previous cross section measurements, indicating that if a heretofore unknown systematic error does exist in the cross section measurements, then it is intrinsic to all such measurements.

Figure 1

(Color online) Single-photon exchange diagram for ep elastic scattering.

Figure 2

Fractional contribution of $G_E$ to the cross section assuming $G_M∕{\mu }_p=G_E$ (form factor scaling).

Figure 3

Schematic of the Hall C beamline.

Figure 4

Representation of the cryogenic and dummy target assembly.

Figure 5

Relative hydrogen target yield versus beam current.

Figure 6

(Color online) Schematic drawing of the HMS spectrometer.

Figure 7

Schematic drawing of the HMS detector stack.

Figure 8

(Color online) Reconstructed $W$ vs HMS central angle for elastic scattering kinematics. Open symbols represent data before kinematic corrections were applied, while the solid symbols represent the data after applying the calibration corrections.

Figure 9

Distribution of the number of photoelectrons collected in the Čerenkov detector for elastic kinematics of $E=2.2\mathrm{GeV}$ and $p=1\mathrm{GeV}∕c$.

Figure 10

Distribution of the fractional energy deposition in the calorimeter for events both before (open area) and after (shaded area) applying a requirement of $>2$ photoelectrons in the Čerenkov detector.

Figure 11

HMS effective solid angle plotted in $\theta -\delta P∕P$ space, using the binning described in the text.

Figure 12

Sample $W^2$ count distribution measured for elastically scattered electrons in a single $\theta$ bin after subtraction of the Al quasielastic contribution determined from the dummy target.

Figure 13

(Color online) Ratio of the cross section calculated with a cutoff in the tail integration of $W^2=1.10{\mathrm{GeV}}^2$ (top), $W^2=1.05{\mathrm{GeV}}^2$ (middle), and $W^2=1.0{\mathrm{GeV}}^2$ (bottom), relative to a cutoff of $W^2=1.15{\mathrm{GeV}}^2$

Figure 14

Cross section extracted in each $\theta$ bin across the HMS acceptance.

Figure 15

Feynman diagrams for higher order QED processes, including (a) vacuum polarization, (b) vertex corrections, (c) two-photon exchange, and (d) internal bremsstrahlung emission from electrons. Not shown are diagrams for proton bremsstrahlung, or external bremsstrahlung.

Figure 16

(Color online) The ratio of measured $ep$ elastic cross sections to the Arrington fit of previous cross section data, as a function of scattering angle, longitudinal photon polarization, and scattering energy. The solid line indicates the average ratio of 1.006 and the dashed lines indicate $\pm 2\%$ of this value.

Figure 17

Rosenbluth separations of the form factors. Plotted is the reduced cross sections $(\times 1000)$ vs $\epsilon$.

Figure 18

(Color online) Extracted values of $\mu G_E∕G_M$. Also shown are those extracted from previous Rosenbluth and polarization transfer measurements. The error bars on the data include the full point-to-point uncertainties, while the hatched band at the top indicates the uncertainty due to the absolute uncertainty in the scattering angle of $0.4\mathrm{mrad}$.