Demonstration of a novel technique to measure two-photon exchange effects in elastic $e^{\pm }p$ scattering

Background: The discrepancy between proton electromagnetic form factors extracted using unpolarized and polarized scattering data is believed to be a consequence of two-photon exchange (TPE) effects. However, the calculations of TPE corrections have significant model dependence, and there is limited direct experimental evidence for such corrections.

Purpose: The TPE contributions depend on the sign of the lepton charge in $e^{\pm }p$ scattering, but the luminosities of secondary positron beams limited past measurement at large scattering angles, where the TPE effects are believe to be most significant. We present the results of a new experimental technique for making direct $e^{\pm }p$ comparisons, which has the potential to make precise measurements over a broad range in $Q^2$ and scattering angles.

Methods: We use the Jefferson Laboratory electron beam and the Hall B photon tagger to generate a clean but untagged photon beam. The photon beam impinges on a converter foil to generate a mixed beam of electrons, positrons, and photons. A chicane is used to separate and recombine the electron and positron beams while the photon beam is stopped by a photon blocker. This provides a combined electron and positron beam, with energies from 0.5 to 3.2 GeV, which impinges on a liquid hydrogen target. The large acceptance CLAS detector is used to identify and reconstruct elastic scattering events, determining both the initial lepton energy and the sign of the scattered lepton.

Results: The data were collected in two days with a primary electron beam energy of only 3.3 GeV, limiting the data from this run to smaller values of $Q^2$ and scattering angle. Nonetheless, this measurement yields a data sample for $e^{\pm }p$ with statistics comparable to those of the best previous measurements. We have shown that we can cleanly identify elastic scattering events and correct for the difference in acceptance for electron and positron scattering. Because we ran with only one polarity for the chicane, we are unable to study the difference between the incoming electron and positron beams. This systematic effect leads to the largest uncertainty in the final ratio of positron to electron scattering: $R=1.027\pm 0.005\pm 0.05$ for $\langle Q^2\rangle =0.206$ GeV${}^2$ and $0.830⩽\epsilon ⩽0.943$.

Conclusions: We have demonstrated that the tertiary $e^{\pm }$ beam generated using this technique provides the opportunity for dramatically improved comparisons of $e^{\pm }p$ scattering, covering a significant range in both $Q^2$ and scattering angle. Combining data with different chicane polarities will allow for detailed studies of the difference between the incoming $e^{+}$ and $e^{-}$ beams.

Figure 1

Feynman diagrams for the elastic lepton-proton scattering, including the first-order QED radiative corrections. Diagram (a) shows the electron vertex renormalization term, diagram (b) shows the photon propagator renormalization term, diagrams (c) and (d) show the electron bremsstrahlung terms, diagram (g) shows the proton vertex renormalization term, diagram (h) shows the proton bremsstrahlung term, and diagrams (e) and (f) show the two-photon exchange terms, where the intermediate state can be an unexcited proton, a baryon resonance, or a continuum of hadrons.

Figure 2

Three dimensional view of CLAS showing the beamline, drift chambers (R1, R2, and R3), the Cherenkov counter (CC), the time-of-flight system (TOF), and the electromagnetic calorimeter (EC). In this view, the beam enters the picture from the upper left corner.

Figure 3

Beamline sketch for the CLAS TPE experiment. Shielding elements around the chicane and tagger are not shown. The chicane bends the electron and positron trajectories in the horizontal plane, not the vertical plane. The electron and positron directions are selected by the chicane polarity. Drawing is not to scale.

Figure 4

Position of the individual lepton beams as a function of the current in the first and third dipoles. Data points are measured beam centroid positions at the fiber detector and the lines are fits to points 2–10.

Figure 5

Reconstructed beam energy (electrons and positrons combined) at the target for elastic events detected in CLAS. Each event is weighted by one over the elastic cross section to recover the initial beam energy distribution.

Figure 6

The experimental acceptance in momentum transfer and virtual photon polarization shown for negative torus polarity and both lepton charges. The red boxes show the binning for the data presented here.

Figure 7

Angle between lepton and proton ($\Delta \varphi$) distributions for event type and torus polarity as indicated. The solid histogram is the data with only the opposite sector cut. The dotted histogram is after all other cuts. The dashed lines show the $\Delta \varphi$ cut.

Figure 8

Reconstructed transverse momentum distributions for event type and torus polarity as indicated. The solid histogram is the data with only the opposite sector cut. The dotted histogram is after all other cuts. The dashed lines show the $p_t$ cut.

Figure 9

$\Delta E_{\mathrm{beam}}$ for event type and torus polarity as indicated. The solid histogram is the data with only the opposite sector cut. The dotted histogram is after all other cuts. The dashed lines show the $\Delta E_{\mathrm{beam}}$ cut.

Figure 10

Reconstructed polar angle of the beam for event type and torus polarity as indicated. The solid histogram is the data with only the opposite sector cut and the dotted histogram is after all other cuts. The dashed lines show the ${\theta }_{P_f}$ cut.

Figure 11

Top two panels show the $W$ distributions (in GeV) for positive torus polarity electron (left) and positron (right) events for $0.820⩽\epsilon ⩽0.840$ and $\langle Q^2\rangle =0.206$ GeV${}^2$ with all cuts applied. The bottom two panels show the same for negative torus polarity events.

Figure 12

Measured ratio $R$ for acceptance matched data at $\langle Q^2\rangle =0.206$ GeV${}^2$ before radiative corrections. Vertical error bars are statistical only and horizontal error bars show the range of the bin. The shaded band (red online) indicates the point-to-point systematic uncertainty ($1\sigma$) of the present data. The 5% luminosity-related systematic uncertainty is not shown.

Figure 13

Ratio $R_{2\gamma }$ overlaid on the world data. Black filled squares are from this experiment at $\langle Q^2\rangle =0.206$ GeV${}^2$ and have had radiative corrections applied, filled circles (blue online) are previous world data at similar $Q^2$, and hollow points (green online) are the rest of the previous world data with $Q^2<2$ GeV${}^2$ [29]. The densely shaded band (red online) indicates the point-to-point systematic uncertainty ($1\sigma$) and the black shaded band represents the scale-type systematic uncertainty (due to relative luminosity) on the present data. The dashed curve (red online) is the BMT calculation [51] at $Q^2=0.2$ GeV${}^2$.