Dispersive approach to two-photon exchange in elastic electron-proton scattering

Abstract

We examine the two-photon exchange corrections to elastic electron-proton scattering within a dispersive approach, including contributions from both nucleon and ∆ intermediate states. The dispersive analysis avoids off-shell uncertainties inherent in traditional approaches based on direct evaluation of loop diagrams, and guarantees the correct unitary behavior in the high energy limit.Using empirical information on the electromagnetic nucleon elastic and N ∆ transition form factors, we compute the two-photon exchange corrections both algebraically and numerically. Results are compared with recent measurements of e + p to e − p cross section ratios from the CLAS, VEPP-3 and OLYMPUS experiments, as well as with polarization transfer observables.

The continuing story of two-photon exchange: results from the OLYMPUS experiment

“…Scattered leptons and recoiling protons were detected in the CLAS spectrometer, a toroidal magnetic spectrometer with nearly 4π coverage. Figure 3: OLYMPUS measured R 2γ to be somewhat lower than theoretical calculations by Blunden et al [23], and Tomalak et al [22], and the phenomenological prediction by Bernauer et al [27].…”

“…The grey band below the data shows the 1σ correlated uncertainty, though the correlations are more complicated than a simple scale factor, and will be described in a future article. The predictions from Blunden et al use a dispersive approach to calculate the TPE diagrams with hadronic propagators; the N-only prediction assumes only a nucleon propagator only, while N + ∆ assumes the coherent sum of nucleon and ∆ propagators [23]. The calculation of Tomalak et al uses subtracted dispersion relations to evaluate the TPE diagrams [22].…”

“…If hard TPE were properly accounted for, it is possible that the polarization asymmetry and Rosenbluth separation measurements would actually be consistent with each other. Unfortunately, there is no model independent method for calculating hard TPE, though there are numerous model-dependent approaches, such as using hadronic intermediate states [18][19][20], dispersion relations [21][22][23], generalized parton distributions [24], and phenomenological fits [25][26][27]. Many predictions suggest that the inclusion of hard TPE would resolve the form factor discrepancy, while some disagree [28,29].…”

Hard Two-Photon Contribution to Elastic Lepton-Proton Scattering Determined by the OLYMPUS Experiment

“…The only significantly large deviation from unity is seen at = 0.46 where R 2γ goes slightly above 2%. Recent dispersion calculations of Blunden [17] seem to overestimate the size of two-photon exchange while capturing its general shape. At the same time, phenomenological predictions of Bernauer and dispersion calculations Tomalak consistently match the data.…”

Overview of recent theoretical work on two-photon exchange

“…The contributions with nucleon only (dashed blue curves) and the sum of nucleon and ∆ (solid red curves) intermediate states are compared with data from the VEPP-3 experiment (triangles) [25], with the statistical and systematic uncertainties indicated by the (black) inner and (gray) outer error bars, respectively. Calculations taken from [20]. approach is that for transitions to excited states, described by effective interactions involving derivative couplings, the off-shell dependence leads to divergences in the ε → 1 (or high energy) limit.…”