Subtracted dispersion relation formalism for the two-photon exchange correction to elastic electron-proton scattering: Comparison with data

Abstract

We apply a subtracted dispersion relation formalism with the aim to improve predictions for the two-photon exchange corrections to elastic electron-proton scattering observables at finite momentum transfers. We study the formalism on the elastic contribution, and make a detailed comparison with existing data for unpolarized cross sections as well as polarization transfer observables.

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

“…However, this approach fails in the unphysical region. To get around this, Tomalak and Vanderhaeghen used a contour integration method [21], and applied it to the calculation of TPE amplitudes with monopole form factors. By summing the residue at the poles enclosed by the contour they were able to obtain algebraic expressions for the TPE amplitudes.…”

“…The results for the F 1 and F 2 form factors are the same for both calculations, as was observed previously in Refs. [19,21]. Numerically, Mo-Tsai infrared result [7].…”

“…The real and imaginary parts can be related through dispersion relations [18,19], which forms the basis of the dispersive method discussed in this section. Our discussion in this section follows the formalism of Tomalak and Vanderhaeghen [21,39]. An alternative treatment by Borisyuk and Kobushkin [19] starts from the annihilation channel, e − + e + → p +p.…”

“…A number of approaches have been adopted to computing the TPE corrections to elastic scattering, including direct calculation of the loop contributions in terms of hadronic degrees of freedom [4,[8][9][10][11][12][13][14][15], modeling the high energy behavior of box diagrams at the quark level through generalized parton distributions [16,17], or more recently dispersion relations [18][19][20][21]. Each of these methods has its own advantages as well as limitations (for reviews, see Refs.…”

“…The dispersive method involves the exclusive use of on-shell transition form factors, thereby avoiding the problem of unphysical violation of unitarity in the high energy limit. The dispersive approach to TPE was developed at forward angles by Gorchtein [18], and at non-forward angles by Borisyuk and Kobushkin [19,20,29,30], and more recently by Tomalak and Vanderhaeghen [21]. A feature of the latter two analyses has been the use of monopole form factor parametrizations, which allowed the computations to be performed semi-analytically.…”