Two-photon exchange in nonrelativistic approximation

TL;DR

This paper derives analytical formulas for two-photon exchange amplitudes in nonrelativistic elastic electron-hadron scattering, compares results with relativistic calculations, and highlights limitations of the approximation for certain observables.

Contribution

It provides the first analytical nonrelativistic formulas for two-photon exchange amplitudes and compares them with relativistic results for proton and helium-3 targets.

Findings

Real part of amplitude matches relativistic results at moderate Q^2

Imaginary part significantly differs from relativistic calculations

Nonrelativistic approximation unsuitable for observables depending on the imaginary part

Abstract

We calculate two-photon exchange amplitudes for the elastic electron-hadron scattering in the nonrelativistic approximation, and obtain analytical formulae for them. Numerical calculations are performed for proton and $^3$He targets. Comparing our numerical results with relativistic calculations, we find that the real part of the amplitude is described well at moderate $Q^2$, but the imaginary part strongly differs from the relativistic result. Thus the nonrelativistic approximation should not be used for calculation of observables which depend on the imaginary part of the amplitude, such as single-spin asymmetries.