Perturbative QCD predictions for two-photon exchange

Abstract

We study two-photon exchange (TPE) in the elastic electron-nucleon scattering at high ${Q}^{2}$ in the framework of perturbative quantum chromodynamics. The obtained TPE amplitude is of order $\ensuremath{\alpha}/{\ensuremath{\alpha}}_{s}$ with respect to Born approximation. Its shape and value are sensitive to the choice of nucleon wave function, thus study of TPE effects can provide important information about nucleon structure. With the wave functions based on quantum chromodynamics sum rules, TPE correction to the electron-proton cross section has a negative sign, is almost linear in $\ensuremath{\epsilon}$, and grows logarithmically with ${Q}^{2}$ up to 7% at ${Q}^{2}=30\text{ }\text{ }{\mathrm{GeV}}^{2}$. The results of existing hadronic calculations, taking into account just the nucleon intermediate state, can be smoothly connected with the perturbative quantum chromodynamics result near ${Q}^{2}\ensuremath{\sim}3\text{ }\text{ }{\mathrm{GeV}}^{2}$. Above this point two methods disagree, which implies that the hadronic approach becomes inadequate at high ${Q}^{2}$. Other relevant observables, such as the electron/positron cross section ratio, are also discussed.