Forward two-photon exchange in elastic lepton-proton scattering and hyperfine-splitting correction

Abstract

We relate the forward two-photon exchange (TPE) amplitudes to integrals of the inclusive lepton-proton scattering cross sections. These relations yield an alternative way for the evaluation of the TPE correction to hyperfine-splitting (HFS) in the hydrogen-like atoms with an equivalent to the standard approach (Iddings, Drell and Sullivan) result implying the Burkhardt-Cottingham sum rule. For evaluation of the individual effects (e.g., elastic contribution) our approach yields a distinct result. We compare both methods numerically on examples of the elastic contribution and the full TPE correction to HFS in electronic and muonic hydrogen.

27 pages, 7 figures, correct description of corrections

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• Two-photon exchange correction to the hyperfine splitting in muonic hydrogen
• Dispersion relation formalism for the two-photon exchange correction to elastic muon-proton scattering: elastic intermediate state
• Accessing the nucleon transverse structure in inclusive deep inelastic scattering
• Hyperfine splitting in ordinary and muonic hydrogen
• Precision calculation of the recoil--finite-size correction for the hyperfine splitting in muonic and electronic hydrogen
• Two-photon exchange on neutron and the hyperfine splitting
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• Boer-Mulders function of the pion and pretzelosity distribution of the proton in the polarized pion-proton Drell-Yan process at COMPASS