Two-photon exchange corrections in elastic muon-proton scattering

We extend the general formalism of two-photon exchange to elastic lepton-nucleon scattering by accounting for all lepton mass terms. We then perform a numerical estimate of the muon-proton scattering at low momentum transfer in view of the future MUSE experiment. For this purpose, we estimate the two-photon exchange corrections to muon-proton scattering observables by considering the contribution of the proton intermediate state, which is expected to dominate at very low momentum transfers. We find that the two-photon exchange effect to the unpolarized muon-proton scattering cross section in the MUSE kinematical region is of the order of 0.5%.

Figure 1

Elastic muon-proton scattering.

Figure 2

Direct and crossed TPE diagrams.

Figure 3

F1F1 (upper left panel), F2F2 (upper right panel), and F1F2 (lower panels) structure of photon-proton-proton vertices. The vertex with (without) the cross denotes the contribution proportional to $F_2$ ($F_1$) form factor.

Figure 4

TPE correction to the unpolarized elastic ${\mu }^{-}p$ cross section for three different muon beam momenta. The total correction is shown by the black solid curves, the contribution from the F1F1 structure of photon-proton-proton vertices is shown by the red dashed curves, the contribution from the F1F2 structure by the green dashed-dotted curves, and the contribution from the F2F2 structure by the blue dotted curves.

Figure 5

TPE correction to the unpolarized cross section for three different muon beam momenta. The TPE correction to elastic ${\mu }^{-}p$ scattering is shown by the blue solid curves, the black dashed-dotted curves show the elastic $e^{-}p$ scattering correction, the elastic ${\mu }^{-}p$ scattering correction without account of muon helicity flip is shown by the red dashed curves.

Figure 6

$ϵ$ dependence of the TPE correction to the unpolarized cross section for the elastic electron-proton scattering for different momentum transfers.

Figure 7

$ϵ$ dependence of the TPE correction to the unpolarized elastic ${\mu }^{-}p$ cross section.