Abstract:
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%.

Abstract:
We derive from first principles, as the C-invariance of the electromagnetic interaction and the crossing symmetry, the general properties of two-photon exchange in electron-proton elastic scattering. We show that the presence of this mechanism destroys the linearity of the Rosenbluth separation.

Abstract:
We use the world's data on elastic electron--proton scattering and calculations of two-photon exchange effects to extract corrected values of the proton's electric and magnetic form factors over the full Q^2 range of the existing data. Our analysis combines the corrected Rosenbluth cross section and polarization transfer data, and is the first extraction of G_Ep and G_Mp including explicit two-photon exchange corrections and their associated uncertainties. In addition, we examine the angular dependence of the corrected cross sections, and discuss the possible nonlinearities of the cross section as a function of epsilon.

Abstract:
We calculate the effects on the elastic electron-proton scattering cross section of the two-photon exchange contribution with an intermediate $\Delta$ resonance. The $\Delta$ two-photon exchange contribution is found to be smaller in magnitude than the previously evaluated nucleon contribution, with an opposite sign at backward scattering angles. The sum of the nucleon and $\Delta$ two-photon exchange corrections has an angular dependence compatible with both the polarisation transfer and the Rosenbluth methods of measuring the nucleon electromagnetic form factors.

Abstract:
We address the discrepancy between the Rosenbluth and polarization transfer data for the electromagnetic form factors of the nucleon. Assuming that the effect of two-photon corrections on the polarization transfer data is negligible, we obtain a model-independent estimate of the two-photon correction Delta^(2\gamma). We analyze the polarization transfer data and the cross section data separately using dispersion relations. A central value as well as an error estimate for Delta^(2\gamma) is then obtained from a comparison of the two analyses. The resulting values for Delta^(2\gamma) are in good agreement with direct calculations available in the literature.

Abstract:
The two-photon exchange contribution to the single spin asymmetries with the spin orientation normal to the reaction plane is discussed for elastic electron-proton scattering in Regge regime. For this, the equivalent photon approximation is adopted. In this case, hadronic part of the two-photon exchange amplitude describes real Compton scattering (RCS). The imaginary part of helicity conserving RCS amplitudes are related to total photoabsorption cross section. The contribution of the photon helicity flipping amplitudes is estimated by the two pion exchange in the $t$-channel. We observe the double logarithmic enhancement in the electron mass but find it's contribution to the asymmetry negligibly small in the forward kinematics. These results are in strong disagreement with the existing calculation.

Abstract:
We consider exclusive $\pi^0$ production in ep-scattering. At high energies odderon and photon exchange contribute. The photon exchange contribution is evaluated exactly using data for the total virtual photon-proton absorption cross section. The odderon exchange contribution is calculated in nonperturbative QCD, using functional integral techniques and the model of the stochastic vacuum. For the proton we assume a quark-diquark structure as suggested by the small odderon amplitude in pp and $p \bar{p}$ forward scattering. We show that odderon exchange leads to a much larger inelastic than elastic $\pi^0$ production cross section. Observing our process at HERA would establish the soft odderon.

Abstract:
We extract the two-photon exchange (TPE) contributions to electron--proton elastic scattering using two parametrizations and compare the results to different phenomenological extractions and direct calculations of the TPE effects. We find that many of the extractions give similar results, and highlight the common assumptions and the impact of not including such assumptions. We provide a simple parametrization of the TPE contribution to the unpolarized cross section, along with an estimate of the fit uncertainties and the uncertainties associated with the assumptions made in the extraction. We look at the contributions as extracted from various e--p elastic scattering observables, and make predictions for ratio $R^{e^{+} e^{-}}$ of positron-proton to electron-proton elastic scattering cross sections.

Abstract:
We study two-photon exchange for elastic electron-proton scattering at low Q^2. Compact approximate formulae for the amplitudes are obtained. Numerical calculations are done for Q^2 < 0.1 GeV^2 with several realistic form factor parameterizations, yielding similar results. They indicate that the corrections to magnetic form factor can visibly affect cross-section and proton radii. For low-Q^2 electron-neutron scattering two-photon exchange corrections are shown to be negligibly small.

Abstract:
We study a parity-conserving single-spin beam asymmetry of elastic electron-proton scattering induced by an absorptive part of the two-photon exchange amplitude. It is demonstrated that excitation of inelastic hadronic intermediate states by the consecutive exchange of two photons leads to logarithmic and double-logarithmic enhancement due to contributions of hard collinear quasi-real photons. The asymmetry at small electron scattering angles is expressed in terms of the total photoproduction cross section on the proton, and is predicted to reach the magnitude of 20-30 parts per million. At these conditions and fixed 4-momentum transfers, the asymmetry is rising logarithmically with increasing electron beam energy, following the high-energy diffractive behavior of total photoproduction cross section on the proton.