Dmitry Borisyuk

Two-photon exchange in a dispersion approach

We calculate the two-photon exchange amplitude for the elastic electron-proton scattering in the framework of dispersion relations. The imaginary part of the amplitude is determined by unitarity. Since in the unitarity relation intermediate states are on shell, off-shell form factors are not needed for the calculation. The real part is then evaluated using analytical properties of the amplitude. The expression for the elastic contribution to the amplitude, obtained in our approach, differs from the results of traditional calculations with on-shell form factors. Nevertheless, numerically the difference is minor for Q{sup 2} up to 6 GeV{sup 2}.

Box diagram in the elastic electron-proton scattering

We present an evaluation of the box diagram for elastic ep scattering with the proton in the intermediate state. Using analytic properties of the proton form factors we express the amplitude via a twofold integral that involves the form factors in the spacelike region only. Therefore experimentally measured form factors can be used in the calculations directly. The numerical calculation is done with the form factors extracted by Rosenbluth separation, as well as polarization transfer method. The dependence of the results on the form factor choice is small for Q{sup 2}(less-or-similar sign)6 GeV{sup 2} but becomes sizable at higher Q{sup 2}.

Perturbative QCD predictions for two-photon exchange

We study two-photon exchange (TPE) in the elastic electron-nucleon scattering at high Q{sup 2} in the framework of perturbative quantum chromodynamics. The obtained TPE amplitude is of order {alpha}/{alpha}{sub 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 {epsilon}, and grows logarithmically with Q{sup 2} up to 7% at Q{sup 2}=30 GeV{sup 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{sup 2}{approx}3 GeV{sup 2}. Above this point two methods disagree, which implies that the hadronic approach becomes inadequate at high Q{sup 2}. Other relevant observables, such as the electron/positron cross section ratio, are also discussed.

Two-photon-exchange amplitude with

We consider two-photon exchange (TPE) in the elastic electron-proton scattering and evaluate the effect of \pi N (pion + nucleon) intermediate hadronic states. Among different \pi N states, we concentrate on the P33 channel; thus we effectively include Delta(1232) resonance with realistic width and shape and corresponding background as well. In agreement with the previous result, obtained for the zero-width resonance, we observe that the TPE correction to the electric form factor is the largest one; it grows with Q^2 and at Q^2 > 2.5 GeV^2 exceeds the corresponding elastic contribution.

\pi

We consider two-photon exchange (TPE) in the elastic electron-proton scattering and study the contribution arising from the production of Delta(1232) resonance in the intermediate state. We calculate all three TPE amplitudes (generalized form factors), and find that the Delta contribution mainly influences generalized electric form factor (contrary to the elastic contribution, which affects magnetic form factor), and the effect grows with Q^2. If the corresponding correction is applied to the recent polarization transfer measurements of proton form factors, their results will change markedly. Thus we suggest that TPE corrections due to inelastic intermediate states are important to polarization experiments at high Q^2, and should not be neglected.

N intermediate states: P

We studied two-photon exchange for elastic electron-proton scattering at low Q{sup 2}. Compact approximate formulas for the amplitudes were obtained. Numerical calculations were done for Q{sup 2}{<=}0.1 GeV{sup 2} with several realistic form factor parametrizations, yielding similar results. They indicate that the corrections to the magnetic form factor can visibly affect the cross-section and proton radii. For low-Q{sup 2} electron-neutron scattering two-photon exchange corrections were shown to be negligibly small00.

_{33}

We extract two-photon exchange amplitudes for the elastic electron-proton scattering at Q{sup 2}=2.5 GeV{sup 2} from the unpolarized cross section and recent polarization transfer measurements. There are three independent amplitudes, but only one of them, {delta}G{sub M}, can be determined with a reasonable accuracy (about 10%). The result is in good agreement with theoretical predictions. Rough estimates for two other amplitudes are obtained.

channel

We perform a model-independent phenomenological analysis of experimental data on proton form factor ratio. We find that only one of the two-photon exchange amplitudes, which we call {delta}G{sub M}, is responsible for the discrepancy between Rosenbluth and polarization methods. The linearity of Rosenbluth plots implies that {delta}G{sub M} is approximately linear function of {epsilon}. The slope of {delta}G{sub M} is extracted from experimental data and is shown to be consistent with theoretical calculations.

On

We calculate two-photon exchange (TPE) amplitudes for the elastic electron-proton scattering, and take into account intermediate hadronic states containing \pi N system with total angular momentum 1/2 or 3/2, which includes 8 different channels. This is the improvement of our previous calculation, where only the \pi N states with quantum numbers of \Delta(1232) resonance were included. The results show good consistency with recent experimental data. At high Q^2, newly-calculated contributions affect the correction to the measured proton form factor ratio \mu G_E/G_M. The total correction becomes somewhat smaller compared to our previous work, but is still significant and grows approximately linearly with Q^2. Comparing contributions of different channels, we found that larger contributions come from the channels with quantum numbers of lightest resonances.

\Delta

The beam normal spin asymmetry for elastic eN scattering is studied in the leading logarithm approximation, that is, keeping only terms proportional to