Two-photon Exchange Corrections Research Articles

Two-photon exchange in theℓ+p→ℓ+pprocess with a massive lepton

Stimulated by the proton size puzzle and the proposal of $\ensuremath{\mu}p$ scattering at the Paul Scherrer Institute (PSI), we study the two-photon exchange corrections to the massive-lepton--proton scattering. The leptonic helicity broken caused by lepton mass introduces new form factors. We estimate the two-photon exchange corrections to these form factors as well as to the unpolarized differential cross sections.

Two-photon exchange corrections to elastic electron-proton scattering at large momentum transfer within the SCET approach

We calculate the two-photon exchange (TPE) corrections in the region where the kinematical variables describing the elastic $ep$ scattering are moderately large momentum scales relative to the soft hadronic scale. For such kinematics we use the QCD factorization approach formulated in the framework of the soft-collinear effective theory (SCET). Such technique allows us to develop a description for the soft-spectator scattering contribution which is found to be important in the region of moderately large scales. Together with the hard-spectator contribution we present the complete factorization formulas for the TPE amplitudes at the leading power and leading logarithmic accuracy. The momentum region where both photons are hard is described by only one new nonperturbative SCET form factor. It turns out that the same form factor also arises for wide-angle Compton scattering which is also described in the framework of the SCET approach. This allows us to estimate the soft-spectator contribution associated with the hard photons in a model independent way. The main unknown in our description of the TPE contribution is related with the configuration where one photon is soft. The nonperturbative dynamics in this case is described by two unknown SCET amplitudes. We use a simple model in order to estimate their contribution. The formalism is then applied to a phenomenological analysis of existing data for the reduced cross section as well as for the transverse and longitudinal polarization observables.

GFactor of Lithiumlike SiliconSi11+28

The g factor of lithiumlike 28Si11+ has been measured in a triple-Penning trap with a relative uncertainty of 1.1x10^{-9} to be g_exp=2.0008898899(21). The theoretical prediction for this value was calculated to be g_th=2.000889909(51) improving the accuracy to 2.5x10^{-8} due to the first rigorous evaluation of the two-photon exchange correction. The measured value is in excellent agreement with the state-of-the-art theoretical prediction and yields the most stringent test of bound-state QED for the g factor of the 1s^22s state and the relativistic many-electron calculations in a magnetic field.

Flavor decomposition of the nucleon electromagnetic form factors

Background: The spatial distribution of charge and magnetization in the proton and neutron are encoded in the nucleon electromagnetic form factors. The form factors are all approximated by a simple dipole function, normalized to the charge or magnetic moment of the nucleon. The differences between the proton and neutron form factors and the deviation of GEn from zero are sensitive to the difference between up- and down-quark contributions to the form factors. Methods: We combine recent measurements of the neutron form factors with updated extractions of the proton form factors, accounting for two-photon exchange corrections and including an estimate of the uncertainties for all of the form factors to obtain a complete set of measurements up to Q^2 approximately 4 (GeV/c)^2. We use this to extract the up- and down-quark contributions which we compare to recent fits and calculations. Results: We find a large differences between the up- and down-quark contributions to G_E and G_M, implying significant flavor dependence in the charge and magnetization distributions. The rapid falloff of the ratio GEp/GMp does not appear in the individual quark form factors, but arises from a cancellation between the up- and down-quark contributions. We see indications that the down-quark contributions to the Dirac and Pauli form factors deviate from the suggested 1/Q^4 scaling behavior suggested by a previous analysis. Finally, while recent models provide a generally good qualitative description of the data, the down-quark contribution to G_E/G_M and F_2/F_1 are not reproduced by any of the models. Finally, we note that while the inclusion of recent $\gmn$ data from CLAS modifies the high-$Q^2$ slightly, the tension between these data and previous measurements at lower $Q^2$ has a more significant impact, suggesting the need for additional data in this region.

Δ-resonance contribution to the two-photon exchange amplitude

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.

Two-Boson Exchange Physics: A Brief Review

Current status of the two-boson exchange contributions to elastic electron-proton scattering, both for parity conserving and parity-violating, is briefly reviewed. How the discrepancy in the extraction of elastic nucleon form factors between unpolarized Rosenbluth and polarization transfer experiments can be understood, in large part, by the two-photon exchange corrections is discussed. We also illustrate how the measurement of the ratio between positron-proton and electron-proton scattering can be used to differentiate different models of two-photon exchange. For the parity-violating electron-proton scattering, the interest is on how the two-boson exchange (TBE), \gamma Z-exchange in particular, could affect the extraction of the long-sought strangeness form factors. Various calculations all indicate that the magnitudes of effect of TBE on the extraction of strangeness form factors is small, though can be large percentage-wise in certain kinematics.

Test of Many-Electron QED Effects in the Hyperfine Splitting of Heavy High-ZIons

A rigorous evaluation of the two-photon exchange corrections to the hyperfine structure in lithiumlike heavy ions is presented. As a result, the theoretical accuracy of the specific difference between the hyperfine splitting values of H- and Li-like Bi ions is significantly improved. This opens a possibility for the stringent test of the many-electron QED effects on a few percent level in the strongest electromagnetic field presently available in experiments.

Reexamination of phenomenological two-photon exchange corrections to the proton form factors ande±pscattering

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.

Two-photon exchange effect studied with neural networks

An approach to the extraction of the two-photon exchange (TPE) correction from elastic $ep$ scattering data is presented. The cross section, polarization transfer (PT), and charge asymmetry data are considered. It is assumed that the TPE correction to the PT data is negligible. The form factors and TPE correcting term are given by one multidimensional function approximated by the feed forward neural network (NN). To find a model-independent approximation the Bayesian framework for the NNs is adapted. A large number of different parametrizations is considered. The most optimal model is indicated by the Bayesian algorithm. The obtained fit of the TPE correction behaves linearly in epsilon but it has a nontrivial Q2 dependence. A strong dependence of the TPE fit on the choice of parametrization is observed.

Two-Photon Exchange Corrections to Single Spin Asymmetry of Neutron and 3He

In a simple hadronic model, the two-photon exchange contributions to the single spin asymmetries for the nucleon and the 3He are estimated. The results show that the elastic contributions of two-photon exchange to the single spin asymmetries for the nucleon are rather small while those for the 3He are relatively large. Besides the strong angular dependence, the two-photon contributions to the single spin asymmetry for the 3He are very sensitive to the momentum transfer.

Two-photon exchange corrections to the polarizationPyof the deuteron

The corrections of two-photon exchange to the polarization ${P}_{y}$ of the deuteron are studied based on an effective Lagrangian approach. In addition, the two-photon exchange effect on the imaginary part of the deuteron electromagnetic form factors is also discussed.

Two-photon-exchange contribution to proton form factors in both space-like and time-like regions

The two two-photon exchange corrections to the unpolarized cross section and polarized observable PT, PL in elastic ep scattering are discussed in a simple hadronic model. Comparing with previous results, the Δ contribution are re-analysed. And the similar corrections in e+e− → pp̄ are also discussed.

Two-photon exchange corrections to the pion form factor

We compute two-photon exchange corrections to the electromagnetic form factor of the pion, taking into account the finite size of the pion. Compared to the soft-photon approximation for the infrared-divergent contribution, which neglects hadron structure effects, the corrections are found to be $\ensuremath{\lesssim}1%$ for low ${Q}^{2}$ values (${Q}^{2}<0.1$ GeV${}^{2}$) but increase to several percent for ${Q}^{2}\ensuremath{\gtrsim}1$ GeV${}^{2}$ at extreme backward angles.

Nucleon form factors in a light-cone quark model with two-photon exchange

We estimate the two-photon exchange corrections to both proton and neutron electromagnetic physical observables in a relativistic light cone quark model. At a fixed Q 2 the corrections are found to be small in magnitudes, but strongly dependent on scattering angle. Our results are comparable to those obtained from simple hadronic model in the medium momentum transfer region.

Estimate of the two-photon exchange effect on deuteron electromagnetic form factors

The corrections of two-photon exchange on deuteron electromagnetic form factors are estimated based on an effective Lagrangian approach. Numerical results for the form factors $G_{C,M,Q}$ of the deuteron with the corrections are compared to its empirical ones. Moreover, the two new form factors, due to the two-photon exchange, are analyzed. Possible way to test the two-photon exchange corrections to the deuteron form factors is discussed.

Electromagnetic form factors of the nucleon: New fit and analysis of uncertainties

Electromagnetic form factors of proton and neutron, obtained from a new fit of data, are presented. The proton form factors are obtained from a simultaneous fit to the ratio ${\ensuremath{\mu}}_{p}{G}_{\mathit{Ep}}/{G}_{\mathit{Mp}}$ determined from polarization transfer measurements and to $\mathit{ep}$ elastic cross section data. Phenomenological two-photon exchange corrections are taken into account. The present fit for protons was performed in the kinematical region ${Q}^{2}\ensuremath{\in}(0,6)$ ${\mathrm{GeV}}^{2}$. For both protons and neutrons we use the latest available data. For all form factors, the uncertainties and correlations of form factor parameters are investigated with the ${\ensuremath{\chi}}^{2}$ method.

Two-Photon-Exchange Correction to Elastic ep Scattering in the Forward Angle Limit

The two-photon-exchange (TPE) correction to elastic ep scattering in the forward angle region is discussed based on a simple hadronic model. It is found that the correction is exactly zero in the forward angle limit. This analytical result gives a good explanation of the previous numerical results and shows the clear power behavior of the TPE correction to elastic ep scattering in the forward angle region.

Perturbative QCD predictions for two-photon exchange

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.

Two-photon exchange contribution to proton form factors in the time-like region

We estimate the two-photon exchange contribution to the process ${e}^{+}+{e}^{\ensuremath{-}}\ensuremath{\rightarrow}p+\overline{p} $. The two-photon exchange corrections to double spin polarization observables and form factors in the time-like region are calculated. The corrections are found to be small in magnitude but with a strong angular dependence at fixed momentum transfer. These two features are the same as those in the space-like region. In future experiments, the double spin polarization observable ${P}_{z}$ deserves to be considered.

Rosenbluth nonlinearity from two-photon exchange

We calculate, using a generalized parton distribution based formalism, the nonlinearity of the Rosenbluth plots that arise from hard two-photon exchange corrections that are not included in the classic calculations of the radiative corrections to electron-proton elastic scattering.