Two-photon Exchange Corrections Research Articles

Electron correlation effects on the g factor of lithiumlike ions

We present the systematic QED treatment of the electron correlation effects on the $g$ factor of lithiumlike ions for the wide range of nuclear charge number $Z=14$--82. The one- and two-photon exchange corrections are evaluated rigorously within the QED formalism. The electron-correlation contributions of the third and higher orders are accounted for within the Breit approximation employing the recursive perturbation theory. The calculations are performed in the framework of the extended Furry picture, i.e., with inclusion of the effective local screening potential in the zeroth-order approximation. In comparison to the previous theoretical calculations, the accuracy of the interelectronic-interaction contributions to the bound electron $g$ factor in lithiumlike ions is substantially improved.

Two-photon-exchange effect in ep→enπ+ at small −t with the hadronic model and dispersion relation approach

In this paper, the two-photon-exchange (TPE) effect in $ep\ensuremath{\rightarrow}en{\ensuremath{\pi}}^{+}$ at small $\ensuremath{-}t$ is discussed. In the previous work, the TPE contribution with one $\ensuremath{\pi}$ intermediate state is estimated numerically within a hadronic model under the pion-dominance approximation. Here we extend the discussion to include one $\ensuremath{\rho}$ intermediate state. The TPE contribution can be described by one scalar function in the limit ${m}_{e}\ensuremath{\rightarrow}0$, the dispersion relation (DR) satisfied by this scalar function is analyzed. The analytic expressions for the imaginary parts of the TPE contributions from one $\ensuremath{\pi}$ or one $\ensuremath{\rho}$ intermediate state are given within the hadronic model. Combining these analytic expressions and the DR, the corresponding real parts of the TPE contributions can be estimated easily at any available region. This can help the further experimental analysis to include the TPE contributions in a convenient way. The numeric results show that the TPE correction with one $\ensuremath{\rho}$ intermediate state is much smaller than that with one $\ensuremath{\pi}$ intermediate state in the current energy region. These results suggest that the TPE contribution with an elastic state is the main TPE contribution in $ep\ensuremath{\rightarrow}en{\ensuremath{\pi}}^{+}$ at small $\ensuremath{-}t$.

Radiative corrections to elastic muon-proton scattering at low momentum transfers

We systematically calculate the radiative corrections of order $\alpha/\pi$ to elastic muon-proton scattering at low momentum transfers. These include vacuum polarization, photon-loop form factors of the muon and the proton, two-photon exchange corrections and soft photon radiation. In particular, we discuss these corrections for the kinematics of the upcomimg AMBER experiment with a $100\,$GeV muon beam energy. It is found that for the ratio to the Born cross section, only the minor terms from the photon-loop form factors of the proton and two-photon exchange depend on the proton structure predetermined by the strong interactions. Since a prominent role among the radiative corrections is played by soft photon radiation, the calculation of the bremsstrahlung process $\mu p \to\mu p \gamma$ should be extended beyond the soft photon approximation and tailored to the specific experimental conditions.

Determination of the generalized parton distributions through the analysis of the world electron scattering data considering two-photon exchange corrections

We determine the valence generalized parton distributions (GPDs) $ H_v^q $ and $ E_v^q $ with their uncertainties at zero skewness by performing a $ \chi^2 $ analysis of the world electron scattering data considering two-photon exchange corrections. The data include a wide and updated range of the electric and magnetic form factors (FFs) of the proton and neutron. As a result, we find that there are no enough constraints on GPDs $ E_v^q $ from FFs data solely though $ H_v^q $ are well constrained. By including the new data of the charge and magnetic radius of the nucleon in the analysis, we show that they put new constraints on the final GPDs, especially on $ E_v^q $. Moreover, we calculate the gravitational FF $ M_2 $ and the total angular momentum $ J^q $ using the extracted GPDs and compare them with the FFs obtained from the light-cone QCD sum rules (LCSR) and Lattice QCD. We show that our results are interestingly in a good consistency with the pure theoretical predictions.

Differential cross section predictions for PRad-II from dispersion theory

We predict the differential cross sections for e−p and e+p elastic scattering in the PRad-II energy region. The prediction is based on form factors obtained in our previous high-precision analysis of space- and time-like data from dispersion theory and different sets of two-photon exchange corrections. We investigate the sensitivity of the cross sections to two-photon exchange effects and find that the differences between model calculations and phenomenological extractions of two-photon corrections can not be resolved if the uncertainty in the form factors is taken into account.

A measurement of two-photon exchange in Super-Rosenbluth separations with positron beams

The proton electric and magnetic form factors, $G_E$ and $G_M$, are intrinsically connected to the spatial distribution of charge and magnetization in the proton. For decades, Rosenbluth separation measurements of the angular dependence of elastic e$^-$-p scattering were used to extract $G_E$ and $G_M$. More recently, polarized electron scattering measurements, aiming to improve the precision of $G_E$ extractions, showed significant disagreement with Rosenbluth measurements at large momentum transfers ($Q^2$). This discrepancy is generally attributed to neglected two-photon exchange (TPE) corrections. At larger $Q^2$ values, a new `Super-Rosenbluth' technique was used to improve the precision of the Rosenbluth extraction, allowing for a better quantification of the discrepancy, while comparisons of e$^+$-p and e$^-$-p scattering indicated the presence of TPE corrections, but at $Q^2$ values below where a clear discrepancy is observed. In this work, we demonstrate the significant benefits to combining the Super-Rosenbluth technique with positron beam measurements. This approach provides a greater kinematic reach and is insensitive to some of the key systematic uncertainties in previous positron measurements.

MUSE: The MUon Scattering Experiment

MUSE is a high-precision muon scattering experiment aiming to determine the proton radius. Muon, electron, and pion scattering will be measured at the same time. Two-photon exchange corrections will be determined with data using both beam polarities.

Extraction of elastic scattering cross-section ratio Re+e− from ep elastic scattering experimental data

In this work, we present a new prediction of the positron-proton to electron-proton elastic scattering cross sections ratio ${R}_{{e}^{+}{e}^{\ensuremath{-}}}$. While many phenomenological studies extracted the ratio ${R}_{{e}^{+}{e}^{\ensuremath{-}}}$ using proposed, model-independent parametrizations of the hard two-photon exchange (TPE) corrections to electron-proton ($\text{ep}$) elastic scattering cross section ${\ensuremath{\sigma}}_{R}$, we do not assume prior knowledge of the functional form of the hard TPE corrections to ${\ensuremath{\sigma}}_{R}$, and use combined unpolarized, and polarized $\text{ep}$ elastic scattering experimental data to extract the TPE contributions. We provide a simple parametrization of the TPE corrections to ${\ensuremath{\sigma}}_{R}$, along with the uncertainties associated with the model dependence of the extractions, and use our TPE parametrization to predict the ratio ${R}_{{e}^{+}{e}^{\ensuremath{-}}}$. We compare our prediction of ${R}_{{e}^{+}{e}^{\ensuremath{-}}}$ to several previous phenomenological extractions, TPE-hadronic calculations, and world's data with emphasis mainly on the kinematics range of the recent precise direct measurements from the CLAS, VEPP-3, and OLYMPUS experiments.

New prediction of elastic scattering cross sections ratio Re+ e− based on phenomenological two-photon exchange corrections

The proton’s electric and magnetic form factors (FFs) and their ratio Rp = are fundamental and essential ingredients needed to parametrize the internal structure of the proton as well as many composite particles. However, the inconsistency in the results reported on these FFs and their ratio as measured by the Rosenbluth method and the polarization transfer method has led the community to believe that such a discrepancy is due to a systematic difference between the two methods. It was proposed that missing higher order radiative correction to the electron-proton elastic scattering cross section σR (ϵ, Q 2) and in particular two-photon exchange correction (TPE) should be applied in order to reconcile these measurements. The effect of TPE on electron-proton scattering observables was studied extensively in the last few years. However, the most direct method for measuring TPE contributions is the comparison of positron-proton and electron-proton elastic scattering cross sections ratio Re+ e− (ϵ, Q 2). In this proceedings, I present a new prediction of the ratio Re+ e− as determined using a new parametrization of TPE corrections to σR . I then compare my results to several previous phenomenological extractions, TPE hadronic calculations, and previous and recent direct measurements of Re+ e− .

Two-photon exchange from intermediate state resonances in elastic electron-proton scattering

We use a recently developed dispersive approach to compute the two-photon exchange (TPE) correction to elastic electron-proton scattering, including contributions from hadronic $J^P=1/2^\pm$ and $3/2^\pm$ resonant intermediate states below~1.8~GeV. For the transition amplitudes from the proton ground state to the resonant excited states we employ new exclusive meson electroproduction data from CLAS at $Q^2 \lesssim 5$~GeV$^2$, and we explore the effects of both fixed and dynamic widths for the resonances. Among the resonant states, the $N(1520)~\!3/2^-$ becomes dominant for $Q^2 \gtrsim 2$~GeV$^2$, with a sign opposite to the comparably sized $\Delta(1232)~\!3/2^+$ contribution, leading to an overall increase in the size of the TPE correction to the cross section relative to the nucleon only contribution at higher $Q^2$ values. The results are in good overall agreement with recent $e^+ p$ to $e^- p$ cross section ratio and polarization transfer measurements, and provide compelling evidence for a resolution of the electric to magnetic form factor ratio discrepancy.

Two-photon-exchange effects in e+e−→π+π− at small s

In this work, the two-photon-exchange (TPE) effects in $e^+e^- \rightarrow \pi^+ \pi^-$ at small $\sqrt{s}$ are discussed within a hadronic model. In the limit $m_e\rightarrow 0$, the TPE contribution to the amplitude can be described by one scalar function $\overline{c}_{1}^{(2\gamma)}$. The ratio between this function and the corresponding contribution in one-photon exchange $c_{1}^{(1\gamma)}$ reflects all the information of the TPE corrections. The numerical results on this ratio are presented and an artificial function is used to fit the numerical results. The latter can be used conveniently in the further experimental data analysis. The numerical results show the asymmetry of the differential cross sections in $e^+e^- \rightarrow \pi^+ \pi^-$ is about $-4\%$ at $\sqrt{s}\sim 0.7$ GeV.

Two-photon-exchange effects in ep→enπ+ and their corrections to separated cross sections σL,T,LT,TT at small −t

In this work, the two-photon-exchange (TPE) effects in $ep\rightarrow en\pi^+$ at small $-t$ are discussed within a hadronic model. Under the pion dominance approximation the TPE contribution to the amplitude can be described by a scalar function in the limit $m_e\rightarrow 0$. The TPE contributions to the amplitude and the unpolarized differential cross section are both estimated when only the elastic intermediate state is considered. We find that the TPE corrections to the unpolarized differential cross section are about from $-4\%$ to $-20\%$ at $Q^2=1$--$ 1.6$ GeV$^2$. After considering the TPE corrections to the experimental data sets of unpolarized differential cross section, we analyze the TPE corrections to the separated cross sections $\sigma_{\textrm{L,T,LT,TT}}$. We find that the TPE corrections (at $Q^2=1$--$1.6$ GeV$^2$) to $\sigma_{\textrm{L}}$ are about from $-10\%$ to $-30\%$, to $\sigma_{\textrm{T}}$ are about $20\%$, and to $\sigma_{\textrm{LT,TT}}$ are much larger. By these analysis, we conclude that the TPE contributions in $ep\rightarrow en\pi^+$ at small $-t$ are important to extract the separated cross sections $\sigma_{\textrm{L,T,LT,TT}}$ and the electromagnetic magnetic form factor of $\pi^+$ in the experimental analysis.

How much two-photon exchange is needed to resolve the proton form factor discrepancy?

One possible explanation for the proton form factor discrepancy is a contribution to the elastic electron–proton cross section from hard two-photon exchange (TPE), a typically neglected radiative correction. Hard TPE cannot be calculated in a model-independent way, but it can be determined experimentally by looking for deviations from unity in the ratio of positron-proton to electron–proton cross sections. Three recent experiments have measured this cross section ratio to quantify hard TPE. To interpret the results of these experiments, it is germane to ask: ‘How large of a deviation from unity is necessary to fully resolve the form factor discrepancy?’ With a minimal set of assumptions and using global fits to unpolarized and polarized elastic scattering data, I estimate the necessary size of the TPE correction in the kinematics of the three recent experiments and compare to their measurements. I find wide variation when using different global fits, implying that the magnitude of the form factor discrepancy is not well-constrained. The recent hard TPE measurements can easily accommodate the hypothesis that TPE underlies the proton form factor discrepancy.

Many-electron effects in the hyperfine splitting of lithiumlike ions

The rigorous QED evaluation of the one- and two-photon exchange corrections to the ground-state hyperfine splitting in Li-like ions is presented for the wide range of nuclear charge number $Z= 7 - 82$. The calculations are carried out in the framework of the extended Furry picture, i.e., with inclusion of the effective local screening potential in the zeroth-order approximation. The interelectronic-interaction contributions of the third and higher orders are taken into account in the framework of the Breit approximation employing the recursive perturbation theory. In comparison to the previous theoretical calculations, the accuracy of the interelectronic-interaction contributions to the ground-state hyperfine splitting in Li-like ions is substantially improved.

Lepton-proton two-photon exchange in chiral perturbation theory

We use heavy baryon chiral perturbation theory to evaluate the two-photon exchange corrections to the low-energy elastic lepton-proton scattering at next-to-leading order accuracy, i.e., ${\mathcal O}(\alpha, M^{-1})$, including a non-zero lepton mass. We consider the elastic proton intermediate state in the two-photon exchange together in the soft photon approximation. The infrared singular contributions are projected out using dimensional regularization. The resulting infrared singularity-free two-photon exchange contribution is in good numerical agreement with existing predictions based on standard diagrammatic soft photon approximation evaluations.

Dispersion relation formalism for the two-photon exchange correction to elastic muon\u2013proton scattering: elastic intermediate state

We evaluate the two-photon exchange correction to the unpolarized cross section in the elastic muon–proton scattering within dispersion relations. One of the six independent invariant amplitudes requires a subtraction. We fix the subtraction function to the model estimate of the full two-photon exchange at one of three MUSE beam energies and make a prediction for the two other energies. Additionally, we present single and double polarization observables accounting for the lepton mass.

Two-Photon Exchange Correction in Elastic Lepton–Proton Scattering

We present the dispersion relation approach based on unitarity and analyticity to evaluate the two-photon exchange contribution to elastic electron-proton scattering. The leading elastic and first inelastic $\pi N$ intermediate state contributions are accounted for in the region of small momentum transfer $Q^2 < 1~\mathrm{GeV}^2$ based on the available data input. The novel methods of analytical continuation allow us to exploit the MAMI form factor data and the MAID parameterization for the pion electroproduction amplitudes as input in the calculation. The results are compared to the recent CLAS, VEPP-3 and OLYMPUS data as well as to the full two-photon exchange correction in the near-forward approximation, which is based on the Christy and Bosted unpolarized structure functions fit. Additionally, predictions are given for a forthcoming muon-proton scattering experiment.

The deuteron-radius puzzle is alive: A new analysis of nuclear structure uncertainties

To shed light on the deuteron radius puzzle we analyze the theoretical uncertainties of the nuclear structure corrections to the Lamb shift in muonic deuterium. We find that the discrepancy between the calculated two-photon exchange correction and the corresponding experimentally inferred value by Pohl et al. [1] remain. The present result is consistent with our previous estimate, although the discrepancy is reduced from 2.6 σ to about 2 σ. The error analysis includes statistic as well as systematic uncertainties stemming from the use of nucleon–nucleon interactions derived from chiral effective field theory at various orders. We therefore conclude that nuclear theory uncertainty is more likely not the source of the discrepancy.

Proton and neutron electromagnetic form factors and uncertainties

We determine the nucleon electromagnetic form factors and their uncertainties from world electron scattering data. The analysis incorporates two-photon exchange corrections, constraints on the low-Q2 and high-Q2 behavior, and additional uncertainties to account for tensions between different data sets and uncertainties in radiative corrections.

Two-photon exchange correction to the hyperfine splitting in muonic hydrogen

We reevaluate the Zemach, recoil and polarizability corrections to the hyperfine splitting in muonic hydrogen expressing them through the low-energy proton structure constants and obtain the precise values of the Zemach radius and two-photon exchange (TPE) contribution. The uncertainty of TPE correction to S energy levels in muonic hydrogen of 105 ppm exceeds the ppm accuracy level of the forthcoming 1S hyperfine splitting measurements at PSI, J-PARC and RIKEN-RAL.