Two-photon Exchange Effects Research Articles

Applications of neural networks in hadron physics

The Bayesian approach for the feed-forward neural networks is reviewed. Its potential for usage in hadron physics is discussed. As an example of the application, the study of the two-photon exchange effect is presented. We focus on the model comparison, the estimation of the systematic uncertainties due to the choice of the model and the over-fitting. As an illustration, the predictions of the cross sections ratio are given together with the estimate of the uncertainty due to the parametrization choice.

Meson exchange effects in elasticepscattering at loop level and the electromagnetic form factors of the proton

A new form of two-photon exchange (TPE) effect is studied to explain the discrepancy between unpolarized and polarized experimental data in elastic $ep$ scattering. The mechanism is based on a simple idea that apart from the usual TPE effects from box and crossed-box diagrams, the mesons may also be exchanged in elastic $ep$ scattering by two-photon coupling at loop level. The detailed study shows such contributions to reduced unpolarized cross section (${\ensuremath{\sigma}}_{\mathrm{un}}$) and polarized observables (${P}_{t},{P}_{l}$) at fixed ${Q}^{2}$ are only dependent on proton's electromagnetic form factors ${G}_{E,M}$ and a new unknown universal parameter $g$. After combining this contribution with the usual TPE contributions from box and crossed-box diagrams, the ratio ${\ensuremath{\mu}}_{p}{G}_{E}/{G}_{M}$ extracted from the recent precise unpolarized and polarized experimental data can be described consistently.

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%.

EM Form Factors and OLYMPUS

The elastic form factors of the nucleon characterize the distributions of charge and magnetization in momentum space and are important input for calculations of strong interaction phenomena and nuclear structure. The dramatic discrepancy in the observed ratio of elastic proton form factors between the Rosenbluth separation and polarization transfer methods has invoked numerous theoretical and experimental investigations. The previously neglected effect from two-photon exchange has become the favored explana- tion for the discrepancy. While the effect can not be calculated from first principles, it can be verified experimentally in several ways, most stringently by comparing the positron- proton and electron-proton elastic cross sections. The OLYMPUS experiment at DESY has been carried out to quantify the effect of two-photon exchange using intense stored positron and electron beams along with an internal unpolarized hydrogen target and a large acceptance detector to measure the ratio of the positron-proton and electron-proton elastic scattering cross sections. The status of proton form factor measurements and of the experimental efforts to verify the effect of two-photon exchange is presented, with some emphasis on the OLYMPUS experiment.

Muon Elastic Scattering with MUSE at PSI

The proton radius puzzle is the disagreement between the much more precise radius determined from muonic hydrogen spectroscopy and the numerous atomic hydrogen and electron scattering determinations. The puzzle has several possible resolutions, including physics beyond the Standard Model, missing conventional physics, and errors or underestimated uncertainties in the extraction of the radius from the data. New experiments are needed to confirm and / or resolve the puzzle. The MU on S cattering E xperiment (MUSE) recently approved at PSI has been designed to help resolve the puzzle by measuring the radius in a way not yet done. Similar to electron scattering, the radius will be extracted from the observed change of the charge form factor with momentum transfer. The experiment uses the π M1 beamline to provide a mixed secondary muon and electron (and pion) beam of either positive or negative charge. The comparison of muon and electron scattering measured simultaneously determines the consistency of the form factors in the two cases with high precision. Comparison of yields from both charge signs will at the same time disentangle the effect of two-photon exchange. The proton charge radius can be extracted from each set of scattering data. The physics case and status of MUSE will be discussed.

Comparison of neural network and hadronic model predictions of the two-photon exchange effect

Predictions for the two-photon exchange (TPE) correction to unpolarized $ep$ elastic cross section, obtained within two different approaches, are confronted and discussed in detail. In the first one the TPE correction is extracted from experimental data by applying the Bayesian neural network (BNN) statistical framework. In the other the TPE is given by box diagrams, with the nucleon and the $P_{33}$ resonance as the hadronic intermediate states. Two different form factor parametrizations for both the proton and the $P_{33}$ resonance are taken into consideration. Proton form factors are obtained from the global fit of the full model (with the TPE correction) to the unpolarized cross section data. Predictions of both methods agree well in the intermediate $Q^2$ range, $(1,3)$ GeV$^2$. Above $Q^2=3$ GeV$^2$ the agreement is on $2\sigma$ level. Below $Q^2=1$ GeV$^2$ the consistency between both approaches is broken. The values of the proton radius extracted within both models are given. In both cases predictions for VEPP-3 experiment have been obtained and confronted with the preliminary experimental results.

Demonstration of a novel technique to measure two-photon exchange effects in elastice±pscattering

The discrepancy between proton electromagnetic form factors extracted using unpolarized and polarized scattering data is believed to be a consequence of two-photon exchange (TPE) effects. However, the calculations of TPE corrections have significant model dependence, and there is limited direct experimental evidence for such corrections. We present the results of a new experimental technique for making direct $e^\pm p$ comparisons, which has the potential to make precise measurements over a broad range in $Q^2$ and scattering angles. We use the Jefferson Lab electron beam and the Hall B photon tagger to generate a clean but untagged photon beam. The photon beam impinges on a converter foil to generate a mixed beam of electrons, positrons, and photons. A chicane is used to separate and recombine the electron and positron beams while the photon beam is stopped by a photon blocker. This provides a combined electron and positron beam, with energies from 0.5 to 3.2 GeV, which impinges on a liquid hydrogen target. The large acceptance CLAS detector is used to identify and reconstruct elastic scattering events, determining both the initial lepton energy and the sign of the scattered lepton. The data were collected in two days with a primary electron beam energy of only 3.3 GeV, limiting the data from this run to smaller values of $Q^2$ and scattering angle. Nonetheless, this measurement yields a data sample for $e^\pm p$ with statistics comparable to those of the best previous measurements. We have shown that we can cleanly identify elastic scattering events and correct for the difference in acceptance for electron and positron scattering. The final ratio of positron to electron scattering: $R=1.027\pm0.005\pm0.05$ for $<Q^2>=0.206$ GeV$^2$ and $0.830\leq \epsilon\leq 0.943$.

Transfer of spin squeezing and particle entanglement between atoms and photons in coupled cavities via two-photon exchange

We examine transfer of particle entanglement and spin squeezing between atomic and photonic subsystems in optical cavities coupled by two-photon exchange. Each cavity contains a single atom, interacting with cavity photons with a two-photon cascade transition. Particle entanglement is characterized by evaluating optimal spin squeezing inequalities for the cases of initially separable and entangled two-photon states. It is found that particle entanglement is first generated among the photons in separate cavities and then transferred to the atoms. The underlying mechanism is recognized as an intercavity two-axis twisting spin squeezing interaction, induced by two-photon exchange, and its optimal combination with the intracavity atom&#x2013;photon coupling. Relative effect of nonlocal two-photon exchange and local atom&#x2013;photon interactions of cavity photons on the spin squeezing and entanglement transfer is pointed out.

Resonances contribution to two-photon exchange effects and possible large forward–backward asymmetry in

The resonances ( η c , χ c 0 , c 2 ) contribution to two-photon exchange (TPE) effects in e + e − ↔ p p ¯ is calculated in a simple hadronic model. The calculation shows the TPE contributions by resonance χ c 2 , which are dependent on the unknown phases ϕ E , M of protonʼs time-like form factors G E , M , are much larger than the TPE contributions by non-resonance and are comparable with measurement precision of coming PANDA detector at s ∼ M χ c 2 for most ϕ E , M .

Measurement of the two-photon exchange contribution in elastic ep scattering at VEPP–3

We report on the status of the Novosibirsk experiment on a precision measurement of the ratio R of the elastic e + p and e − p scattering cross sections. Such measurements determine the two-photon exchange effect in elastic electron-proton scattering. The experiment is conducted at the VEPP–3 storage ring using a hydrogen internal gas target. The ratio R is measured with a beam energy of 1.6 GeV (electron/positron scattering angles are θ = 55 ÷ 75 ° and θ = 15 ÷ 25 ° ) and 1 GeV ( θ = 65 ÷ 105 ° ). We briefly describe the experimental method, paying special attention to the radiative corrections. Some preliminary results are presented.

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.

Empirical parametrization of the two-photon-exchange effect contributions to the electron-proton elastic scattering cross section

The most recent electron-proton elastic scattering data were re-analyzed using an empirical parametrization of the two-photon-exchange (TPE) effect contributions to ${\ensuremath{\sigma}}_{R}$. The TPE effect contribution $F({Q}^{2},\ensuremath{\varepsilon})$ was double Taylor series expanded as a polynomial of order $n$ keeping only terms linear in $\ensuremath{\varepsilon}$ to account for the experimentally observed and verified linearity of the Rosenbluth plots. We fix the ratio $R={G}_{\mathit{Ep}}/{G}_{\mathit{Mp}}$ to be that obtained from a fit to the recoil-polarization data and parametrize ${\ensuremath{\sigma}}_{R}$ first by a three-parameter formula (fit I) and then by a two-parameter formula (fit III). In contrast to previous analyses, the fit parameter ${G}_{\mathit{Mp}}^{2}$ as obtained from these fits is either smaller or equal to the values obtained from our conventional Rosenbluth fit (fit II) but never larger. The ratio $g({Q}^{2})/{G}_{\mathit{Mp}}^{2}$ which represents the ratio of the TPE and one-photon-exchange (OPE) effect contributions to the intercept of ${\ensuremath{\sigma}}_{R}$ is large and it ranges 3%$\ensuremath{-}$88%. The ratio ${R}_{1\ensuremath{\gamma}\ensuremath{\bigotimes}2\ensuremath{\gamma}}=\ensuremath{\tau}f({Q}^{2})/{G}_{\mathit{Ep}}^{2}$ which represents the ratio of the TPE and OPE effect contributions to the slope of ${\ensuremath{\sigma}}_{R}$ is also large, reaching a value of 12.0$\ensuremath{-}$14.4 at ${Q}^{2}=$ 5.25 (GeV/c)${}^{2}$. The ratio ${R}_{1\ensuremath{\gamma}\ensuremath{\bigotimes}2\ensuremath{\gamma}}$ as obtained from fits I and III is consistent, within error, with those obtained from previous analyses. Our formulas seem to explain the linearity of ${\ensuremath{\sigma}}_{R}$. Moreover, our analysis shows that the extracted ${G}_{\mathit{Ep}}^{2}$ and ${G}_{\mathit{Mp}}^{2}$ using the conventional Rosenbluth separation method can in fact be broken into the usual OPE and TPE contributions. Therefore, ${\ensuremath{\sigma}}_{R}$ can in fact be derived under weaker conditions than those imposed by the Born approximation. Our results show that the TPE amplitudes, $g({Q}^{2})/{G}_{\mathit{Mp}}^{2}$ and $f({Q}^{2})/{G}_{\mathit{Mp}}^{2}$, are sizable and grow with ${Q}^{2}$ value up to ${Q}^{2}~$ 6 (GeV/c)${}^{2}$ in agreement with previous studies. A revision of and comparison to previous analyses are also presented.

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.

An estimate of two-photon exchange effect on deuteron electromagnetic form factors

The effect of the two-photon exchange on the deuteron electromagnetic form factors is estimated based on an effective Lagrangian approach. A numerical estimate calculation of the effect is discussed. In particular, the effect on the polarization observables is analyzed.

Effect of two-photon exchange on the charged pion form factor

The effect of the two-photon exchange on the charged pion electromagnetic form factor is discussed. The ϵ-dependence of the effect is shown. It is seen that the effect plays a sizeable role to the form factor in the large backward angle.

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.

Two-photon exchange effect on deuteron electromagnetic form factors

Corrections of two-photon exchange to proton and neutron electromagnetic form factors are employed to study the effect of two-photon exchange on the deuteron electromagnetic form factors. Numerical results of the effect are given. It is suggested to test the effect in the measurement of Pz in a small angle limit.

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.

Measurement of two-photon exchange effect with CLAS

Measurement of two-photon exchange effect with CLAS