Two-photon Exchange Effects Research Articles

Nuclear Structure Effects on Hyperfine Splittings in Ordinary and Muonic Deuterium.

Precision spectroscopy of hyperfine splitting (HFS) is a crucial tool for investigating the structure of nuclei and testing quantum electrodynamics. However, accurate theoretical predictions are hindered by two-photon exchange (TPE) effects. We propose a novel formalism that accounts for nuclear excitations and recoil in TPE, providing a model-independent description of TPE effects on HFS in light ordinary and muonic atoms. Combining our formalism with pionless effective field theory at next-to-next-to-leading order, the predicted TPE effects on HFS are 41.7(4.4)kHz and 0.117(13)meV for the 1S state in deuterium and the 2S state in muonic deuterium. These results align within 1σ and 1.3σ from recent measurements and highlight the importance of nuclear structure effects on HFS and indicate the value of more precise measurements in future experiments.

Target normal single-spin asymmetry in inclusive electron-nucleon scattering in the 1/Nc expansion

The target normal single-spin asymmetry in inclusive electron-nucleon scattering is studied in the low-energy regime that includes the $\mathrm{\ensuremath{\Delta}}$ resonance. The particular interest in the asymmetry resides in that it is driven by two-photon exchange effects. It probes the spin-dependent absorptive part of the two-photon exchange amplitude, which is free of infrared and collinear singularities and represents the most pristine expression of two-photon exchange dynamics. The study presented here uses the $1/{N}_{c}$ expansion of QCD, which combines the $N$ and $\mathrm{\ensuremath{\Delta}}$ through the emergent $SU(4)$ spin-flavor symmetry in the baryon sector and allows for a systematic construction of the transition electromagnetic (EM) currents. The analysis includes the first subleading corrections in the $1/{N}_{c}$ expansion and presents results for elastic and inelastic final states. The asymmetry is found to be in the range ${10}^{\ensuremath{-}3}\ensuremath{-}{10}^{\ensuremath{-}2}$. The $\mathrm{\ensuremath{\Delta}}$ resonance plays an important role as an intermediate state in the elastic asymmetry and as a final state in the inclusive asymmetry.

Lepton Universality Test with MUSE at PSI

Lepton universality (LU) typically refers to the lepton coupling, which is considered to be the same for e, μ, and τ leptons, if the interaction is electroweak according to the Standard Model, and it is hence a compelling probe for New Physics. The same principle of universal electroweak lepton interaction leads to the expectation that lepton scattering yields are equal for e and μ beams under the same kinematic condition. The mere mass difference between e and μ affects kinematic quantities (such as the relation between scattering angle and Q 2), and the lepton mass dependence of elastic cross sections for leptons scattered from structured and pointlike objects are taken into account. By comparing e +, e −, μ +, and μ − scattering yields, two-photon exchange (TPE) effects, universal or not, can be separated from the general LU test of the e/μ yield ratio. With its separable mixed beams of e +/μ + and e −/μ −, respectively, the MUSE experiment at PSI is not only designed to measure the proton charge radius with four lepton species, but is also uniquely suited to probe TPE and LU, while benefitting from partial cancellations of certain shared systematics. An overview will be given of the MUSE experiment, the sensitivity, and the present status.

Charge-asymmetric correlations in elastic lepton- and antilepton-proton scattering from real photon emission

Observation of charge asymmetry by comparing electron and positron, or muon and anti-muon, scattering on a hadronic target presently serves as an experimental tool to study two-photon exchange effects. In addition to two-photon exchange, real photon emission also contributes to the charge asymmetry. We present a theoretical formalism, explicit expressions, and a numerical analysis of hard photon emission for the charge asymmetry in lepton- and antilepton-proton scattering. Different kinematic conditions are considered, namely, either fixed transferred momentum squared or a fixed lepton scattering angle. The infrared divergence from real photon emission is treated by the Bardin-Shumeiko technique and canceled with the soft part of the two-photon exchange contribution extracted and calculated using Tsai approach. All final expressions are obtained beyond the ultrarelativistic approximation with respect to the lepton mass that allows to evaluate numerically of the considered effects not only for ultrarelativistic leptons (JLab) and but for moderately relativistic (MUSE) kinematics, too.

Form Factors and Two-Photon Exchange in High-Energy Elastic Electron-Proton Scattering.

We present new precision measurements of the elastic electron-proton scattering cross section for momentum transfer (Q^{2}) up to 15.75 (GeV/c)^{2}. Combined with existing data, these provide an improved extraction of the proton magnetic form factor at high Q^{2} and double the range over which a longitudinal or transverse separation of the cross section can be performed. The difference between our results and polarization data agrees with that observed at lower Q^{2} and attributed to hard two-photon exchange (TPE) effects, extending to 8 (GeV/c)^{2} the range of Q^{2} for which a discrepancy is established at >95% confidence. We use the discrepancy to quantify the size of TPE contributions needed to explain the cross section at high Q^{2}.

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.

Direct TPE measurement via $$e^+p/e^-p$$ scattering at low $$\varepsilon $$ in Hall A

The proton elastic form factor ratio can be measured either via Rosenbluth separation in an experiment with unpolarized beam and target, or via the use of polarization degrees of freedom. However, data produced by these two approaches show a discrepancy, increasing with $Q^2$. The proposed explanation of this discrepancy - two-photon exchange - has been tested recently by three experiments. The results support the existence of a small two-photon exchange effect but cannot establish that theoretical treatments at the measured momentum transfers are valid. At larger momentum transfers, theory remains untested, and without further data, it is impossible to resolve the discrepancy. A positron beam at Jefferson Lab allows us to directly measure two-photon exchange over an extended $Q^2$ and $\epsilon$ range with high precision. With this, we can validate whether the effect reconciles the form factor ratio measurements, and test several theoretical approaches, valid in different parts of the tested $Q^2$ range. In this proposal, we describe a measurement program in Hall A that combines the Super BigBite, BigBite, and High Resolution Spectrometers to directly measure the two-photon effect. Though the limited beam current of the positron beam will restrict the kinematic reach, this measurement will have very small systematic uncertainties, making it a clean probe of two photon exchange.

Polarization transfer in $$\varvec{e}^+p \rightarrow e^+ \varvec{p}$$ scattering using the Super BigBite Spectrometer

The effects of multi-photon-exchange and other higher-order QED corrections on elastic electron-proton scattering have been a subject of high experimental and theoretical interest since the polarization transfer measurements of the proton electromagnetic form factor ratio \(G_E^p/G_M^p\) at large momentum transfer \(Q^2\) conclusively established the strong decrease of this ratio with \(Q^2\) for \(Q^2 \gtrsim 1\) \(\hbox {GeV}^2\). This result is incompatible with previous extractions of this quantity from cross section measurements using the Rosenbluth Separation technique. Much experimental attention has been focused on extracting the two-photon exchange (TPE) effect through the unpolarized \(e^+p/e^-p\) cross section ratio, but polarization transfer in polarized elastic scattering can also reveal evidence of hard two-photon exchange. Furthermore, it has a different sensitivity to the generalized TPE form factors, meaning that measurements provide new information that cannot be gleaned from unpolarized scattering alone. Both \(\epsilon \)-dependence of polarization transfer at fixed \(Q^2\), and deviations between electron-proton and positron-proton scattering are key signatures of hard TPE. A polarized positron beam at Jefferson Lab would present a unique opportunity to make the first measurement of positron polarization transfer, and comparison with electron-scattering data would place valuable constraints on hard TPE. Here, we propose a measurement program in Hall A that combines the Super BigBite Spectrometer for measuring recoil proton polarization, with a non-magnetic calorimetric detector for triggering on elastically scattered positrons. Though the reduced beam current of the positron beam will restrict the kinematic reach, this measurement will have very small systematic uncertainties, making it a clean probe of TPE.

Exact relations for two-photon-exchange effect in elastic ep scattering by dispersion relation and hadronic model * *Supported in part by the National Natural Science Foundation of China (11375044,11975075)

The two-photon-exchange (TPE) effect plays a key role in extracting the form factors (FFs) of the proton. In this work, we discuss several exact properties of the TPE effect in the elastic scattering. By taking four low energy interactions as examples, we analyze kinematical singularities, asymptotic behaviors, and branch cuts of TPE amplitudes. The analytical expressions clearly indicate several exact relations between the dispersion relation (DR) and hadronic model (HM) methods. This suggests that the two methods must be modified to general forms, while novel forms yield the same results. After the modification, new DRs include a non-trivial term with two singularities. Furthermore, new DRs automatically include contributions due to the seagull interaction, meson-exchange effect, contact interactions, and off-shell effect. To analyze the elastic scattering data sets, the new forms must be used.

Determination of two-photon exchange via $$e^+p/e^-p$$ scattering with CLAS12

The proton elastic form factor ratio shows a discrepancy between measurements using the Rosenbluth technique in unpolarized beam and target experiments and measurements using polarization degrees of freedom. The proposed explanation of this discrepancy is uncorrected hard two-photon exchange (TPE), a type of radiative correction that is conventionally neglected. The effect size and agreement with theoretical predictions has been tested recently by three experiments. While the results support the existence of a small two-photon exchange effect, they cannot establish that theoretical treatments are valid. At larger momentum transfers, theory remains untested. This proposal aims to measure two-photon exchange over an extended and so far largely untested $Q^2$ and $\varepsilon$ range with high precision using the {\tt CLAS12} experiment. Such data are crucial to clearly confirm or rule out TPE as the driver for the discrepancy as well as test several theoretical approaches, believed valid in different parts of the tested $Q^2$ range.

Elements of QED-NRQED effective field theory. II. Matching of contact interactions

In 2010 the first extraction of the proton charge radius from muonic hydrogen was found be be five standard deviations away form the regular hydrogen value. Eight years later, this proton radius puzzle is still unresolved. One of the most promising avenues to resolve the puzzle is by a muon-proton scattering experiment called MUSE. The typical momenta of the muons in this experiment are of the order of the muon mass. In this energy regime the muons are relativistic but the protons are non-relativistic. The interaction between them can be described by QED-NRQED effective field theory. In a previous paper we have shown how QED-NRQED reproduces Rosenbluth scattering up to $1/M^2$, where $M$ is the proton mass, and relativistic scattering off a static potential at ${\cal O}(Z^2\alpha^2)$ and leading power in $M$. In this paper we determine the Wilson coefficients of the four-fermion contact interactions at ${\cal O}(Z^2\alpha^2)$ and power $1/M^2$. Surprisingly, we find that the coefficient of the spin-independent interaction vanishes, implying that MUSE will be sensitive mostly to the proton charge radius and not spin-independent two-photon exchange effects.

Two-photon exchange effects in e+e−→π+π− and timelike pion electromagnetic form factor

The two-photon-exchange (TPE) effects in the process $e^+e^- \rightarrow \pi^+\pi^-$ at large momentum transfer are discussed within the perturbative QCD (pQCD). The contributions from the twist-2 and twist-3 distribution amplitudes (DAs) of pion are considered in the estimation. Different with the results under the one-photon-exchange (OPE) approximation, the TPE effects result in an asymmetry of the differential cross section on the scattering angle. The precise measurement of this asymmetry by the further experiment is an precise test of pQCD at large momentum transfer. The time-like electromagnetic form factor of pion at the leading order of pQCD is re-discussed and the comparison of our results with those in the references are presented.

Two-Photon Exchange: Future Experimental Prospects

The proton elastic form factor ratio is accessible in unpolarized Rosenbluth-type experiments as well as experiments which make use of polarization degrees of freedom. The extracted values show a distinct discrepancy, growing with $Q^2$. Three recent experiments tested the proposed explanation, two-photon exchange, by measuring the positron-proton to electron-proton cross section ratio. In the results, a small two-photon exchange effect is visible, significantly different from theoretical calculation. Theory at larger momentum transfer remains untested. This paper discusses the possibilities for future measurements at larger momentum transfer.

Two-photon exchange corrections to γ*NΔ form factors for Q2≤4(GeV/c)2

We evaluate the corrections of the two-photon exchange (TPE) process on the $\gamma^* N\Delta$ transition form factors. The contributions of the TPE process to the $eN\rightarrow e\Delta(1232)\rightarrow eN\pi$ are calculated in a hadronic model with the inclusion of only the elastic nucleon intermediate states, to estimate its effects on the multipoles $M^{(3/2)}_{1^+}, E^{(3/2)}_{1^+}, S^{(3/2)}_{1^+}$ at the $\Delta$ peak. We find that TPE effects on $G^*_M$ is very small. $G^*_E,$ and $ G^*_C$ are also little affected at small $Q^2 $. For $G^*_E$, the TPE effects reach about $3 - 8\%$ near $Q^2\sim 4$ GeV$^2$, depending on the model, MAID or SAID, used to emulate the data. For $G^*_C$, the TPE effects decrease rapidly with increasing $\epsilon$ while growing with increasing $Q^2$ to reach $\sim 6 - 15\%$ with $Q^2 \sim 4$ GeV$^2$ at $\epsilon = 0.2$. Sizeable TPE corrections to $G^*_E$ and $G^*_C$ found here points to the need of including TPE effects in the multipole analysis in the region of high $Q^2$ and small $\epsilon$. The TPE corrections to $R_{EM}$ and $R_{SM}$ obtained in our hadronic calculation are compared with those obtained in a partonic calculation for moderate momentum transfer of $2<Q^2<4$ GeV$^2$.

Measurement of two-photon exchange effect by comparing elastic e±p cross sections

[Background] The electromagnetic form factors of the proton measured by unpolarized and polarized electron scattering experiments show a significant disagreement that grows with the squared four momentum transfer ($Q^{2}$). Calculations have shown that the two measurements can be largely reconciled by accounting for the contributions of two-photon exchange (TPE). TPE effects are not typically included in the standard set of radiative corrections since theoretical calculations of the TPE effects are highly model dependent, and, until recently, no direct evidence of significant TPE effects has been observed. [Purpose] We measured the ratio of positron-proton to electron-proton elastic-scattering cross sections in order to determine the TPE contribution to elastic electron-proton scattering and thereby resolve the proton electric form factor discrepancy. [Methods] We produced a mixed simultaneous electron-positron beam in Jefferson Lab's Hall B by passing the 5.6 GeV primary electron beam through a radiator to produce a bremsstrahlung photon beam and then passing the photon beam through a convertor to produce electron/positron pairs. The mixed electron-positron (lepton) beam with useful energies from approximately 0.85 to 3.5 GeV then struck a 30-cm long liquid hydrogen (LH$_2$) target located within the CEBAF Large Acceptance Spectrometer (CLAS). By detecting both the scattered leptons and the recoiling protons we identified and reconstructed elastic scattering events and determined the incident lepton energy. A detailed description of the experiment is presented.

Two-photon exchange correction to2S−2Psplitting in muonicHe3ions

We calculate the two-photon exchange correction to the Lamb shift in muonic helium-3 ions within the dispersion relations framework. Part of the effort entailed making analytic fits to the electron-$^3$He quasielastic scattering data set, for purposes of doing the dispersion integrals. Our result is that the energy of the 2$S$ state is shifted downwards by two-photon exchange effects by 15.14(49) meV, in good accord with the result obtained from a potential model and effective field theory calculation.

Dispersion theoretical analysis of the nucleon form factors

We review the achievements of the project C.2 , that deals with a dispersion theoretical analysis of the nucleon form factors. We have analyzed the world data for the space-like and time-like form factors to extract nucleon radii and vector meson coupling constants. Our proton charge radius r P E ≃ 0.85 fm has gained prominence in the so-called proton radius puzzle, see Ref. [1]. We also have analyzed the strong energy dependence of the e + e − → pp amplitude at the nucleon-antinucleon threshold, two-photon exchange effects and isospin violation in the isovector nucleon form factors.

Contribution of Δ(1232) to real photon radiative corrections for elastic electron–proton scattering

Here we consider the contribution of the Δ(1232) resonance to the real photon radiative corrections for elastic ep-scattering. The effect is found to be small for past experiments studying the unpolarized cross section, as well as for the recent VEPP-3 experiment investigating two-photon exchange effects by the precision measurement of the -scattering cross section ratio.

Weighted difference ofgfactors of light Li-like and H-like ions for an improved determination of the fine-structure constant

A weighted difference of the $g$-factors of the Li- and H-like ion of the same element is studied and optimized in order to maximize the cancellation of nuclear effects. To this end, a detailed theoretical investigation is performed for the finite nuclear size correction to the one-electron $g$-factor, the one- and two-photon exchange effects, and the QED effects. The coefficients of the $Z\alpha$ expansion of these corrections are determined, which allows us to set up the optimal definition of the weighted difference. It is demonstrated that, for moderately light elements, such weighted difference is nearly free from uncertainties associated with nuclear effects and can be utilized to extract the fine-structure constant from bound-electron $g$-factor experiments with an accuracy competitive with or better than its current literature value.

Measurement of the Two-Photon Exchange Contribution to the Elastice±pScattering Cross Sections at the VEPP-3 Storage Ring

The ratio of the elastic e(+)p to e(-)p scattering cross sections has been measured precisely, allowing the determination of the two-photon exchange contribution to these processes. This neglected contribution is believed to be the cause of the discrepancy between the Rosenbluth and polarization transfer methods of measuring the proton electromagnetic form factors. The experiment was performed at the VEPP-3 storage ring at beam energies of 1.6 and 1.0 GeV and at lepton scattering angles between 15° and 105°. The data obtained show evidence of a significant two-photon exchange effect. The results are compared with several theoretical predictions.