Two-photon Exchange Research Articles

Calculating the two-photon exchange contribution to KL→μ+μ− decay

We present a theoretical framework within which both the real and imaginary parts of the complex, two-photon exchange amplitude contributing to KL→μ+μ− decay can be calculated using lattice quantum chromodynamics. The real part of this two-photon amplitude is of approximately the same size as that coming from a second-order weak strangeness-changing neutral-current process. Thus a test of the standard model prediction for this second-order weak process depends on an accurate result of this two-photon amplitude. A limiting factor of our proposed method comes from low-energy three-particle ππγ states. The contribution from these states will be significantly distorted by the finite volume of our calculation—a distortion for which there is no available correction. However, a simple estimate of the contribution of these three-particle states suggests their contribution to be at most a few percent allowing their neglect in a lattice calculation with a 10% target accuracy. Published by the American Physical Society 2024

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.

The two-photon exchange experiment at DESY

We propose a new measurement of the ratio of positron-proton to electron-proton elastic scattering at DESY. The purpose is to determine the contributions beyond single-photon exchange, which are essential for the Quantum Electrodynamic (QED) description of the most fundamental process in hadronic physics. By utilizing a 20 cm long liquid hydrogen target in conjunction with the extracted beam from the DESY synchrotron, we can achieve an average luminosity of 2.12×1035\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$2.12\ imes 10^{35}$$\\end{document} cm-2·\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{-2}\\cdot $$\\end{document}s-1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{-1}$$\\end{document} (≈200\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\approx 200$$\\end{document} times the luminosity achieved by OLYMPUS). The proposed two-photon exchange experiment (TPEX) entails a commissioning run at a beam energy of 2 GeV, followed by measurements at 3 GeV, thereby providing new data up to Q2=4.6\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Q^2=4.6$$\\end{document} (GeV/c)2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^2$$\\end{document} (twice the range of current measurements). We present and discuss the proposed experimental setup, run plan, and expectations.

Analytical evaluation of elastic lepton-proton two-photon exchange in chiral perturbation theory

Analytical evaluation of elastic lepton-proton two-photon exchange in chiral perturbation theory

Normal single-spin asymmetries in electron-proton scattering: Two-photon exchange with intermediate-state resonances

Normal single-spin asymmetries in electron-proton scattering: Two-photon exchange with intermediate-state resonances

Impact of NNLO QED corrections on lepton-proton scattering at MUSE

We present the complete next-to-next-to-leading order (NNLO) pure pointlike QED corrections to lepton-proton scattering, including three-photon-exchange contributions, and investigate their impact in the case of the MUSE experiment. These corrections are computed with no approximation regarding the energy of the emitted photons and taking into account lepton-mass effects. We contrast the NNLO QED corrections to known next-to-leading order corrections, where we include the elastic two-photon exchange (TPE) through a simple hadronic model calculation with a dipole ansatz for the proton electromagnetic form factors. We show that, in the low-momentum-transfer region accessed by the MUSE experiment, the improvement due to more sophisticated treatments of the TPE, including inelastic TPE, is of similar if not smaller size than some of the NNLO QED corrections. Hence, the latter have to be included in a precision determination of the low-energy proton structure from scattering data, in particular for electron-proton scattering. For muon-proton scattering, the NNLO QED corrections are considerably smaller.

Test of streaming and triggered readout schemes for the TPEX lead tungstate calorimeter

Tests of a prototype lead tungstate calorimeter were made over two weeks at the end of September, 2019, at the DESY II Test Beam Facility in Hamburg, Germany. The purpose of these tests was to gain experience with the construction, operation, and performance of a simple lead tungstate calorimeter, and also to compare a traditional triggered readout scheme with a streaming readout approach. These tests are important for the proposed Two-Photon Exchange experiment at DESY [1] and for work towards a future electromagnetic calorimeter that could be used in an Electron-Ion Collider detector. Details onthe comparison of streaming and triggered readout schemes are presented here.

Two-loop electron factor contribution to lamb shift in muonium and positronium

We calculate hard spin-independent contributions to energy levels in muonium and positronium which are due to radiatively corrected electron factor insertion in two-photon exchange diagrams. Calculation of these corrections is motivated by the new round of precise measurements of spin-independent transition frequencies in muonium and positronium.

Multi-target two-photon dual-comb LiDAR.

By substituting two-photon cross-correlation in a wide-bandgap photodiode for the coherent gating conventionally used in dual-comb ranging, two-photon dual-comb LiDAR exchanges data-intensive interferometric acquisition for a single time-stamp from which an absolute distance can be inferred. Here, we report the application of two-photon dual-comb LiDAR to obtain real-time ranging to three independent targets with only a single silicon-photodiode detector. We show precisions of 197-255 nm (2 seconds averaging time) for static targets, and real-time simultaneous ranging to three dynamic targets driven by independent sinusoidal, saw-tooth and square waveforms. Finally, we demonstrate multi-target ranging to three points on a rigid body to provide simultaneous pitch and yaw angular measurements with precisions of 27.1 arcsec (130 µrad) on a 25 mm baseline.

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.

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.

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.

Target normal single-spin asymmetry in inclusive electron-nucleon scattering with two-photon exchange: Analysis using 1/Nc expansion

We calculate the target normal single-spin asymmetry caused by two-photon exchange in inclusive electron-nucleon scattering in the resonance region. Our analysis uses the 1/Nc expansion of low-energy QCD and combines N and Δ intermediate and final states using the contracted SU(4) spin-flavor symmetry. The normal spin asymmetry obtained in leading-order accuracy in 1/Nc has magnitude ∼10−2 and different sign in ep and en scattering. It can be measured in electron scattering at lab energies ∼0.5–1.5 GeV and provides a clean probe of two-photon exchange dynamics.

Two-photon exchange in (muonic) deuterium at N3LO in pionless effective field theory

We present a study of the two-photon-exchange (2upgamma -exchange) corrections to the S-levels in muonic (mu D) and ordinary (D) deuterium within the pionless effective field theory (EFT). Our calculation proceeds up to next-to-next-to-next-to-leading order (N3LO) in the EFT expansion. The only unknown low-energy constant entering the calculation at this order corresponds to the coupling of a longitudinal photon to the nucleon–nucleon system. To minimise its correlation with the deuteron charge radius, it is extracted using the information about the hydrogen–deuterium isotope shift. We find the elastic 2upgamma -exchange contribution in mu D larger by several standard deviations than obtained in other recent calculations. This discrepancy ameliorates the mismatch between theory and experiment on the size of 2upgamma -exchange effects, and is attributed to the properties of the deuteron elastic charge form factor parametrisation used to evaluate the elastic contribution. We identify a correlation between the deuteron charge and Friar radii, which can help one to judge how well a form factor parametrisation describes the low-virtuality properties of the deuteron. We also evaluate the higher-order 2upgamma -exchange contributions in mu D, generated by the single-nucleon structure and expected to be the most important terms beyond N3LO. The uncertainty of the theoretical result is dominated by the truncation of the EFT series and is quantified using a Bayesian approach. The resulting extractions of the deuteron charge radius from the mu D Lamb shift, the 2S{-}1S transition in D, and the 2S{-}1S hydrogen–deuterium isotope shift, with the respective 2upgamma -exchange effects evaluated in a unified EFT approach, are in perfect agreement.

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.

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 $\ensuremath{-}t$.

Combined Dissipative and Hamiltonian Confinement of Cat Qubits

Quantum error correction with biased-noise qubits can drastically reduce the hardware overhead for universal and fault-tolerant quantum computation. Cat qubits are a promising realization of biased-noise qubits as they feature an exponential error bias inherited from their non-local encoding in the phase space of a quantum harmonic oscillator. To confine the state of an oscillator to the cat qubit manifold, two main approaches have been considered so far: a Kerr-based Hamiltonian confinement with high gate performances, and a dissipative confinement with robust protection against a broad range of noise mechanisms. We introduce a new combined dissipative and Hamiltonian confinement scheme based on two-photon dissipation together with a Two-Photon Exchange (TPE) Hamiltonian. The TPE Hamiltonian is similar to Kerr nonlinearity, but unlike the Kerr it only induces a bounded distinction between even- and odd-photon eigenstates, a highly beneficial feature for protecting the cat qubits with dissipative mechanisms. Using this combined confinement scheme, we demonstrate fast and bias-preserving gates with drastically improved performance compared to dissipative or Hamiltonian schemes. In addition, this combined scheme can be implemented experimentally with only minor modifications of existing dissipative cat qubit experiments.

Characterization of muon and electron beams in the Paul Scherrer Institute PiM1 channel for the MUSE experiment

The MUon Scattering Experiment, MUSE, at the Paul Scherrer Institute, Switzerland, investigates the proton charge radius puzzle, lepton universality, and two-photon exchange, via simultaneous measurements of elastic muon-proton and electron-proton scattering. The experiment uses the PiM1 secondary beam channel, which was designed for high precision pion scattering measurements. We review the properties of the beam line established for pions. We discuss the production processes that generate the electron and muon beams, and the simulations of these processes. Simulations of the $\pi$/$\mu$/$e$ beams through the channel using TURTLE and G4beamline are compared. The G4beamline simulation is then compared to several experimental measurements of the channel, including the momentum dispersion at the IFP and target, the shape of the beam spot at the target, and timing measurements that allow the beam momenta to be determined. We conclude that the PiM1 channel can be used for high precision $\pi$, $\mu$, and $e$ scattering.

Lattice QCD Calculation of the Two-Photon Exchange Contribution to the Muonic-Hydrogen Lamb Shift.

We develop a method for lattice QCD calculation of the two-photon exchange contribution to the muonic-hydrogen Lamb shift. To demonstrate its feasibility, we present the first lattice calculation with a gauge ensemble at m_{π}=142 MeV. By adopting the infinite-volume reconstruction method along with an optimized subtraction scheme, we obtain with statistical uncertainty ΔE_{TPE}=-28.9(4.9) μeV+93.72 μeV/fm^{2}·⟨r_{p}^{2}⟩, or ΔE_{TPE}=37.4(4.9) μeV, which is consistent with the previous theoretical results in a range of 20-50 μeV.

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.