S1: Accomplishments of the second funding period

  • A. Dispersive estimates of two-photon exchange (TPE): inelastic states and lepton mass terms
    1. Extension of dispersive analysis of TPE in \(e^- p \) scattering including inelastic states
      We have evaluated the TPE corrections to the elastic electron-proton scattering cross section within a dispersive framework. Besides the elastic contribution, we have accounted for all \(\pi N \) intermediate state contributions using the phenomenological MAID fit as an input. In a first work, we have calculated the corresponding TPE corrections to the unpolarized \(e p \) scattering cross section in the region of low momentum transfer \( Q^2 ≲ 0.064~\mathrm{GeV}^2\), where no analytical continuation into the unphysical region of the TPE scattering amplitudes is required. In a second work, we have developed a novel method for the analytical continuation of the TPE amplitudes into the unphysical region, thus generalizing our approach to the momentum transfer region \( 0.064~\mathrm{GeV}^2 ≲ Q^2 ≲ 1~\mathrm{GeV}^2\). We have compared our results with recent OLYMPUS, CLAS and VEPP-3 data as well as with empirical fits in the forward angular region. Both works are published in Phys. Rev. D.
      Furthermore, a review paper on dispersion theory in electromagnetic interactions has been published in Ann. Rev. Nucl. Part. Sci.
    2. Dispersive analysis of TPE in \(\mu p \) scattering and beam normal spin asymmetry for \(e^- p \to e^- \Delta \)
      We have evaluated the TPE correction to the muon-proton elastic scattering at small momentum transfer. Besides the elastic (nucleon) intermediate state contribution, which is calculated exactly, we have accounted for the inelastic intermediate states by expressing the TPE process approximately through the forward doubly virtual Compton scattering. The input in this evaluation is given by the unpolarized proton structure functions and by one subtraction function. For the latter, we have provided an explicit evaluation based on a Regge fit of high-energy proton structure function data. It was found that, for the kinematics of the forthcoming muon-proton elastic scattering data of the MUSE experiment, the elastic TPE contribution dominates, and the size of the inelastic TPE contributions is within the anticipated error of the forthcoming data.
      In a second work, we have evaluated 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, which we fixed to the model estimate obtained in the work above for the full two-photon exchange at one of three MUSE beam energies. This allows to make a prediction for the two other MUSE energies. Both works are published in Eur. Phys. J. C.
      In a third work, we have calculated the single spin asymmetry for the \(e p \to e \Delta(1232) \) process, for an electron beam polarized normal to the scattering plane. Such single spin asymmetries vanish in the one-photon exchange approximation, and are directly proportional to the absorptive part of a two-photon exchange amplitude. As the intermediate state in such two-photon exchange process is on its mass shell, the asymmetry allows one to access for the first time the on-shell \(\Delta \to \Delta \) as well as \(N^\ast \to \Delta \) electromagnetic transitions. We developed the general formalism to describe the \(e p \to e \Delta \) beam normal spin asymmetry, and provided a numerical estimate of its value using the nucleon, \(\Delta(1232) \), \(S_{11}(1535) \), and \(D_{13}(1520) \) intermediate states. We have compared our results with the first data from the Qweak@JLab experiment and have given predictions for the A4@MAMI experiment. This work is published in Phys. Rev. D.
  • B. Lepton universality test in the photoproduction of \(e^- e^+ \) versus \(\mu^- \mu^+\) pairs on a proton
    In view of the significantly different proton charge radius extracted from muonic hydrogen Lamb shift measurements as compared to electronic hydrogen spectroscopy or electron scattering experiments, we have proposed the photoproduction of a lepton pair on a proton target in the limit of very small momentum transfer as a way to provide a test of the lepton universality when extracting the proton charge form factor. By detecting the recoiling proton in the \(\gamma p \to l^- l^+ p\) reaction, we have shown that a measurement of a ratio of \(e^-e^+ + \mu^-\mu^+\) over \(e^-e^+\) cross sections with an absolute precision of \(7 \times 10^{-4} \), has the sensitivity to distinguish, at the \(3 \sigma \) level, between the two different proton charge radii currently extracted from muonic and electronic observables. This work by Pauk and Vanderhaeghen was published in Phys. Rev. Lett. 115, no. 22, 221804 (2015). In order to interpret forthcoming data for such process, we have calculated the soft-photon radiative corrections to the \(\gamma p\rightarrow l^+l^-p\) reaction, and published this work in Phys. Rev. D.
    We have extended the dilepton production study to the case of a deuteron target, and studied the sensitvity of the \(\gamma p \to e^- e^+ p\) reaction, to the deuteron charge radius. We have found that for small momentum transfers the Bethe-Heitler process dominates, and that it is sensitive to the charge radius such that a cross section ratio measurement of about 0.1 % relative accuracy could give a deuteron charge radius more accurate than the current electron scattering value and sufficiently accurate to distinguish between the electronic and muonic atomic values. This result has been submitted for publication to Phys. Rev. Lett.
  • C. Lattice QCD program of nucleon form factors
    Calculation of isovector form factors down to \(m_\pi=190\,\)MeV at three lattice spacings with 8 to 10 times the statistics achieved in the first funding period.
    Implementation of O( \(a\)) improvement of the vector current: extrapolations to the continuum linear in \(a^2\).
    A \(96^3\times192\) lattice ensemble has been generated with physical pion mass using a large computing-time grant on Hazelhen in Stuttgart; substantial computing-time grant obtained for nucleon correlation functions on that ensemble on JUWELS in Jülich.
    Calculation of disconnected diagram contributions performed for strangeness vector ( \(G_M^s(Q^2)\), \(G_E^s(Q^2) \)) and axial (\(G_A^s(Q^2)\), \(G_P^s(Q^2)\)) form factors.
    Conceptual developments to reduce the influence of excited states in the extraction of nucleon form factors.
  • D. Spacelike electromagnetic form factor program at MAMI
    We have developed a new experimental method based on initial-state radiation (ISR) in \(e-p \) scattering, in which the radiative tail of the elastic \(e-p \) peak contains information on the proton charge form factor ( \(G_{Ep}\)) at extremely small \(Q^2\). The ISR technique was validated in a dedicated experiment using the spectrometers of the A1-Collaboration at the Mainz Microtron (MAMI). A first measurements of \(G_{Ep} \) for \(0.001 \leq Q^2 \leq 0.004 \)~(GeV/c) \(^2\) was published in 2017. A reanalysis of this data with improved description of the external radiative corrections will provide an improved extraction of the proton radius.
    To improve among others future ISR measurements, the hypersonic gas jet target, designated for the future use in the MAGIX experiment at MESA, was installed in the A1 hall. A first cluster jet beam could be demonstrated in a test experiment.
    The construction of a neutron polarimeter to measure \(G_{En}\) is close to completion.
  • E. Baryon timelike form factor measurements at BES-III
    The radiative return channel \(e^+ e^- \to p \bar p \gamma\), where \(\gamma\) is a hard photon emitted by initial state radiation (ISR), allows for a complementary approach to the energy scan technique in proton FF measurements. We performed the measurements of proton form factors at BESIII using the ISR technique and data sets, corresponding to an integrated luminosity of 7.4 fb \(^{-1}\) collected at center of mass energies between 3.773 and 4.600 GeV. Two independent analyses have been performed. The first one uses the events where the ISR photons can be detected using the electromagnetic calorimeter (large angles, tagged ISR analysis). The second analysis uses the events where the ISR photons are emitted in the region which is not covered by the electromagnetic calorimeter (small angles, untagged ISR analysis). The oscillations seen by BaBar have been reproduced by our analyses. Two release notes summarizing the tagged and untagged ISR analysis were written and reviewed by the collaboration. Two paper drafts for reviewed journal publications are currently under review within the collaboration.
    Precision measurements of the proton form factor can be reached using the scan data sets of about 688.5 pb \(^{-1}\) at 22 center-of-mass energies (\(\sqrt{s}\)) from 2.0 to 3.08 GeV at BESIII. The proton and anti-proton are produced directly from \(e^{+}e^{-}\) annihilation, eventually under emission of a soft ISR photon. The Born cross sections of \(e^+e^-\to p \bar p \) and the effective form factors ( \(|G|\)) of the proton are measured. Besides, the electromagnetic form factor ratios ( \(|G_E/G_M| \)) and the absolute value of the magnetic form factors ( \(|G_M|\)) are investigated by studying the helicity angle of the proton at \(16 \) center-of-mass energies. The Born cross sections and the effective form factors are consistent with previous experimental results, the precision of \(|G_E/G_M|\) and \(|G_M| \) is much improved with respect to previous measurements. One internal note has been released in BESIII and one paper draft for PRL is under BESIII collaboration wide review.
    Measurement of neutron form factors (G \(_E \) and G \(_M \)) in the time like-region have never been done so far. Attempts are performed to extract the neutron form factors in three different experiments (FENICE, DM2 and SND) but in none of them, the neutron FFs G \(_E \) and G \(_M \) were measured. Only the effective form factor could be determined due to the low statistics. A large data samples of e \(^{+}\)e \(^{-}\) energy scan in the region between 2.0 and 3.08 GeV with a total luminosity of around 651 pb \(^{-1}\) has been collected in 2014/15 with the BESIII experiment. According to our run proposal which is based on MC simulation studies, it is possible to extract the TL FFs of the neutron with the direct scan method. With this data the ratio of the neutron form factors in the time-like region will be extracted for the first time. The main selection combines three independent parts using different methods, including time-of-flight measurement, the use of multivariate analysis and selection criteria based on the electromagnetic (EM) calorimeter. To suppress \(e^+e^-\to \gamma\gamma (\gamma)\) shower shapes variables are used because the development of the electromagnetic showers in the EMC calorimeter is faster than those in the hadronic showers. Signal yield form data is extracted by fitting the opening angle between neutron and anti-neutron candidates in the large angle region. After correcting the signal yield by signal efficiency, radiative corrections, we could extract the born cross section at 11 centre of mass energies and the effective form factor. A fit on the angular distribution of the (anti-)neutron gives us the possibility to measure the ratio of the electromagnetic form factors as well as the separated \(G_E \) and \(G_M \). The electric and magnetic form factors \(G_E \) and \(G_M\) have been determined for the first times at only two centre of mass energies ( \(\sqrt{s} \)= 2.125 and \(\sqrt{s} \)= 2.396 GeV) due the statistics limit. A release note summarizing the whole analysis is written and it is under review by the collaboration.