# S1: Accomplishments of the second funding period

• Dispersive estimates of two-photon exchange (TPE): inelastic states and lepton mass term
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 πN 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 ep scattering cross section in the region of low momentum transfer Q2≲ 0.064 GeV2, 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 GeV2≲ Q2≲ 1 GeV2. 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.
2. Dispersive analysis of TPE in μp 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. The paper is published in Eur. Phys. J. C. We have calculated the single spin asymmetry for the $$ep~\to~e\Delta(1232)$$ 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 $$N^*~\to~\Delta$$ electromagnetic transitions. We developed the general formalism to describe the $$ep~\to~e\Delta$$ 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 has been submitted for publication to Phys. Rev. D.
• 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 γp → ll+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 × 10−4, has the sensitivity to distinguish, at the 3σ 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).We have extended the above work 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. The results are being prepared for publication.
• Lattice QCD program of nucleon form factors
Calculation of isovector form factors down to mπ = 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 a2.
Started production of a 963 × 192 lattice with mπ = 130 MeV on Mogon II.
Code development and calculation of disconnected diagram contributions for strangeness form factors GsM(Q2), GsE(Q2).
• 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 (GEp) at extremely small Q2. The ISR technique was validated in a dedicated experiment using the spectrometers of the A1-Collaboration at the Mainz Microtron (MAMI). This provided first measurements of GEp for 0.001 ≤ Q2 ≤ 0.004 (GeV/c)2.
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 GEn is in progress. 80% of the detector is completed.
• Baryon timelike form factor measurements at BES-III
For the neutron effective FFs in the time-like region only three measurements (FENICE, DM2 and SND) exist. A determination of the ratio of the electric vs magnetic FF has never been done.
A large data sample of $$e^+e^-$$ scan data in the region between 2.0 and 3.08 GeV with a total luminosity of 688 pb-1 has been collected in 2014/15 with the BESIII experiment according to our run proposal. It is used to extract the TL FF 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 calorimeter. In Mainz, we are concentrating on the EM calorimeter.The main selection is based on cuts of the shapes of the EM showers. The most energetic shower is regarded as shower arising from the annihilation of the the anti-neutron, while the second most energetic one is taken as the hadronic shower of the neutron in the EM calorimeter. The main background comes from the machine (elastic and inelastic beam-gar scattering, cosmic rays and others), as well as from the $$e^+e^- \to \gamma \gamma (\gamma)$$ channel. To suppress this background effectively, we concentrate on the two-particle-event kinematics of our signal channel and require the angle between anti-neutron and neutron to be large. After correcting the selected data by signal efficiency, radiative corrections and background contributions, we can extract the born cross section 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 GE and GM.