# S1: Accomplishments of ﬁrst funding period

• Global analysis of the proton form factors (FFs)
A coherent new analysis of the precise Mainz measurement of electron scattering off the proton at momentum transfers of 0.003 ≤ Q2 ≤ 1 GeV2 has been performed together with all world data of unpolarized and polarized electron scattering from the very smallest to the highest momentum transfers so far measured. A consistent ﬁt could be achieved once a normalisation parameter was introduced for each data set. The data reaching very low Q2 values are used for a new determination of the electric and magnetic radii conﬁrming the ”large” value of 0.88 fm for charge radius. An empirical determination of the Two-Photon-Exchange (TPE) correction was also presented in that work.
• Proton Radius Puzzle Workshop (Mainz, June 2-6, 2014)
To discuss the puzzling ﬁndings that the proton radius appears to be different when mea- sured with muons vs. electrons, we organized a workshop (MITP sponsored with strong CRC1044 participation) dedicated to this topic, bringing together atomic, nuclear, and be- yond standard model physicists. A vibrant and useful meeting was held with around 40 participants, where the progress, new data, and new thinking in this ﬁeld was reviewed and were further ideas were generated to ﬁnd a solution to this puzzle that could impact several ﬁelds.
• Hadronic two-photon exchange (TPE) contributions to the Lamb shift in muonic atoms
We have evaluated the TPE contribution to the 2P-2S Lamb shift in muonic deuterium in the framework of forward dispersion relations, by using experimental data on elastic deuteron form factors and inelastic electron-deuteron scattering, both in the quasielastic and hadronic range. This work extends previous works of the TPE correction for muonic hydrogen and is of relevance to interpret recent Lamb shift experiments for muonic deuterium. Based on phenomenological information, we obtain for the Lamb shift ∆E2P −2S = 2.01 ± 0.74 meV. The main source of the uncertainty of the dispersion analysis is due to lack of quasielastic data at low energies and forward angles. It was shown how a targeted measurement of the deuteron electrodesintegration in the kinematics of experiments A1 and MESA can help quenching this uncertainty signiﬁcantly.
• TPE processes in elastic lepton-nucleon scattering
We have developed a subtracted dispersion relation formalism with the aim to improve predictions for the TPE corrections to elastic electron-proton scattering observables at ﬁnite momentum transfers. In a ﬁrst study this formalism was tested in detail on the elastic intermediate state contribution which is expected to dominate in the low Q2 region. A detailed comparison with existing data for unpolarized cross sections as well as polarization transfer observables was performed. Furthermore, in the forward direction, a ﬁrst study of the inelastic intermediate state contribution was performed using a forward sum rule. The TPE have also been studied in the elastic muon-proton scattering, which will be relevant for the upcoming MUSE@PSI experiment. Our study focussed in particular on the lepton mass terms which are relevant in the case of low-energy elastic muon-proton scattering, in contrast to the electron scattering case, where such terms are negligible. Furthermore, a quantitative study of the lepton TPE effects on the cross section in the kinematics of the MUSE experiment was performed.
• High precision measurements of proton electric FF at very low momentum transfers using ISR at MAMI
The measurement of the cross-section for elastic scattering of electrons off hydrogen has been successfully performed. In the four-week experiment in August 2013, data with liquid hydrogen target, empty cell and thin carbon target were collected. The experiment was accompanied by another three-week beam time dedicated to a precise study of the optical properties of the spectrometers. The data collected in this supplementary experiment were used to determine new reconstruction matrices, and the efﬁciencies of all considered detectors were determined with sub-percent precision. The results of all parts of the calibration were then incorporated in the analysis software. Furthermore, a precise, time dependent study of the residual cryogens gathered around the target has been performed, which allows for a precise corrections of luminosity and particle energy losses. In order to complete the analysis, the following steps are presently considered: subtraction of empty cell contributions, correction for nitrogen and oxygen contaminations from cryogenic depositions, study of multiple scattering effects. By the end of the ﬁrst funding period we plan to extract a ﬁnal value of the proton charge form factor from the data of this ﬁrst ISR experiment.
• Radiative corrections to virtual Compton scattering for the ISR@MAMI experiment
The radiative corrections which are relevant to extract the proton electric FF from the ISR@MAMI experiment were studied. This work is based on previous studies of these radiative corrections to the Bethe-Heitler process in the virtual Compton scattering pro- cess. The previous work was extended to the kinematics of the ISR experiment, with a precision aim below the 1 % level. These corrections have been implemented and are being used in the current data analysis of the ISR experiment.
• Measurement of GMp at larger Q2 at MAMI
A measurement of electron scattering off the proton is scheduled for early 2015. The experiment will focus on the determination of the magnetic FF of the proton at large four-momentum transfers. Combining the new data with the Mainz 2010 measurement it will allow to extend the upper limit of a reliable separation of GEp and GMp in the range Q2 = 0.6 − 1.3 (GeV/c)2 (or up to Q2 ∼ 1.7 (GeV/c)2 if MAMI is able to deliver 1400 MeV beam). Data taking is foreseen for January 2015, so that by the reviewing of the proposal of the second funding period foreseen for September 2015 online spectra of the different setting used and a status report of the on going analysis will be presented.
• Neutron detector for future neutron FF measurements at MAMI
The material studies for the neutron detector were completed with the test of a small scale prototype of six scintillator bars. The results led to a successful funding application granted by the DFG. Material for the ﬁrst two full layers of the neutron detector have been ordered and the assembly of 128 channels was carried out in summer this year. A beamtime for proof of principle is scheduled for early October. With the tools and techniques developed during the construction process of the ﬁrst layers, 2/3 of the whole neutron detector will be built by the end of the ﬁrst funding period.
• Baryon timelike FF measurements at BES-III
The neutron effective FFs in the timelike region are not well constrained yielding surprisingly high values by almost a factor of 2 as compared to the proton.The last FF measure- ment of FENICE is based on a very small number of events. A determination of the ratio of the electric vs magnetic FF has never been done. We have concentrated on the anal- ysis of the neutron FF in the timelike region using initial state radiation (ISR) events from the BES-III detector which have been taken at the ψ′′-resonance $$(e^+e^-\to \eta^-\eta\gamma)$$. Three neutral particles in the ﬁnal state constitute a difﬁcult case, where the hadrons can get reconstructed only in a very incomplete way. A ﬁrst attempt using hard cuts, yielding an overal efﬁciency of 10−4 could stepwise be improved by multi variate methods by a factor of 100-500 up to 5×10-2. If the high value for the neutron timelike FFs can be conﬁrmed by the BES-III data, this his will not only allow a determination of the neutron effective FF, but also for the ﬁrst time a separation of electric and magnetic FFs in the timelike region. In addition we have prepared a run proposal for a FF-scan with several energies between 2.0 GeV and 3.1 GeV allowing to analyse the process $$e^+e^-\to B^-B$$ ($$B$$ = proton, neutron, Λ, etc.), to match the precision of the space like FF at the corresponding q2-value for example for the proton. In detailed simulations we have investigated the expected precision of such a scan and optimized the needed luminosity, taking into account the expectations for proton, neutron, Lambda, and other hyperon FFs. Especially for the Lambda, the ef- ﬁciency will be high enough for a determination of the phase between the electric and magnetic form factor by using the self-analyzing decay. The BES-III collaboration has decided during her summer 2014 collaboration meeting, to to run this proposal of a FF scan between 2.0 GeV and 3.1 GeV in early 2015.
Several analysis tasks are ongoing, concentrating on the timelike proton FF from ISR events. This work will be published at the end of the ﬁrst funding period.
• Lattice QCD program
We have performed a calculation of the axial charge of the nucleon in QCD with two flavors of quarks, including a study of the main sources of systematic error - in particular the excited state contributions in the Euclidean correlation functions. Before this publication, most calculations gave results lying 10-15 % below the experimental determination of the axial charge. We raised awareness in the community of the importance of excited-state contributions. Other collaborations have since adopted the 'summation method'. We have extended our analysis to include the axial and induced pseudoscalar form factors.
Furthermore, we have completed a calculation of the electromagnetic form factors of the nucleon on two-flavor lattice configurations. This study took much longer than the analysis of the axial charge, due to the more complicated structure of excited contaminations for non-forward matrix elements. We show evidence that the reason lattice calculations have so far failed to reproduce the experimental charge radius is that excited states contributions were not sufficiently accounted for in the calculations. We find good agreement with experimental data for the magnetic moment and the magnetic radius.
In coordination with the other members of the CLS group (Coordinated Lattice Simulations), configurations have been generated which will allow our calculations to be carried over to QCD with a more physical quark content.