This paper describes a precise measurement of electron scattering off the proton at momentum transfers of 0.003 Q 2 1 GeV 2 . The average point-to-point error of the cross sections in this experiment is ∼0.37%. These data are used for a coherent new analysis together with all world data of unpolarized and polarized electron scattering from the very smallest to the highest momentum transfers so far measured. The extracted electric and magnetic form factors provide new insight into their exact shape, deviating from the classical dipole form, and of structure on top of this gross shape. The data reaching very low Q 2 values are used for a new determination of the electric and magnetic radii. An empirical determination of the two-photon-exchange correction is presented. The implications of this correction on the radii and the question of a directly visible signal of the pion cloud are addressed.

New precise results of a measurement of the elastic electron-proton scattering cross section performed at the Mainz Microtron MAMI are presented. About 1400 cross sections were measured with negative four-momentum transfers squared up to Q² = 1 (GeV/c)² with statistical errors below 0.2%. The electric and magnetic form factors of the proton were extracted by fits of a large variety of form factor models directly to the cross sections. The form factors show some features at the scale of the pion cloud. The charge and magnetic radii are determined to be ½ = 0.879(5)stat(4)syst(2)model(4)group fm and ½ = 0.777(13)stat(9)syst(5)model(2)group fm.

Precise data on the neutron magnetic form factor G mn have been obtained with measurements of the ratio of cross sections of D(e, e ′ n) and D(e, e ′ p) up to momentum transfers of Q 2 = 0.9 (GeV/c) 2 . Data with typical uncertainties of 1.5% are presented. These data allow for the first time to extract a precise value of the magnetic radius of the neutron.

A massive, but light abelian U (1) gauge boson is a well motivated possible signature of physics beyond the Standard Model of particle physics. In this paper, the search for the signal of such a U (1) gauge boson in electron-positron pair-production at the spectrometer setup of the A1 Collaboration at the Mainz Microtron (MAMI) is described. Exclusion limits in the mass range of 40 MeV/c 2 up to 300 MeV/c 2 with a sensitivity in the mixing parameter of down to 2 = 8 × 10 −7 are presented. A large fraction of the parameter space has been excluded where the discrepancy of the measured anomalous magnetic moment of the muon with theory might be explained by an additional U (1) gauge boson.

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