Formfaktor des π-Mesons und Struktur der Nukleonen

Abstract

Recent measurements of electron-proton scattering at Stanford have shown that the electric and magnetic form factors are not equal. Therefore, the isotopic vector parts of the form factorsGev andGmv are recalculated with unsubtracted dispersion relations in the 2π-approximation. For the isotopic scalar parts we useGes(s)≈Gev(s) andGms(s)≈ 0 which is known to be valid for moderate energy-momentum transfers. We obtain a simple closed expression for the electromagnetic form factor of the pionFπ in terms of the scattering lengtha1 and the effective ranger1 of the π-π-scattering in the stateL=T=1.a1 is roughly known from pion production by pions. With this value and a suitabler1,Fπ has a resonance in the region of time-like energy-momentum transfer; and the pion rms-radius becomes\(\overline {v_\pi ^2 } = (0.82 \times 10^{ - 13} cm)^2 \). The calculated anomalous magnetic moment, the electric and the magnetic rms-radii of the proton are then within 10% of the experimental values, the electric charge within 30%. Moreover, the proton form factors are different from each other and up to an energy-momentum transfer of\(s = \frac{{ - q^2 }}{{m_\pi ^2 }} = 23\) within the experimental error of the new measurements. The deviations for higher values of the energy-momentum transfer may be explained in terms of the isotopic scalar parts of the form factors. In this case the electric form factor of the neutron will be different from zero in that region and the magnetic form factor of proton and neutron will no longer be equal. For comparison with other experiments we also calculate the π+−π− cross section with neglect of other states thanL=T=1. Under this assumption the π−π cross section has a resonance for low energy-momentum transfer.