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Form Factors

Physics program > Nucleon Structure

Nucleons, proton and neutron, are not point-like particles as experimentally shown by the measurement of the proton anomalous magnetic moment by O. Stern in 1933; they have an extended electric charge and magnetism distributions measured for the first time in the 1950s by R. Hofstadter and collaborators at Stanford using elastic electron scattering. This internal structure is described by the electroweak Form Factors, which are fundamental functions of the transferred 4-momentum Q^2 in the electron-nucleon elastic scattering (or the 3-momentum transfer in the specific Breit reference frame). At Q^2=0 electric and magnetic Form Factors correspond to the electric charge and magnetic moment of the nucleon and in the non-relativistic limit, their Q^2 derivatives express the root-mean-square of the electric or magnetic radii of the nucleon respectively. Therefore the proton electric form factor is important for the determination of the Lamb shift in hydrogen atom, one of the most precise calculations of QED, the theory of electroweak interactions. Moreover, the Form Factors are related to first moments of the Generalized Parton Distributions (GPD), a recent theoretical approach introduced to get a complete picture on the structure of the nucleon, but hardy to measure. GPDs appear to be the key quantities to access the important, but unknown orbital angular momenta (OAM) of the quarks and gluons in the nucleon; in this novel framework, the Form Factors can contribute in the determination of the OAMs.

Form factors can be formally derived from QCD, the theory of strong interaction, where quark confinement is dominant. At present, this derivation is terrific challenging, and therefore predictions are possible only in the perturbative region (at high Q^2) or in lattice QCD which is starting to produce consistent results. In fact high Q^2 measurements seem to offer an indirect (model dependent) way to get information on the quark OAM. In this direction move the new experiments proposed to measure the nucleon Form Factors in the 12 GeV JLab era, extending the JLab leadership gained after the breaking breakthrough measurements in electron-proton elastic polarization transfer reactions. Specifically three experiments which require the SBS spectrometer  have already been approved for running; they will basically use all recent techniques (polarization transfer, double polarization, and cross section ratio) to extend the measurements of the proton and neutron electromagnetic Form Factors at Q^2 above 10 GeV^2.

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