The Charge and Magnetization Distributions of the Proton

GEp and GMp

Although the protons and neutrons in atomic nuclei account for nearly all of the observed mass in the universe, these particles have a complicated structure that is poorly understood. This situation arises from the fundamental theory of strong interactions, quantum chromodynamics (QCD), which gives the nucleons their very rich structure, but which is also nonperturbative and extremely difficult to solve.

The first indication that nucleons have an internal structure was a measurement of the proton magnetic moment, which led to the 1943 Nobel Prize being awarded to Otto Stern. Quantum mechanics predicts that point-like spin-1/2 particles, such as the electron, have a magnetism (magnetic moment) with a magnitude g = 2, aside from very small quantum mechanical corrections. But for the spin-1/2 proton, g = 5.586. Thus, the proton has an internal structure; it cannot be a point-like particle.

In nonrelativistic quantum mechanics, the probability of scattering an electron from the proton is directly related to its charge and magnetic distributions. The investigation of the spatial structure of the proton was led by Stanford experiments in the 1950s, for which Robert Hofstadter was awarded the 1961 Nobel Prize. These measurements showed that the charge and magnetization of the proton have a simple form, both having essentially the same exponential shape -- equivalent to a dipole shape in momentum space.

Measuring the charge distribution of the proton with finer precision requires measurements at higher momentum transfer, but as the momentum transfer increases electrons scatter increasingly from the magnetization, rather than the charge, of the proton. As a result, the magnetization distribution is well known at large momentum transfer, but the charge distribution becomes less and less precise.


Figure 1: The ratio of the charge distribution of the proton to the magnetic distribution, as a function of the momentum transfer, shows an almost linear decrease. The standard "textbook"' description is that the ratio is unity. Three examples of recent calculations are shown, vector meson dominance (VMD), soliton model, and constituent quark model (CQM).

Figure 2: Six examples illustrating the nonspherical shape of the proton. See text for details.

In the 1960s, Akhiezer and Rekalo, and separately Dombey, proposed that polarization observables could be used instead of scattering probabilities to precisely determine the charge distribution. With the spin of an electron beam oriented along its direction of motion, one can either measure the spin direction of the proton after the scattering, or the variation in the scattering probability as the spin direction of a polarized target is changed. Over twenty years passed before the technical elements were in place for the first polarization measurements, performed at the beginning of the 1990s in low momentum polarization transfer measurements on the neutron and proton at Bates and Mainz laboratories.

Measurements led by Charles Perdrisat of William & Mary, Vina Punjabi of Norfolk State, Mark Jones of Jefferson Lab, and Ed Brash of Regina [M. Jones et al., Phys. Rev. Lett. 84, 1398 (2000), and O. Gayou et al., Phys. Rev. Lett. 88, 092301 (2002)], performed at the Thomas Jefferson National Accelerator Facility over the past several years, have pushed high-precision studies of the charge distribution of the proton to much higher momentum transfer, previously measured only with lower precision at SLAC. As the SLAC measurements had indicated that the charge and magnetization have about the same exponential shape, it was a great surprise when the Jefferson Lab measurements found instead that the ratio of the charge to the magnetic distribution falls almost linearly with momentum transfer. A new polarization transfer experiment will continue these measurements to even larger momentum transfers, to see if the ratio of charge to magnetization continues to decrease and even becomes negative, as was suggested by Dombey, nearly thirty years ago. The ratio in momentum space is shown in Figure 1.

Although experts generally do not think in terms of the shape of the proton, G. A. Miller showed [Phys. Rev. C 68, 022201(R) (2003)] that the data can also be interpreted in relativistic constituent quark models as a change in the intrinsic shape of the proton. Even though the proton overall has a spherical shape, if a photon couples to a quark with spin parallel (antiparallel) to the spin of the proton, then the shape becomes like that of a peanut (donut). The exact shape probed depends on the momentum transferred to the proton. Some representative shapes are shown in Figure 2.

The first understanding of the proton structure came from the constituent quark model , which describes the proton, and other subatomic particles, as being made up of 3 massive quarks. Quantum mechanics requires that in addition to 3 valence quarks there be quark-antiquark pairs, a meson cloud. The structure of the proton, when probed at low momentum transfer, appears to be dominated by the meson cloud, whereas at high momentum transfer the three valence quarks are more important.

For theorists, the new results at high momentum transfer have helped lead a change in thinking about the structure of the proton. The important point in relativistic quark models goes by the technical name of Poincare invariance - this is a relativistic generalization of the idea that physics is independent of the reference frame of the observer. The result is that the spin of the nucleon arises not just from the spin angular momentum of the quarks, but also from the orbital angular momentum of the quarks as they move within the nucleon. The importance of orbital angular momentum is an idea long advocated by Ralston, Pire, and colleagues. This change in the understanding of the spin of the proton has important implications for a number of reactions.

The unexpected result that the electric and magnetic structures are different has generated great excitement. Several attempts are being made to confirm or refute it. Preliminary results of new cross section (scattering probability) measurements at Jefferson Lab confirm the earlier SLAC results. How is this discrepancy between the two techniques to be resolved?

Recent theoretical work [A. Afanasev, I. Akusevich, and N.P. Merenkov, hep-ph/0208260; P.A.M. Guichon and M. Vanderhaeghen, hep-ph/0306007, Phys. Rev. Lett. 91, 142303 (2003); and P. Blunden, W. Melnitchouk, and J. Tjon, hep-ph/0306076, Phys. Rev. Lett. 91, 142304 (2003)] stresses the importance of mechanisms in which the electron scatters from the proton by exchanging two photons rather than just one. This mechanism is believed to affect the cross section measurements by a few percent, but since the electric contribution to the cross section is only several percent, it possibly leads to the difference with the polarization results - which are largely unaffected. The first data from experiments that cleanly indicate this physical effect have begun to appear [S.P. Wells et al., Phys. Rev. C 63, 064001 (2001)], and several new experiments are currently being planned.

The structure of the neutron is a related problem of great interest. The neutron structure is difficult to measure experimentally, as there is no good free neutron target. Modern experiments have made great progress, often using spin measurements in combination with nuclear structure theory, to determine the neutron structure. At this point there is great difficulty constructing a theory that gives good descriptions of both the neutron and proton structure. The proton and neutron structure are described by essentially identical theoretical techniques, so a resolution of this problem is of great importance.