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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.

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.

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).

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.

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

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.

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Last modified March 4, 2005

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