SAMPLE: The First Measurement of the Proton's Weak Magnetism

A collaboration of Caltech, Univ. of Illinois, Univ. of Maryland, MIT/Bates and Rensselaer Polytechnic Institute

The magnetic moment of the proton, first measured in 1933 by Frisch and Stern, was the earliest experimental evidence for the internal structure of the nucleon. Although the theory of strong interactions, Quantum Chromodynamics (QCD), is over 20 years old, a quantitative description of the magnetic moments of the nucleons based on QCD remains an elusive goal. The phenomenal quantitative success of the standard electroweak theory now allows one to use the weak interaction to obtain additional information on the magnetic properties of the nucleon. In particular, the measurement of the strength of the magnetic interaction with the neutral weak boson Z₀ (when combined with the usual magnetic interaction with the photon) enables a decomposition of the nucleon magnetism into the contributions arising from the three relevant quark flavors (up, down, and strange).

The first measurement of the neutral weak magnetism of the proton was recently performed by the SAMPLE collaboration at the Bates Linear Accelerator Center. The experimental method involves the detection of the parity violation in the elastic scattering of longitudinally polarized electrons. The interference of weak (Z₀ exchange) and electromagnetic (photon exchange) amplitudes causes the cross section to depend on the helicity of the incident electron. (This helicity dependence corresponds to a breakdown of parity symmetry and thus is a signal of the presence of the neutral weak interaction.) The effect is quite small (few parts per million, or ppm) due to the feeble strength of the weak interaction at low energies, and its measurement represents a formidable experimental challenge.

A schematic diagram indicating the configuration of the experimental equipment is shown in the accompanying figure. The experimenters employed a 200 MeV polarized electron beam incident on a 40 cm long cryogenic liquid hydrogen target. The scattered electrons were detected in a large solid angle (approximately 1.5 steradian) air Cerenkov detector system consisting of 10 mirrors and 10 large photomultipier tubes. The reliable determination of the small parity-violating asymmetry in the scattering cross section required great care in eliminating sources of systematic error associated with reversal of the beam helicity.

The first set of data from the experiment was obtained during running periods in 1995 and 1996. The experimenters have recently reported a result for the parity-violating asymmetry [B. A. Mueller et al., Phys. Rev. Lett. 78, 3824 (1997)]:

where the first error is statistical and the second is the estimated systematic error. This value of the parity-violating asymmetry corresponds to a first determination of the neutral weak magnetic coupling of the proton (in nuclear magnetons)

at Q²=0.1 (GeV}² (the squared 4-momentum transfer to the nucleon).

It is interesting to note that the first reported measurement of the proton's magnetic moment by Frisch and Stern in 1933 was ``between 2 and 3 nuclear magnetons'', not very precise but certainly in disagreement with the generally expected value of 1 n.m. from Dirac theory. The ``Dirac'' proton value for G_M^Z is about 0.02 n.m. so the reported measurement of G_M^Z is clearly also very sensitive to the internal structure of the proton.

One question of current interest is whether the strange quark-antiquark pairs contribute significantly to the proton's magnetic moment. (Such information is complementary to other experimental results bearing on the issue of the strange quark content of the nucleon: spin-dependent deep inelastic scattering, elastic neutrino-proton scattering, and the pion-nucleon sigma term. All of these other measurements indicate that the strange quarks play a significant role in the structure of the nucleon.) Theoretical expectations for the magnetic matrix element associated with the strange quark-antiquark pairs are typically G_M^s = -0.3 n.m. The value of G_M^Z determined in the SAMPLE experiment can be used to yield the first determination of

The precision of the measurement will improve with additional planned running of the SAMPLE experiment. The statistical error can be reduced by at least a factor of two, and the systematic errors will be reduced also. Additional future experiments to explore other features of neutral weak currents and strange form factors of the nucleon are planned at Mainz (MAMI-B) and Jefferson Lab (CEBAF). These experiments will open a promising new window on the quark structure of the nucleon, and hopefully will provide important information towards a more complete understanding of nucleon structure in the context of QCD.

This research is funded by the National Science Foundation and the Department of Energy.