A Coulomb Experiment for the Weak Nuclear Force

Physicists at the SLAC accelerator have measured, with much greater precision than ever before, the variation in the weak nuclear force, one of the four known physical forces, over an enormous size scale (a distance of more than ten proton diameters) for so feeble a force. Although the results were not surprising (the weak force diminished with distance as expected) this new quantitative study of the weak force helps to cement physicists’ view of the sub-nuclear world.

The SLAC work is, in effect, a 21st century analog of the landmark 18th experiments in which the intrinsic strength of the electromagnetic and gravitational forces were measured (by Charles Coulomb and Henry Cavendish, respectively) through careful observation of test objects causing a torsion balance to swing around. The weak force, in the modern way of thinking, is a cousin of the electromagnetic (EM) force; both of them are considered as different aspects of a single “electroweak” force.

The EM force is much better known to physicists and to non-experts: it’s responsible for all electric, magnetic, and optical phenomena, and keeps atoms intact and holds atoms together in all the molecular and crystalline forms which make up our world. Over sizes larger than the atom, the strength of the EM force is prescribed by Coulomb’s law, which states that the force between two charged objects (say, two electrons) is proportional to the charges of the electrons and inversely to the square of the distance between them.

For sub-atomic distances the Coulomb way of describing electron scattering gets complicated because of vacuum polarization, a process which takes into account the fact that at short distances an electron can longer be portrayed as a lone pointlike particle; instead we must view it as accompanied by a cloud of virtual particles sprouting out of the vacuum. These extra short-lived particles serve to redefine, or “renormalize,” the effective electron charge and along with it the very nature of the EM force mediating the interaction with the other electron.

The weak force is an important force---responsible for some kinds of radioactivity and for select fusion reactions vital to energy production inside the sun---but is very different from the electromagnetic force and generally operates only over the tight confines of the nucleus. In this realm, the weak force is right there along with the EM force, a doppelganger that can often be ignored because it is so very weak. But physicists, in search of a fuller explanation of the universe, don’t want to ignore the weak force.

At SLAC they painstakingly extract weak effects from the much larger EM effects involved when two electrons interact. In the case of their present experiment (E158), a powerful electron beam scatters from electrons bound to hydrogen atoms in a stationary target. By using electrons that have been spin polarized---that is, the electron’s internal magnetism (or spin) has been oriented in a certain direction---the weak force can be studied by looking for subtle asymmetries in the way electrons with differing polarizations scatter from each other.

One expects an intrinsic falloff in the weak force with the distance between the electrons. It should also fall off owing to the cumbersome mass possessed by the Z boson. Finally, the weak force weakens because the electron's "weak charge" becomes increasingly shielded (just as the electron’s electrical charge had been) owing to a polarization of the vacuum---but this time with virtual quarks, electrons, and W and Z bosons needing to be taken into account.

Previously, the weak charge has been well measured only at a fixed distance scale, a small fraction of the proton's diameter. The SLAC result over longer distances confirms the expected falloff. According to E158 researcher Yury Kolomensky (yury@physics.berkeley.edu), the result is precise enough to rule out certain theories that invoke new types of interactions, at least at the energy scale of this experiment. (Anthony et al., Physical Review Letters, upcoming article; lab website, http://www-project.slac.stanford.edu/e158)