PARITY, NONCONSERVATION OF

The 1957 discovery that parity was not conserved in weak interactions hit the world of particle physics like a minibombshell. Before then it had been assumed that parity was conserved in all interactions. However, on close scrutiny this assumption turned out to have no firm foundation, and nature, as it were, took advantage of the loophole. Even now some of the repercussions of parity violation are not understood at a profound level, but nevertheless parity violation has been incorporated successfully into the Standard Model.

Definition of Parity

Parity is concerned with the inversion of the space coordinates: The question is, "Are the laws of nature invariant under this operation?" In a world that differs from our world in this way, are the laws of nature the same as those we know, or not? It is important to remark that other questions of a very similar type have very clear answers. For example, one knows that the laws of nature are the same when a rotation is performed in space. Invariance under rotations is intimately related to the conservation of angular momentum, and there is abundant evidence that this holds. But it turns out, surprisingly, that parity is different: the laws of nature are not quite invariant under parity.

The Puzzle of K Decays

The first hint of trouble came with the observation of the decay of neutral kaon particles. These are spinless particles that are generally expected to have a parity quantum number η = ±1; in fact, the kaons, and also the pions into which they decay, actually have negative parity, η = -1. The problem began when it was found that kaons can decay in two distinct ways—either into two pions or into three: In these decays the parity of the decay products in each case is simply the product of the parities of the pions, that is, (1)² = +1 in the first decay and (1)³ =-1 in the second. If parity were conserved, since the kaon has negative parity, only the second decay would be allowed (and, of course, if it had positive parity, then only the first decay). The fact that κ⁰ decays into two final states with opposite parity posed a real puzzle in 1956.

Parity Violation in Beta Decay

The solution to this puzzle was suggested by two Chinese-American physicists, Tsung Dao Lee and Chen Ning Yang, who made the highly interesting suggestion that weak interactions, as a class, do not in general conserve parity. The previously mentioned decays of the kaon result from weak interactions. This proposal clearly solves the problem of κ decays (the solution being that the first decay above violates parity, while the second conserves it), but it also implies that parity is violated in nuclear beta decay, since this is also due to the weak interaction. The most compelling feature of this prediction is that it should be possible to see directly—with the naked eye, as it were—whether or not parity is conserved in beta decay. Nuclear beta decay is, in essence, neutron decay (the beta particles being the electrons e -): Lee and Yang proposed an experiment that was carried out by Chien-Shiung Wu and collaborators in1957. They investigated the decay of ⁶⁰Co nuclei, in which a neutron decays into a proton, emitting an electron, as described above. The decaying nuclei are polarized by placing them in a strong magnetic field. This means that the neutron spin is aligned in space. What Wu and her collaborators found was that the electrons are emitted in an opposite direction to the nuclear spin. This is direct proof of parity violation. Perhaps the easiest way to see this is to note that the parity operation just defined may be expressed as a combination of two operations: (1) x →-x , y →-y , z unchanged, and (2) x and y unchanged, z →-z .

The first operation is simply a rotation about the z -axis through 180⁰—and it is already known that the laws of nature are invariant under rotations. The second operation is a mirror reflection, the mirror being in the xy -plane. A test of invariance under parity is therefore a test of invariance under mirror reflection. Figure 1 shows ⁶⁰Co decay, with the nuclear spin aligned in a magnetic field generated by a solenoid. The experimental result (left half of the diagram) is that the electron momentum is antiparallel to the nuclear spin. In the mirror (right half of diagram), however, the magnetic field is reversed because the solenoid windings are reversed, but the electron momentum is not reversed, so in the "mirror experiment" the electron

FIGURE 1

momentum and nuclear spin would be parallel. The experiment and its mirror image are thus different: beta decay violates parity. It distinguishes between left and right and is the only fundamental interaction to do so. (If it were the case that weak interactions, and therefore beta decay, conserved parity, then in the Wu experiment it would have been observed that electrons were emitted with no preferential direction, that is, they would travel equally in all directions. This would clearly look the same in a mirror.)

Left-handed Neutrinos

Why does beta decay violate parity? It turns out that the blame can be laid on the neutrino. In 1957 Lee and Yang, and Lev Landau in the Soviet Union and Abdus Salam in England, made the suggestion that the neutrino was a purely left-handed particle. That is, the projection of its spin in the direction of motion is always negative. This immediately has the consequence that any experiment involving neutrinos is bound to violate parity. The experiment observed in a mirror is bound to look different since a (left handed) neutrino, looked at in the mirror, will be a right-handed neutrino, which does not exist. Now this suggestion is not a trivial one for it can only hold if the neutrino has no rest mass. To see this, consider a neutrino observed in the lab traveling at a speed of ν(<c ). It is left-handed, so its spin is in the opposite direction of its momentum. Now consider the situation in a moving frame of reference. If one "overtakes" the neutrino, its velocity will be reversed, but not its spin, so in this frame it would then appear right-handed. If the neutrino is only ever to be left-handed, this observation must be forbidden. It must be impossible to overtake the neutrino, which means that it must travel at the speed of light, and this, in turn, means it must be massless (like a photon). Traditionally, neutrinos have been considered to be massless, but recently doubt has been cast on this assumption, particularly in the theory of neutrino oscillations. Interestingly, this idea does not deal a deathblow to parity violation. For, even if neutrinos do have a mass (and oscillations are therefore possible), it may be so small (in comparison with their kinetic energy) that they behave as if they were massless.

The way in which parity violation is built into the Standard Model is actually quite straightforward. It is simply stated, as an axiom, that the fundamental leptons in electroweak theory are the (weak isospin) doublet of left-handed particles (v–_e, e_L) and the right-handed singlet e_R. The neutrino is purely left-handed, and the left-handed and right-handed parts of the electron enter the theory on a different footing. This automatically yields parity violation in beta decay, and in the weak interactions in general, and almost miraculously nowhere else, just as desired!