SPIN AND PARITY DETERMINATION OF ELEMENTARY PARTICLESl

A central problem in the physics of elementary particles concerns the establishment of their quantum numbers. Recent developments in the theoretical classification of particles states have added impetus to this ac­ tivity as a means of making meaningful confrontation between theoretical proposals and experiment. In this review we confine our attention to the in­ ternal quantum numbers of spin and parity. Particular emphasis is placed on the more recently discovered unstable states, usually called resonances, which decay by strong interactions, although metastable states, which decay by electromagnetic or weak interactions, and energetically stable states are also discussed. The spin J is the intrinsic angular momentum in units of fj associated with a particle such that the square of this angular momentum is J(J + 1)fj2. For a resonant state it consists of the vector sum of the orbital angular momentum 1 and the intrinsic spins of its constituents. By parity is meant the intrinsic behavior of the particle state under an inversion of spatial co­ ordinates, this operation having eigenvalues ± 1. The formal theory of parity has been reviewed by Wick (1) . Although the concept appears to have some profound aspects, the following simple operational understanding suffices for its experimental determination. The parity of a system consists of the prod­ uct of the parities of its constituents. This includes the parity of orbital motion given by (_1)l, as well as the intrinsic parities of the subsystems. I f the transformation from one state to another conserves parity, the system will have the same parity before and after the transformation. Measuring the change in orbital states of the subsystems thereby measures the relative parity of the constituents in the initial and final states. We may illustrate this by two examples. First consider a two-particle collision in which a new pair of particles is produced. A measurement of the initial and final orbital angular momenta then establishes the relative parity of any one of the par­ ticles with respect to the product of the other three. Another example is the decay of a particle of unknown parity into three particles. When the orbital parity of any pair of particles and also of that pair with respect to the third have been determined, the relative parity of the initial particle is fixed with respect to the final particles.