Polarization analysis of reactions with four spin-½ particles

The complete polarization structure is developed for a reaction with four spin-½ (plus any number of spin-zero) particles, using the general optimal formalism. The aim is twofold: present practical results for this particular reaction, which is a commonly occurring one in nuclear and particle physics; and to exhibit, on a concrete example, the enormous simplification brought about by the use of this formalism as compared to the more traditional formalisms. The optimal-type formalism, being an infinite class of formalisms, includes, as special cases, helicity- and transversity-type formalisms which can be obtained from the general case by a mere interpretation of the spin indices. With an eye on utility also for inelastic reactions (e.g., $N+N\to N+N+\pi$), besides the general case with only rotation (or Lorentz) invariance, the structure with the sole additional constraint of identical particles is also given. The results are formulated both in terms of entirely polarized and partially unpolarized observables. The experiments needed to obtain information on the amplitudes are described, and it is shown that one can define a "distance" between amplitudes so that the complexity of the experiments needed to obtain information about amplitudes is related to this distance. Besides being applicable to a large array of specific reactions, the results are of interest for the most general particle reaction (involving particles with arbitrary spins), since it can be shown that this latter consists of links of structures of the kind exhibited by the reaction with four spin-½ particles.