Theory of Pionization

In this paper we make a detailed study of the phenomenon of pionization. We first concentrate on processes in which the two incident particles are identical, e.g., proton-proton scattering. By assuming that the c.m. system has no special significance in high-energy scattering or, more precisely, by assuming that the distribution of pionization products has a forward-backward symmetry not only in the c.m. system but also in a class of coordinate systems called the $C$ systems (this assumption will be called the symmetry hypothesis), we can get rather precise information about the dependence of pionization distribution on the longitudinal momenta. In particular, the one-particle distribution function is $\frac{f\left({\mathbf{p}}_{\perp }\right)d^{3}p}{E}$. These results are then explicitly verified in the model of quantum electrodynamics. Next, the considerations are extended to processes in which the two incident particles are different. For such processes, we propose the limiting hypothesis: The distribution of the pionization products is independent of the momenta of either of the incident particles in the limit the incident momenta are both infinite. With this hypothesis we can again obtain quantitative information on the dependence of the pionization distribution on the longitudinal momenta. When applied to the special case of identical particles, the limiting hypothesis is equivalent to the symmetry hypothesis. For the more general case where the two incident particles are not identical, it follows from the limiting hypothesis that the one-particle distribution function is again $\frac{f\left({\mathbf{p}}_{\perp }\right)d^{3}p}{E}$, but the results on the multiparticle distribution functions are slightly weaker than those for identical particles. The limiting hypothesis is then shown to be valid in various field-theory models. The process of photon-fermion scattering is studied in particular detail. We also investigate the process of bremsstrahlung and show that it gives no pionization products. Finally, the above results are examined in the context of scalar electrodynamics, and all of the qualitative features are found to be the same.