Classification of the Fundamental Particles

Abstract

The decay and production processes of the pions, $K$-mesons, nucleons, and hyperons are classified in terms of selection rules for an integral quantum number, $a$, called the "attribute," which is assigned a definite value for each particle and assumed to be additive when particles are combined. No attempt is made to relate the attribute to other physical properties of the particles. The scheme suggests relationships between processes which have yet to be observed such as the associated production of a cascade particle with two (positive or neutral) $K$-mesons. When it is combined with the notion of isotopic spin ($I$) conservation, it suggests the existence of several new particles, the ${\ensuremath{\Sigma}}^{0}$ of Gell-Mann and Nishijima, a ${\ensuremath{\Xi}}^{0}$ and a neutral $K$-meson differing in its properties from the ${\ensuremath{\theta}}^{0}$. Results of isotopic spin assignments suggest the rule (odd-even rule) that even-$a$ fermions have half-integral $I$, odd-$a$ fermions have integral $I$, and conversely for the bosons. There are also implications concerning the interactions between various particles: the range of the potential binding the ${\ensuremath{\Lambda}}^{0}$ to a nucleon should be of the order of the $K$-meson Compton wave length.The classification is extended to include electrons, neutrinos, and muons with the result that their attributes must be half-integral. In order to exclude certain unobserved processes, it is necessary to assume that the neutrino is the source of the weak (Fermi) interaction of fermions, in contrast to the notion of the universal Fermi interaction. The existence of an antineutrino is strongly suggested. The ${K}_{\ensuremath{\mu}3}$ and ${K}_{e3}$ (considered as one particle) may be interpreted as a boson ($K$) or fermion ($\ensuremath{\kappa}$). In the former case, the decay schemes ${K}^{\ifmmode\pm\else\textpm\fi{}}\ensuremath{\rightarrow}{e}^{\ifmmode\pm\else\textpm\fi{}}+\ensuremath{\nu}$, ${K}^{0}\ensuremath{\rightarrow}2\ensuremath{\nu}$, and ${K}^{0}\ensuremath{\rightarrow}\ensuremath{\pi}+\ensuremath{\mu}+\ensuremath{\nu}$ are expected to occur. In the latter case, production of the $\ensuremath{\kappa}$ through the decay process $K\ensuremath{\rightarrow}\ensuremath{\kappa}+\ensuremath{\nu}$ is suggested.Several unusual new events are classified in Sec. VI in order to illustrate the method. A table of thresholds for production of the various particles is included in an Appendix. No excuse is offered for the nonoccurrence of $\ensuremath{\pi}\ensuremath{-}e$ decay.