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 ${\Sigma }^0$ of Gell-Mann and Nishijima, a ${\Xi }^0$ and a neutral $K$-meson differing in its properties from the ${\theta }^0$. 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 ${\Lambda }^0$ to a nucleon should be of the order of the $K$-meson Compton wave length.