Empirical Mass Relations Involving the Strongly Interacting Particles

Abstract

A set of mass relations which connect the masses of the strongly interacting particles is presented. All of the observed particle masses can be represented with good accuracy by a simple additive relation, in which there enter only two fundamental constants. We have also obtained many examples of the relation $m_3=m_1+m_2$ where $m_1$, $m_2$, and $m_3$ are the masses of three strongly interacting particles. It is shown that there exist many cases of particle pairs having the same mass difference, i.e., $m_1-m_2=m_3-m_4$. Moreover, there are about 20 sequences of particles, where a sequence is defined as a group of three or more particles with the same mass spacing. A set of simple mass relations has been obtained for the $K$ meson, and the $K^{*}\mathrm{}\left(725\right)\mathrm{}$ and $K^{*}\mathrm{}\left(888\right)\mathrm{}$ resonances. The relation of the mass of the $\mu$ meson to the mass spectrum of the strongly interacting particles has been investigated. Finally, it has been found that for a large number of particle pairs ($a, b$), we have the relation $m_b=\lambda m_a$, where $\lambda$ is a simple fraction.