Universal Mass Equation for Equal-Quantum Excited-States Sets I

Abstract

The masses of fifteen baryon sets and twenty-four meson sets of three or more equal-quantum excited states, using Breit-Wigner PDG masses and their uncertainties at fixed $J^P$ for baryons and $J^{PC}$ for mesons, are fitted by a simple two-parameter logarithmic function, $M_n = \alpha Ln(n) + \beta$, where $n$ is the level of radial excitation. The conjecture is made that accurately measured masses of all equal-quantum baryons (including LHCb exotic $P_{c\bar{c}}^+$s) and meson excited states (including $s\bar{s}$, $s\bar{c}$, $c\bar{c}$, $c\bar{b}$, and $b\bar{b}$ states) are related by the logarithmic function used here; at least for the mass range of currently known excited states. The baryon ``star'' rating case is evaluated. The Cornell potential is an example of how a logarithmic behavior can be explained by an appropriate potential. Thus, a ``universal mass equation'' (UME) for equal-quantum excited-state sets is presented.