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 = αLn(n)+β, 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.