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.