Baryon and Meson Excited States

TL;DR

This paper proposes a simple logarithmic function to fit the masses of baryon and meson excited states, suggesting a universal relation that accurately describes their mass spectra across various quantum states.

Contribution

It introduces a universal two-parameter logarithmic mass formula for excited baryon and meson states, validated with recent PDG2024 data.

Findings

The mass formula fits 15 baryon and 24 meson sets with high accuracy.

The formula applies across different quantum numbers and exotic states.

It provides a unified description of excited state masses.

Abstract

The masses of fifteen baryon sets and twenty-four meson sets of three or more equal-quantum excited states are fitted by a simple two-parameter logarithm function, $M_n = \alpha Ln(n) + \beta$, where $n$ is the level of radial excitation. The conjecture is made that accurately measured masses using Breat-Wigner PDG2024 data at fixed $J^P$ for baryons and $J^{PC}$ for mesons of all equal-quantum baryons (including LHCb exotic $P_{c\bar{c}}^+$s) and meson (including $s\bar{s}$, $s\bar{c}$, $c\bar{c}$, $c\bar{b}$, and $b\bar{b}$) excited states are related by the logarithm function used here; at least for the mass range of currently known excited states. Thus, a universal mass equation for equal-quantum excited-states sets is presented. The masses of twelve baryon sets and sixteen meson sets, with only two equal-quantum excited states in each set, using Breit-Wigner PDG2024 masses and their uncertainties, are fitted by thr universal mass equation.