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

TL;DR

This paper extends a universal logarithmic mass equation to predict baryon and meson excited states, demonstrating accurate fits and predictive power for higher mass states, especially in bottomonium systems.

Contribution

It introduces a simple one-parameter logarithmic model for excited-state masses and applies it to multiple baryon and meson sets, including predictions for unknown states.

Findings

The model fits 12 baryon and 16 meson sets accurately.

The parameter $eta$ for $b\bar{b}$ states lies on a straight line, enabling predictions.

Predicted higher mass states show good agreement with known data.

Abstract

We extend our recent study of the universal mass equation for equal-quantum excited-states sets reported by Roper and Strakovsky~\cite{Roper:2024ovj}. 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 at fixed $J^P$ for baryons and $J^{PC}$ for mesons, are fitted by a simple one-parameter logarithmic function, $M_n = \alpha Ln(n) + M_1$, where $n$ is the level of radial excitation. Two accurate masses that start a set are used to calculate four higher masses in the set accurately. It is noted that $\alpha$ values for $b\bar{b}$ equal-quantum excited-states sets accurately lie on a straight line, whose line parameters can be used to calculate $\alpha$ and predict higher mass states for $b\bar{b}$ sets that have only one known member.