Dynamical $\mathbf{O(4)}$-Symmetry in the Light Meson Spectrum within the Framework of the Regge Approach

TL;DR

This paper investigates the approximate $O(4)$-symmetry in the light meson spectrum, showing that meson masses depend on the sum of angular and radial quantum numbers, consistent with a hydrogen-like symmetry, using Regge trajectories and data analysis.

Contribution

It demonstrates that the light meson spectrum exhibits an $O(4)$-symmetry, with masses depending on the sum of quantum numbers, supported by data fits and semiclassical analysis.

Findings

Meson masses follow linear Regge trajectories.

Masses depend on the sum of angular and radial quantum numbers.

Data supports $a eq b$, indicating $l + n_r$ dependence.

Abstract

The light mesons tend to cluster near certain values of mass. As was noticed almost twenty years ago, the emergent degeneracy is of the same type as the dynamical $O(4)$-symmetry of the Coulomb potential in the hydrogen atom. The meson mass spectrum can be well approximated by the linear Regge trajectories of the kind $M^2=al+bn_r+c$, where $l$ and $n_r$ are angular momentum and radial quantum numbers and $a$, $b$, $c$ are parameters. Such a spectrum arises naturally within the hadron string models. Using 2024 data from the Particle Data Group, various fits for $M^2(l,n_r)$ were performed. Our analysis seems to confirm that $a\approx b$ in the light non-strange mesons, i.e., their masses depend on the sum $l+n_r$ as prescribed by the hydrogen-like $O(4)$-symmetry. Using the semiclassical approximation, we discuss on a simple qualitative level which kind of string-like semirelativistic approaches are more favored by the experimental data.