Linearity, Nonlinearity and Universality of Regge Trajectories in Light Mesons: a Statistical Approach

Abstract

The masses of light non-strange mesons can be parameterized as a function of the radial quantum number $n$ and the orbital angular momentum $L$. We perform a comprehensive statistical and phenomenological comparative analysis of competing Regge-like formulas evaluated against two experimental datasets: a benchmark sample of 27 well-established states from the 2024 Particle Data Group (PDG) data, and an expanded sample of 85 states compiled within a recently proposed $(L,n)$-classification. Two linear Regge models for $M^2(L,n)$ are tested: one featuring distinct slopes for $L$ and $n$, $M^2(L,n)\propto an+bL$ (Model 1), and another assuming a universal slope, $M^2(L,n)\propto a(n+L)$ (Model 2). Model selection is conducted quantitatively using the Residual Sum of Squares (RSS), the adjusted RSS, the Akaike Information Criterion (AIC), and the Bayesian Information Criterion (BIC). Within the 27 benchmark states, Model 2 is statistically disfavored. We argue, however, that this discrepancy is driven by the specific behavior of $S$-wave ($L=0$) states. Upon their exclusion, the difference in performance between the two models becomes statistically insignificant, with information criteria selecting Model 2 as the more parsimonious description. Furthermore, we demonstrate that the masses of $S$-wave states can be successfully accommodated by a physically motivated, nonlinear $L$-dependent correction. A parallel analysis of the extended 85-state dataset, where the relative contribution of $S$-wave states is significantly smaller, reveals that Model 2 is statistically preferred, thereby restoring the Coulomb-like degeneracy in the Regge spectrum under consideration.