Systematics of radial and angular-momentum Regge trajectories of light nonstrangeqq¯-states

Abstract

We reanalyze the radial (n) and angular-momentum (J) Regge trajectories for all light-quark states with baryon number zero listed in the 2011 edition of the Particle Data Tables. The parameters of the trajectories are obtained with linear regression, with weight of each resonance inversely proportional to its half-width squared, $(\Gamma/2)^2$. That way we are side-stepping possible channel-dependent and model-dependent extractions of the resonance parameters and are able to undertake an error analysis. The method complies to the fact that the pole position of the resonance is typically shifted from channel-dependent extractions by $\sim\Gamma/2$. This is also a feature of the large-$N_c$ limit of QCD, where the masses change by $ \Gamma/2$ when evolving from $N_c=3$ to $N_c=\infty$. Our value for the slope of the radial Regge trajectories is $a=1.35(4) GeV^2$. We discuss the fundamental issue whether the masses of the light-quark non-strange states fit into a universal pattern $M_{nJ}^2 = a(n+J) +b$, as suggested by Afonin, and also predicted by some holographic models. Our joint linear-regression analysis in the $(n,J,M^2)$ Regge planes indicates, at a statistically significant level of 4.5 standard deviations, that the slopes of the radial Regge trajectories are larger from the angular-momentum slopes. Thus no strict universality of slopes occurs in the light non-strange meson spectra.