The sigma meson from QCD sum rules for large-$N_c$ Regge spectra

TL;DR

This paper uses QCD sum rules and Regge spectra in the large-$N_c$ limit to analyze meson spectra, proposing an improved method that predicts a light scalar meson consistent with $f_0(500)$.

Contribution

It introduces an enhanced analysis method for meson spectra using Regge trajectories, overcoming previous limitations in fixing ground state masses.

Findings

The method yields realistic meson mass values.

Predicts a light scalar meson near the $f_0(500)$ mass.

Supports the Regge phenomenology for scalar mesons.

Abstract

The QCD sum rules in the large-$N_c$ limit for the light non-strange vector, axial and scalar mesons are considered assuming a string-like linear spectrum for the radially excited states. We propose a improved method for combined analysis of these channels that gives a reasonable description of the observed spectrum. In the vector-axial case, fixing the pion decay constant and the gluon condensate we obtain more or less physical values for the masses of ground states and the quark condensate. Thus a typical need for this method to fix the mass of some ground state is overcome. Using in the scalar channel the values of presumably universal slope of radial trajectories and the quark condensate obtained in the vector-axial channel, we find that, in contrast to some strong claims in the literature, a prediction of light scalar state with a mass close to the mass of $f_0(500)$ seems to be natural in the considered approach and may follow in a natural way from the Regge phenomenology.