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

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 an 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.

Towards a theory of bottom-up holographic models for linear Regge trajectories of light mesons

“…[74] was (in GeV (crosses) mesons according to the Refs. [92,109]. The horizontal lines are drawn to distinguish better the position of scalar resonances [91].…”

“…It means that if a radial trajectory is fitted using only the excited states and after that the mass of ground state is predicted, the prediction will appreciably overestimate the real mass (see, e.g., the discussions in Ref. [92] and the Fig. 6 in the Appendix E).…”

The Large-$N_{\rm c}$ Masses of Light Scalar Mesons from QCD Sum Rules for Linear Radial Spectrum

“…Within the latter assumption, the mass of σ-meson can be derived as a function of the intercept parameter m 2 s (we refer to Ref. [8] for details, the chiral limit is considered),…”

The linear radial spectrum of scalar mesons from QCD sum rules in the planar limit

“…Within the latter assumption, the mass of σ-meson can be derived as a function of the intercept parameter m 2 s (we refer to Ref. [6] for details, the chiral limit is considered),…”

“…1 [6]. The mass of the first radially excited state M S (1) is rather stable and seems to reproduce the mass of a 0 (1450)-meson, M a 0 (1450) = 1474 ± 19 MeV [7].…”