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

arXiv commentMany new discussions concerning the origin of sigma-meson mass, its angular Regge trajectory, comparison with other results etc. are added to Sections 5 and 6. The new text corresponds to the version published in Eur. Phys. J. C

References in corpus (51)

• Glueballs, Hybrids, Multiquarks. Experimental facts versus QCD inspired concepts
• From controversy to precision on the sigma meson: a review on the status of the non-ordinary $f_0(500)$ resonance
• Systematics of q anti-q states in the (n,M^2) and (J,M^2) planes
• Four Sorts of Mesons
• Systematics of radial and angular-momentum Regge trajectories of light non-strange q\bar{q}-states
• Duality violations and spectral sum rules
• Scalar Particles in Lattice QCD
• QCD string in light-light and heavy-light mesons
• Highly Excited Mesons, Linear Regge Trajectories and the Pattern of the Chiral Symmetry Realization
• Snapshots of Hadrons, or the Story of How the Vacuum Medium Determines the Properties of the Classical Mesons Which Are Produced, Live and Die in the QCD Vacuum
• Properties of new unflavored mesons below 2.4 GeV
• Universal description of radially excited heavy and light vector mesons
• QCD Sum-Rule Consistency of Lowest-Lying Quark Scalar Resonances
• Light meson spectrum and classical symmetries of QCD
• Matching Regge Theory to the OPE
• Large-Nc QCD meets Regge theory: the example of spin-one two-point functions
• Generalizing the Noether theorem for Hopf-algebra spacetime symmetries
• Towards understanding broad degeneracy in non-strange mesons
• Semiclassical Quantization of Effective String Theory and Regge Trajectories
• Constraining Quark-Hadron Duality at Large-Nc
• Parity doubling in particle physics
• Experimental indication on chiral symmetry restoration in meson spectrum
• On the use of the Operator Product Expansion to constrain the hadron spectrum
• Quark condensate and deviations from string-like behaviour of meson spectra
• Perturbative expansions in QCD and analytic properties of alpha_s
• Dimension-two gluon condensate from large-Nc Regge models
• Holographic like models as a five-dimensional rewriting of large-Nc QCD
• Qualitative solution of QCD sum rules
• Identification of non-ordinary mesons from the dispersive connection between their poles and their Regge trajectories: the f0(500) resonance
• Scalar-isoscalar states in the large-Nc Regge approach
• Scalar Mesons in QCD
• Lattice QCD study of four-quark components of the isosinglet scalar mesons: Significance of disconnected diagrams
• Hydrogen like classification for light nonstrange mesons
• Cluster duality
• Analytic Quantization of the QCD String
• Spin-1 Correlators at Large NC: Matching OPE and Resonance Theory up to O(alpha_s)
• Is the spectrum of highly excited mesons purely coulombian?
• Meson and glueball spectra with the relativistic flux tube model
• Note on universal description of heavy and light mesons
• The large degeneracy of excited hadrons and quark models
• Reply to "Comment on 'Systematics of radial and angular-momentum Regge trajectories of light non-strange qqbar-states' "
• Dimension-2 condensates, zeta-regularization and large-Nc Regge Models
• Constraints on Regge models from perturbation theory
• Comments on `Systematics of radial and angular-momentum Regge trajectories of light non-strange $q\bar{q}$ states', Masjuan, Arriola and Broniowski
• Implications of the Crystal Barrel data for meson-baryon symmetries
• Contribution of higher meson resonances to the electromagnetic $\pi$-meson mass difference
• Parity doubling from Weinberg sum rules
• Current correlators in QCD: OPE versus large distance dynamics
• Weinberg like sum rules revisited
• Lower and upper bounds on the mass of light quark-antiquark scalar resonance in the SVZ sum rules
• Lagrangian alternative to QCD string

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• Towards a theory of bottom-up holographic models for linear Regge trajectories of light mesons
• Electromagnetic couplings of radially excited light vector mesons from QCD sum rules
• Exact relativistic Green's functions for the time-independent potentials
• Large-$N_c$ masses of light mesons from QCD sum rules for non-linear radial Regge trajectories
• The large-Nc limit of borelized spectral sum rules and the slope of radial Regge trajectories
• The case of equivalence of low and high energy constraints on Regge vector spectrum in AdS/QCD
• The linear radial spectrum of scalar mesons within the QCD sum rules in the planar limit