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.
Highlights
It is widely known that the physics of non-perturbative strong interactions is encoded in the hadron masses
The given resonance is identified as f0(500) [1] and is indispensable for description of the chiral symmetry breaking in many phenomenological field models for the strong interactions
Our intention was to confirm the absence of a light scalar particle among usual mesons using the QCD sum rules in the large-Nc limit combined with the Regge phenomenology
Summary
It is widely known that the physics of non-perturbative strong interactions is encoded in the hadron masses. A well-known phenomenological way for extraction of masses and other characteristics from the correlators is provided by various QCD sum rules. The zero-width approximation (and simultaneously the absence of multiparticle cuts) arises in the large-Nc (called planar) limit of QCD [7,8] In this limit, the only singularities of the two-point correlation function of a hadron current J are one-hadron states [8]. The logarithmic behavior of the right-hand side of (1) emerges naturally if one has the following large-n asymptotics: Fn2 ∼ const, Mn2 ∼ 2n Such a Regge-like behavior for masses of radially excited states appears in the twodimensional QCD in the planar limit [9], Veneziano dual amplitudes [10,11], and various hadron string models [12– 17]. Our intention was to confirm the absence of a light scalar particle among usual mesons using the QCD sum rules in the large-Nc limit combined with the Regge phenomenology.
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