S. S. Afonin

Matching Regge theory to the OPE

The spectra of masses and decay constants for non-strange meson resonances in the energy range 0–2.5 GeV is analyzed. It is known from meson phenomenology that for given quantum numbers these spectra approximately follow linear trajectories with a universal slope. These facts can be understood in terms of an effective string description for QCD. For light meson states the trajectories deviate noticeably from the linear behavior. We investigate the possible corrections to the linear trajectories by matching two-point correlators of quark currents to the Operator Product Expansion (OPE). We find that the allowed modifications to the linear Regge behavior must decrease rapidly with the principal quantum number. After fitting the lightest states in each channel and certain low-energy constants the whole spectrum for meson masses and residues is obtained in a satisfactory agreement with phenomenology. We briefly speculate on possible implications for the QCD effective string.

Properties of possible new unflavored mesons below 2.4 GeV

The global features of spectrum of highly excited light nonstrange mesons can be well understood within both chiral symmetry restoration scenario combined with the relation M 2 ∼ J + n and within a nonrelativistic description based on the relation M 2 ∼ L + n. The predictions of these two alternative classifications for missing states are different and only future experiments can distinguish between the two. We elaborate and compare systematically the predictions of both schemes, which may serve as a suggestion for future experiments devoted to the search for missing states.

Quark condensate and deviations from string-like behaviour of meson spectra

Abstract I analyze the hypothesis that deviations from the linear meson mass spectra appear due to the dynamical chiral symmetry breaking in QCD. It is shown that the linear mass spectrum for the light, non-strange vector and axial-vector mesons is then parametrized by the constant f π , being successful phenomenologically. The toy model for deviations from linearity is proposed.

Experimental indication on chiral symmetry restoration in meson spectrum

Abstract The spectroscopic predictions of the Ademollo–Veneziano–Weinberg dual model are critically tested in view of the modern experimental data. The predicted equidistance of masses squared for chiral partners is shown to be violated high in energies, instead one observes an approximate degeneracy of these quantities. This phenomenon can be interpreted as the restoration of Wigner–Weyl realization of chiral symmetry for highly excited states. The scale of complete restoration is expected to be 2.5 GeV. A multispin-parity cluster structure of meson spectrum is revealed.

Qualitative solution of QCD sum rules

We show how such important features of QCD as chiral symmetry breaking or the formation of a mass-gap can be directly traced from QCD sum rules for two point functions assuming, in the large number of colors limit, exact duality between the operator product expansion and the spectrum described by linearly (or nearly linear) rising Regge trajectories as predicted by string theory. We see how the presence of chiral symmetry breaking is intimately related to confinement in this scenario, as expected from general arguments, and how Regge trajectories change when chiral symmetry is broken. As a result the whole meson mass spectrum can be parametrized with a good accuracy by the constant fπ only, thus realizing the program proposed by Migdal some time ago.

Low-energy holographic models for QCD

We consider bottom-up holographic models for quantum chromodynamics (QCD) that are constrained by the ultraviolet (UV) cutoff. Such models are supposed to exclusively describe the low-energy sector of QCD. The introduction of the UV cutoff in the soft-wall model is shown to result in a model with qualitatively different predictions. The ensuing model seems able to incorporate the constituent quark mass. We also demonstrate that in order to reproduce the results of the usual soft-wall model for the vector and higher-spin mesons in the presence of the UV cutoff, one can consider the flat bulk space with a modified dilaton background.

Generalized Soft Wall model

Abstract We develop an exactly solvable generalization of the Soft Wall holographic model for the vector mesons. The generalization preserves the ultraviolet and infrared asymptotics of the Soft Wall model and contains an additional free parameter. This new parameter provides an arbitrary intercept in the Regge like spectrum of radial excitations and leads to a substantial modification of asymptotic expansion of the vector correlator at large momentum. The matching to the Operator Product Expansion from QCD allows to estimate the value of the new parameter which is shown to be in a good agreement with the phenomenology. In addition, the mass splitting between the vector and axial mesons arises naturally via the opposite sign of the introduced contribution to the intercept.

Contribution of higher meson resonances to the electromagnetic pion-mass difference

Some modifications of the formula for calculating the electromagnetic pion-mass difference are proposed on the basis of the chiral-symmetry-restoration phenomenon at high energies and the operator-product expansion of quark densities for vector (ρ) and axial-vector (a1) meson fields. All calculations are performed through taking into account higher meson resonances in the vector and axial-vector channels. It is shown that the inclusion of only the first ρ0 and a1 radial excitations improves the results of the calculation for the electromagnetic pion-mass difference in relation to the known ones. The electromagnetic ρ-and a1-meson decay constants and the constant L10 of the effective chiral Lagrangian are estimated with the aid of the generalized Weinberg sum rules.

MATCHING MESON RESONANCES TO OPE IN QCD

We investigate the possible corrections to the linear Regge trajectories for the light-quark meson sector by matching two-point correlators of quark currents to the Operator Product Expansion. We find that the allowed modifications to the linear behavior must decrease rapidly with the principal quantum number. After fitting the lightest states in each channel and certain low-energy constants the whole spectrum for meson masses and residues is obtained in a satisfactory agreement with phenomenology. The perturbative corrections to our results are discussed.

Weinberg like sum rules revisited

The generalized Weinberg sum rules containing the difference of isovector vector and axial-vector spectral functions saturated by both finite and infinite number of narrow resonances are considered. We give a historical survey and summarize the status of these sum rules analyzing their overall agreement with phenomenological Lagrangians, low-energy relations, parity doubling, hadron string models, and experimental data.PACS codes: 11.55.Hx, 11.30.Rd