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 $f_{\pi}$ only, thus realizing the program proposed by Migdal some time ago.Comment: Version published in JHE

Towards understanding broad degeneracy in non-strange mesons

The spectroscopic regularities of modern empirical data on the non-strange mesons up to 2.4 GeV can be summarized as a systematic clustering of states near certain values of energy. It is getting evident that some unknown X-symmetry triggers the phenomenon. We review the experimental status of this symmetry and recent theoretical attempts put forward for explanation of broad degeneracy.Comment: Brief review, 16 pages, 1 figur

Constraints on Regge models from perturbation theory

We study the constraints that the operator product expansion imposes on large $N_c$ inspired QCD models for current-current correlators. We focus on the constraints obtained by going beyond the leading-order parton computation. We explicitly show that, assumed a given mass spectrum: linear Regge behavior in $n$ (the principal quantum number) plus corrections in $1/n$, we can obtain the logarithmic (and constant) behavior in $n$ of the decay constants within a systematic expansion in $1/n$. Our example shows that it is possible to have different large $n$ behavior for the vector and pseudo-vector mass spectrum and yet comply with all the constraints from the operator product expansion.Comment: 14 pages, 6 figures; two references added, numerical analysis extended, main conclusions unchange

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.Comment: 4 pages, talk given at the First Workshop on Quark Hadron Duality and the Transition to pQCD (June 2005, Frascati, Italy) and at the International Conference on QCD and Hadronic Physics (June 2005, Beijing, China

Theory of phonon-drag thermopower of extrinsic semiconducting single-wall carbon nanotubes and comparison with previous experimental data

A theoretical model for the calculation of the phonon-drag thermopower, $S^{g}$, in degenerately doped semiconducting single-wall carbon nanotubes (SWCNTs) is proposed. Detailed calculations of $S^{g}$ are performed as a function of temperature, tube radius and position of the Fermi level. We derive a simple analytical expression for $S^{g}$ that can be utilized to determine the free carrier density in doped nanotubes. At low temperatures $S^{g}$ shows an activated behavior characteristic of the one-dimensional (1D) character of carriers. Screening effects are taken into account and it is found that they dramatically reduce the magnitude of $S^{g}$. Our results are compared with previous published experimental data in bulk p-doped SWCNT materials. Excellent agreement is obtained in the temperature range 10-200 K for a consistent set of parameters. This is a striking result in view of the complexity of these systems.Comment: 21 pages, 6 figures. This version has been accepted for publication in Phys. Rev.

About the possibility of five-dimensional effective theories for low-energy QCD

The AdS/QCD models suggest an interesting idea that the effective theory of low-energy QCD may be formulated as a 5-dimensional field theory in the weak coupling regime in which the fifth coordinate plays a role of inverse energy scale. Taking the point of view that this is just an efficient parametrization of the non-perturbative dynamics of strong interactions, we discuss on a qualitative level an alternative possibility for a simpler 5-dimensional parametrization of main phenomena in the low-energy QCD. We propose to interpret the effect of chiral symmetry breaking as an effective appearance of compactified extra dimension with the radius of the order of inverse scale of chiral symmetry breaking. Following some heuristic arguments two dual scenarios for the emergence of the excited light mesons are introduced: In the first scenario, the meson resonances are interpreted as the effects of Kaluza-Klein excitations of quarks inside mesons, in the second one, as the formation of gluon strings wound around the compactified dimension an appropriate number of times. Matching of these scenarios permits to express the slope of radial Regge trajectories through the order parameters of the chiral symmetry breaking, with the compactification radius being excluded. This example shows qualitatively that the extra dimension may play an auxiliary role providing a short way for deriving new relations.Comment: 11 pages, accepted by Eur. Phys. J.

1/N_c and 1/n preasymptotic corrections to Current-Current correlators

We obtain the corrections in $1/n$ and in $1/\ln n$ ($n$ is the principal quantum number of the bound state) of the decay constants of scalar and pseudoscalar currents in two and four dimensions in the large $N_c$. We obtain them from the operator product expansion provided a model for the large $n$ mass spectrum is given. In the two-dimensional case the spectrum is known and the corrections obtained in this paper are model independent. We confirm these results by confronting them with the numerical solution of the 't Hooft model. We also consider a model at finite $N_c$ and obtain the associated decay constants that are consistent with perturbation theory. This example shows that that the inclusion of perturbative corrections, or finite $N_c$ effects, to the OPE does not constrain the slope of the Regge trajectories, which remain a free parameter for each different channel.Comment: 29 pages, 11 figures. Two references adde

Implications of the Crystal Barrel data for meson-baryon symmetries

Making use of numerous resonances discovered by the Crystal Barrel Collaboration we discuss some possible relations between the baryon and meson spectra of resonances composed of the light non-strange quarks. Our goal is to indicate new features that should be reproduced by the realistic dynamical models describing the hadron spectrum in the sector of light quarks.Comment: Completely modified version; to appear in Mod. Phys. Lett.