QCD string in the Schwinger-Dyson approach to heavy-light quarkonia

The kernel of the Schwinger-Dyson equation for a heavy-light quarkonium is studied in the limit of potential quark dynamics, and the string correction to the quark-antiquark potential is derived in agreement with the results of the quantum-mechanical QCDs tring approach. Possible ways of further improvement of the method are outlined and discussed.     

Spectrum of heavy-light mesons in the QCD string picture

We describe in detail predictions of the QCD string approach for the masses of the heavy—light D, D _s , B, and B _s mesons, including orbitally and radially excited states. We discuss the role of the proper dynamics of the QCD string in the formation of the spectrum of the heavy—light mesons, with quark self-energy corrections calculated self-consistently in the same picture. We give our predictions in terms of the current quark masses; the string tension—the only dimensional parameter describing the interquark interaction; and the strong coupling constant, which differs for the fine and the hyperfine interactions. The results are compared with the predictions of other models and with the experimental and lattice results.     

Non-perturbative dynamics of the heavy-light quark system in the non-recoil limit

Starting from the relativistic gauge-invariant quark-antiquark Green function we obtain the relevant interaction in the one-body limit, which can be interpreted as the kernel of a non-perturbative Dirac equation. We study this kernel in different kinematic regions, reproducing, in particular, for heavy quark the potential case and sum rules results. We discuss the relevance of the result for heavy-light mesons and the relation with the phenomenological Dirac equations used up to now in the literature.     

Vibration of the QCD string

The large-distance behavior of adiabatic hybrid potentials is studied on the basis of the QCD string model. The calculated spectra are shown to result from the interplay of potential-type longitudinal and string-type transverse vibrations.     

QCD and the string model

Infinitisimal variations of the path-dependent phase factor P exp(i∫_σA_μdz_μ) in gauge theory are studied. They are shown to satisfy differential equations which are equivalent to those for a quantized string if the gauge fields meet certain constraints.     

The Nambu string versus the Dirac string in non-trivial QCD

The global topology of a non-trivial non-abelian gauge theory which displays a remarkable interplay between the Nambu string and the Dirac string is analysed, it is suggested that the non-trivial character of QCD, rather than the non-abelian nature of it, could be directly responsible for the confinement of color.     

Gluelump spectrum in the QCD string model

The spectrum of gluons in the adjoint source field is computed analytically using the QCD string Hamiltonian, containing only one parameter — string tension, fixed by meson and glueball spectrum. Spin splitting is shown to be small. A good agreement is observed with specially generated gluelump states measured on the lattice. The important role of gluelumps defining the behaviour of field-strength correlators is stressed and correspondence with earlier computations of the latter is established.     

Chiral-symmetry breaking and the QCD string

The Lorentz nature of the effective interquark interaction is investigated in a heavy-light quarkonium. The approach of the Dyson-Schwinger-type equation and the quantum-mechanical Hamiltonian method of the QCD string with quarks at the ends are employed to demonstrate that the effective scalar interaction, which appears owing to chiral-symmetry breaking, is responsible for the QCD-string formation. The Hamiltonian of the QCD string with quarks at the ends arises naturally if this effective scalar interaction dominates. If, on the contrary, chiral symmetry is manifest, the effective interquark interaction remains vectorial, and the corresponding bound-state equation is incompatible with the QCD-string Hamiltonian.We conclude therefore that the genuine Lorentz nature of the QCD string is scalar. The text was submitted by the authors in English.     

QCD string in mesons and baryons

The distributions of fields generated by static $Q\bar Q$ and QQQ sources are calculated analytically within the bilocal approximation of the method of vacuum correlation functions. At large distances between the quarks, the fields assume a clear-cut stringlike shape. The main contribution to the string comes from the longitudinal component of the chromoelectric field. The contribution of the transverse chromoelectric field is below 3% of the contribution from the longitudinal component. A baryonic string has a Y-like shape with a deep well in the region of the string-junction position. Field distributions are considered for a quark-diquark configuration and in the case of three quarks occurring on a straight line. The interaction potential is calculated for three quarks residing at the vertices of an equilateral triangle.     

Effects of perturbative exchanges in a QCD string model

The QCD string model for baryons derived by Yu. A. Simonov and used for the calculation of baryon magnetic moments in a previous paper is extended to include also perturbative gluon and meson exchanges. The mass spectrum of the baryon multiplet is studied. For the meson interaction, either pseudoscalar or pseudovector coupling is used. Predictions are compared with the experimental data. Besides these exchanges, the influence of excited quark orbitals on the baryon ground state are considered by performing a multichannel calculation. The nucleon-Δ splitting increases due to the mixing of higher quark states, while the baryon magnetic momenta decrease. The multichannel calculation with perturbative exchanges is shown to yield reasonable magnetic moments, while the mass spectrum is close to experiment.     

Hybrid adiabatic potentials in the QCD string model

The short-and intermediate-distance behavior of the hybrid adiabatic potentials is calculated in the framework of the QCD string model. The calculations are performed with the inclusion of the Coulomb force. The spin-dependent force and the so-called string correction term are treated as a perturbation at the leading-potential-type regime. Reasonably good agreement with lattice measurements takes place for adiabatic curves excited with magnetic components of field strength correlators.     

The renormalization of the string operator in QCD

We shall observe that the renormalization of the string operator U(x₁, x₂; C) = Pexp{ig∫_x1^x2dx_μA^μ(x)} with an open path C (smooth and non-intersecting) is path-independently performed in any order of perturbation. To demonstrate this, the renormalization constants will be calculated up to order g⁴. Next the renormalization effect on the algebraic identity $\text{U(x}{}_1\text{, x}{}_2\text{;}\text{C}\text{)U(x}{}_2\text{, x}{}_3\text{;}\text{C}\text{) = U(x}{}_1\text{, x}{}_3\text{;}\text{C}\text{∪}\text{C}\text{)}$ will be discussed and it will be proved that the renormalization preserves the algebraic identity in any order of perturbation if the paths C and $\text{C}$ are smoothly connected at x₂. Finally, the string operator renormalization is extended to the case when the path C is smoothly closed (the Wilson loop operator). It is then shown that the renormalization factor which multiplicatively renormalizes the string operator in the case of the open path, is cancelled in any order of perturbation by the divergence appearing in the coincidence of the end points. As a results, the Wilson loop operator can be renormalized by the coupling constant renormalization alone.     

Microscopic study of the string breaking in QCD

Theory of strong decays defines in addition to decay widths also the channel coupling and the mass shifts of the levels above the decay thresholds. In the standard decay models of the ³ P ₀ type the decay vertex is taken to be a phenomenological constant γ and such a choice leads to large mass shifts of all meson levels due to real and virtual decays, the latter giving a divergent contribution. Here we show that taking the microscopic details of decay vertex into account, one obtains new string width effect coefficient, which strongly suppresses virtual decay contribution. In addition for a realistic space structure of the decay vertex of highly excited states, the decay matrix elements appear to be strongly different from those, where the constant γ is used. From our analysis also follows that so-called flattening potential can imitate the effects of intermediate decay channels.     

Rotating QCD string and the meson spectrum

The spectra of light–light and heavy–light mesons are described by spinless Salpeter equation and Dirac equation respectively, which predict linear dependence of the meson mass squared M² on angular momentum J and number of radial nodes n. Both spectra are computed by the WKB method and shown to agree with exact numerical data within few percent even for the lowest levels. The drawback of Salpeter and Dirac equation is that (inverse) Regge slopes do not coincide with the string ones, 2πσ and πσ respectively, because the string dynamics is not taken into account properly. The lacking string rotation is introduced via effective Hamiltonian derived from QCD which generates linear Regge trajectories for light mesons with the correct string slope.