Non-perturbative effects inside the QCD bag

Non-perturbative effects are investigated inside the QCD bag, on which perfectly confining boundary conditions are given. The instanton density is evaluated and used to estimate effective quark-antiquark hamiltonians, as well as the magnitude of chiral symmetry breaking for massless quarks.     

Spin effects in instanton models

Nonperturbative nolocal structure of QCD vacuum is well described by instanton model. Specific helicity and flavor structure of zero modes of quarks, in instanton field allows simultaneously to explain some important features of low-and high-energy hadron phenomemology. The basic characteristics of hadron spectrum, partonic sum rules, heavyquark potential etc within the instanton liquid model are briefly discussed.     

The “instanton liquid”

We review the theory of interacting topological fluctuations in the ground state of quantum gauge theories, the so called “instanton liquid”. First we outline some known phenomenological facts, both coming from “real” experiments (for QCD) and from the lattice data. Then we describe interaction of instantons and the statistical mechanics of their ensemble for theSU(2) gauge theory. The very essential role of the light quarks is considered using numerical experiments. One of the main conclusions is that instantons induce chiral symmetry breaking in vacuum, but as they are suppressed (e.g. by the nonzero temperature) this symmetry is restored. Phase transition is found to be very strong and of the first order.     

On contribution of instantons to nucleon sum rules

The contribution of instantons to nucleon QCD sum rules is obtained. It is shown that this contribution does provide stabilization of the sum rules and leads to formation of a nucleon as a bound state of quarks in the instanton field.     

A new mechanism for single-spin asymmetries in strong interactions

It is shown that the contribution of instantons to the fragmentation of quarks leads to the appearance of an imaginary part in diagrams of quark-quark scattering at large transferred momentum. The imaginary part comes from the analytical continuation of the instanton amplitudes from Euclidean to Minkowsky space-time and reflects the quasiclassical origin of the instanton solution of QCD equations of motion. This phenomenon and instanton-induced quark spin-flip give a new nonperturbative mechanism for the observed anomalous single-spin asymmetries in hadron-hadron and lepton-hadron interactions.     

Off-diagonal quark distributions in pions in the effective single-instanton approximation

Nonperturbative functions that parametrize off-diagonal hadronic matrix elements of the light-cone leading-twist quark operators are considered. These functions are calculated within the proposed relativistic quark model allowing for the nontrivial structure of the QCD vacuum, special attention being given to gauge invariance. Hadrons are treated as bound states of quarks; strong-interaction quark-pion vertices are described by effective interaction Lagrangians generated by instantons. The parameters of the instanton vacuum, such as the effective radius of the instanton and the quark mass, are related to the vacuum expectation values of the quark-gluon operators of the lowest dimension and to low-energy pion observables.     

Role of anomalous chromomagnetic interaction in Pomeron and Odderon structures and in gluon distribution

We calculate the contribution arising from nonperturbative quark-gluon chromomagnetic interaction to the high-energy total quark-quark cross section and to gluon distributions in nucleon. The estimation obtained within the instanton model of QCD vacuum leads to the conclusion that this type of interaction gives the dominating contribution to the Pomeron coupling with the light quarks and to gluon distribution in light hadrons at small virtualities of quarks and gluons. We argue that the Odderon, which is the P = C = −1 partner of the Pomeron, is governed by the spin-flip component related to nonperturbative three-gluon exchange induced by anomalous quark-gluon chromomagnetic interaction.     

瞬子效应在0++胶球的QCD求和规则中的作用

利用包含瞬子效应的QCD求和规则计算了0⁺⁺胶球的质量上限,结果为1.3GeV.还探讨了变动瞬子参量时对QCD求和规则的影响,发现包含瞬子修正的QCD求和规则在瞬子大小为1/3fm时变得很稳定     

The role of instantons in quantum chromodynamics: (III). Quark-gluon plasma

With the increase in density and/or temperature of matter in the quark-gluon plasma phase, suppression of instanton-induced effects takes place. At some critical parameters chiral symmetry is restored. In this first-order transition the massive quasiparticles-valons-are substituted by nearly massless quarks and gluons, while the “instanton liquid” dissociates into “instanton molecules” with zero topological charge.     

q-deformed supersymmetric Newton oscillators

We propose that in QCD with dynamical quarks, colour deconfinement occurs when an external field induced by the chiral condensate strongly aligns the Polyakov loop. This effect sets in at the chiral symmetry restoration temperature and thus makes deconfinement and chiral symmetry restoration coincide. The predicted singular behaviour of Polyakov loop susceptibilities at is shown to be supported by finite temperature lattice calculations. Received: 27 September 2000 / Published online: 8 December 2000     

Axial anomaly and low energy tests for instanton vacuum models in QCD

We propose to test instanton models of QCD – in particular the single instanton approximation and the Diakonov and Petrov model – against some exact relations inferred from QCD + QED axial anomaly. One of these relations, in chiral limit, is satisfied by the latter model, but not by the former one. More refined tests, obtained beyond the chiral limit, are not fulfilled by the Diakonov and Petrov model. Received: 24 November 1997 / Published online: 10 March 1998     

Generalized form factors and spin structures of the kaon

We investigate the spin structure of the kaon, based on the nonlocal chiral quark model from the instanton vacuum. We first revisit the electromagnetic form factors of the pion and kaon, improving the results for the kaon. We evaluate the generalized tensor form factors of the kaon in order to determine the probability density of transversely polarized quarks inside the kaon. We consider the effects of flavor SU(3) symmetry breaking, so that the probability density of the up and strange quarks are examined in detail. It is found that the strange quark behaves differently inside the kaon in comparison with the up quark.     

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 and the Lorentz nature of confinement

We address the question of the Lorentz nature of the effective long-range interquark interaction generated by the QCD string with quarks at the ends. Studying the Dyson-Schwinger equation for a heavy-light quark-antiquark system, we demonstrate explicitly how a Lorentz scalar interaction appears in the Dirac-like equation for the light quark as a consequence of chiral symmetry breaking. We argue that the effective interquark interaction in the Hamiltonian of the QCD string with quarks at the ends stems from this effective scalar interaction.     

The QCD sum rule for the delta (1232) in the instanton medium

The QCD sum rule for the Δ (1232) is considered in the instanton medium. It is found that the instanton effect improves the chirally odd sum rule significantly. This indicates that the operator product expansion does not converge rapidly in the delta state. The chirally even sum rule of Δ suggests that the “standard” value of the higher dimensional condensate m₀ is much smaller than that derived from the instanton model.     

Gluon field strength correlation functions within a constrained instanton model

We suggest a constrained instanton (CI) solution in the physical QCD vacuum which is described by large-scale vacuum field fluctuations. This solution decays exponentially at large distances. It is stable only if the interaction of the instanton with the background vacuum field is small and additional constraints are introduced. The CI solution is explicitly constructed in the ansatz form, and the two-point vacuum correlator of the gluon field strengths is calculated in the framework of the effective instanton vacuum model. At small distances the results are qualitatively similar to the single instanton case; in particular, the invariant structure is small, which is in agreement with the lattice calculations. Received: 18 June 1999 / Revised version: 21 July 1999 / Published online: 17 February 2000     

Spatial and temporal hadron correlators below and above the chiral phase transition

Hadronic correlation functions at finite temperature in QCD, with four flavours of dynamical quarks, have been analyzed both above and below the chiral symmetry restoration temperature. We have used both point and extended sources for spatial as well as temporal correlators. The effect of periodic temporal boundary conditions for the valence quarks on the spatial meson correlators has also been investigated. All our results are consistent with the existence of individual quarks at high temperatures. A measurement of the residual interaction between the quarks is presented.     

QCD at large and short distances (annotated version)

A formulation of QCD which contains no divergences and no renormalization procedure is presented. It contains both perturbative and nonperturbative phenomena. It is shown that, due to its asymptotically free nature, the theory is not defined uniquely. The chiral symmetry breaking and the nature of the octet of pseudoscalar particles as quasi-Goldstone states are analyzed in the theory with massless and massive quarks. The U(1) problem is discussed. Received: 15 February 1999 / Published online: 15 July 1999     

Instanton vacuum in thermal QCD

The effects of instanton-anti-instanton interactions in high-temperature QCD with colour SU(2) are studied with and without quarks. The instanton potential proves to have no repulsive core, thus creating troubles with the definition of nonperturbative contributions to physical quantities. Also the chiral condensate is calculated, and it is shown to vanish if number of quark flavoursN _f≧2, whereas forN _f=1 it is nonzero for the arbitrary high temperature.     

On the spontaneous breaking of chiral symmetry in QCD

We calculate the vacuum polarization functions of the vector and axial current for massless quarks in second-order perturbation theory. We find that, contrary to previous speculations, there is no indication, at this level, of spontaneous breaking of chiral symmetry in QCD.