Nonperturbative approach to chiral phase transition in chromodynamics

A nonperturbative approach aimed at the localization of the QCD chiral phase transition atT, π≠0 is presented. We identify this transition with the dynamical quark mass peculiarity which results from the selfconsistent solution of the Schwinger-Dyson equation for the quark propagator. The specific model of the effective quark-gluon interaction, based both on the peculier interpolation for the running coupling constant and on the nonperturbative gluon magnetic and electric masses is exploited. The numerical estimates of the phase diagram are presented and it is shown that phase peculiarities are determined not only by the ultraviolet properties of QCD but also by its infrared structure. The obtained results are discussed, compared with other approaches and a possible interpretation is given.     

On the phase structure of QCD in a finite volume

The chiral phase transition in QCD at finite chemical potential and temperature can be characterized for small chemical potential by its curvature and the transition temperature. The curvature is accessible to QCD lattice simulations, which are always performed at finite pion masses and in finite simulation volumes. We investigate the effect of a finite volume on the curvature of the chiral phase transition line. We use functional renormalization group methods with a two flavor quark-meson model to obtain the effective action in a finite volume, including both quark and meson fluctuation effects. Depending on the chosen boundary conditions and the pion mass, we find pronounced finite-volume effects. For periodic quark boundary conditions in spatial directions, we observe a decrease in the curvature in intermediate volume sizes, which we interpret in terms of finite-volume quark effects. Our results have implications for the phase structure of QCD in a finite volume, where the location of a possible critical endpoint might be shifted compared to the infinite-volume case.     

Nonperturbative phenomena in QCD at finite temperature in a magnetic field

The norperturbative QCD vacuum at finite temperature in a external magnetic field is studied. Equations that relate nonperturbative QCD condensates at finite temperature to the thermodynamic pressure at T ≠ 0 and H ≠ 0 are obtained, and low-energy theorems are derived. The free energy of the QCD vacuum in the hadronic phase at H ≠ 0 is calculated, and expressions for the quark and gluon condensates are obtained. Various limiting cases for the behavior of the condensates at low and high temperatures and in weak and strong magnetic fields are investigated. A new interesting phenomenon that consists in the freezing of the quark condensate by a magnetic field is found. The character of spontaneous chiral-symmetry breaking in finite-temperature QCD in a magnetic field is studied. For this purpose, the Gell-Mann-Oakes-Renner formula relating the pion mass M _π and the axial-vector coupling constant F _π to the quark condensate is derived at T ≠ 0 and H ≠ 0. It is shown that this formula preserves its form at finite temperature after taking into account a magnetic field—that is, no additional terms independent of T and H appear. Thus, the scheme of soft chiral-symmetry breaking remains unchanged. The quark-hadron phase transition in QCD in a magnetic field is studied. It is shown that the phase-transition temperature becomes lower than that in the case of zero magnetic field.     

Intermediate Range Force Contributions to Dynamical Chiral Symmetry Breaking in QCD

We propoee the intermediate range QCD force singular like δ(q) by analysing the gluon propagator in the nonperturbative region from QCD sum rules. With the help of the Slavnov- Taylor-Ward identity we derive the equations for the nonperturbative quark propagator from the Schwinger-Dyson (SD) equation. Solutione for the quark propagator in two special cases are given. We find that the intermediate range force L also responsible for the chiral symmetry breaking in QCD.     

Measurements of the structure of quark and gluon jets in hadronic Z decays

An experimental investigation of the structure of identified quark and gluon jets is presented. Observables related to both the global and internal structure of jets are measured; this allows for tests of QCD over a wide range of transverse momentum scales. The observables include distributions of jet-shape variables, the mean and standard deviation of the subjet multiplicity distribution and the fragmentation function for charged particles. The data are compared with predictions of perturbative QCD as well as QCD-based Monte Carlo models. In certain kinematic regions the measurements are sensitive mainly to perturbatively calculable effects, allowing for a test of QCD. The comparisons are also extended into regions where nonperturbative effects become large, and in this way the transition from hard to soft QCD is investigated. It is found that by including leading and next-to-leading logarithmic contributions in the QCD predictions, the agreement with the data can be extended to lower transverse momentum scales, especially for gluon jets. Received: 2 February 1998 / Published online: August 9, 2000     

Effective field theories for the heavy quarkonium

We briefly review how nonrelativistic effective field theories give us a definition of the QCD potentials and a coherent field-theory-derived quantum-mechanical scheme to calculate the properties of bound states made by two or more heavy quarks. In this framework heavy quarkonium properties depend only on the QCD parameters (quark masses and α _s ) and nonpotential corrections are systematically accounted for. The relation between the form of the nonperturbative potentials and the low-energy QCD dynamics is also discussed.     

QCD phase transition with strange quark in wilson formalism for fermions

The nature of QCD phase transition is studied with massless up and down quarks and a light strange quark, using the Wilson formalism for quarks on a lattice with the temporal direction extensionN _t=4. We find that the phase transition is of first order for the physical strange quark mass.     

QCD phase transition with strange quark in wilson formalism for fermions

The nature of QCD phase transition is studied with massless up and down quarks and a light strange quark, using the Wilson formalism for quarks on a lattice with the temporal direction extensionN _t=4. We find that the phase transition is of first order for the physical strange quark mass.     

Analytic methods in nonperturbative QCD

Recently developed analytic methods in the framework of the Field Correlator Method are reviewed in this series of four lectures and results of calculations are compared to lattice data and experiment. Recent lattice data demonstrating the Casimir scaling of static quark interaction strongly support the FCM and leave very little space for all other theoretical models, e.g. instanton gas/liquid model. Results of calculations for mesons, baryons, quarkgluon plasma and phase transition temperature demonstrate that new analytic methods are a powerful tool of nonperturbative QCD along with lattice simulations.     

QCD Interaction in Pion-Nucleus DCX Reaction

The pion-nucleus double charge exchange (DCX) transition matrix element is under consideration in the framework of QCD. The interactions including the perturbative effect and nonperturbative contributions ofgluon condensate and quark condensate in the DCX process are discussed. The interaction operators are given.     

Flavour symmetry breaking in quark vacuum condensates

We study SU(3) and SU(2) flavour symmetry violations in the vacuum from the viewpoint of nonperturbative quark mass generation and independently from charge symmetry-breaking considerations. The results for the ratios of quark condensates of different flavours are compatible with those of QCD sum rules. However, we find that very large SU(3) violating effects, suggested by some sum rule analyses, are barely accommodated in the present nonperturbative approach.     

High-precision nonperturbative QCD

Recent advances in lattice QCD have resulted in the first simulations with realistic quark vacuum polarization. Consequently a wide variety of high-precision (few percent) nonperturbative calculations are possible now. This paper reviews the recent developments that make this possible, and presents early evidence that the era of high-precision nonperturbative QCD is at hand. It also discusses the future impact of lattice QCD on experiments, and particularly for heavy-quark physics.     

Quark loops and spin-flip effects in pomeron exchange

On the basis of QCD at large distances with taking account of some nonperturbative properties of the theory, the possibility of spin-flip effects in high energy hadron processes at fixed momenta transfer is investigated. It is shown that the diagrams with the quark loops in QCD at large distances may lead to the spin-flip amplitude growing ass fors→∞,t-fixed. The confirmation of this result is obtained by calculations of the nonleading contributions from quark loops int-channel exchange in QED up to the end. Physical mechaisms leading to that behavour of the spin-flip amplitude is discussed. So we conclude that the pomeron has a complicated spin structure.     

The π and Tensor Vacuum Susceptibilities from the Global Color Symmetry Model

A modified method for calculating the nonperturbative quark vacuum condensates from the global color symmetry model is derived. Within this approach it is shown that the treatment of quark vacuum condensates is different from that in the previous studies. As a special case we calculate the π and tensor vacuum susceptibilities. A comparison with the results of the other nonperturbative QCD approaches is given.     

From QCD to Quark Potential Model

The connection between phenomenological parameters in the quark potential model and fundamental QCD parameters is established by studying the fermionic three-point Green's functions in QCD incorporating the effects of nonperturbative vacuum. The scale of chiralsymmetry-breaking leading to the constituent quark picture is estimated.     

The Relation Between Instantons and Nucleon structure

A scheme of combining the theory of many instantons and the effective Lagrangian of QCD is proposed to study the nucleon structure. With this approach, the vacuum structure of nonperturbative QCD is discussed and a reasonable potential of quark confinement is obtained. The calculated results of the constituent quark mass and the decay constant of pion agree with experimental data quite well.     

Derivation of a Closed Expression of the B-S Interaction Kernel for Quark-Antiquark Bound States

The interaction kernel in the Bethe-Salpeter (B-S) equation for quark-antiquark bound states is derivedfrom B-S equations satisfied by the quark-antiquark four-point Green‘s function. The latter equations are establishedbased on the equations of motion obeyed by the quark and antiquark propagators, the four-point Green‘s function andsome other kinds of Green‘s functions, which follow directly from the QCD generating functional. The derived B-Skernel is given by a closed and explicit expression which contains only a few types of Green‘s functions. This expressionis not only convenient for perturbative calculations, but also applicable for nonperturbative investigations. Since thekernel contains all the interactions taking place in the quark-antiquark bound states, it actually appears to be the mostsuitable starting point of studying the QCD nonperturbative effect and quark confinement.     

Phase diagrams in nonlocal Polyakov-Nambu-Jona-Lasinio models constrained by lattice QCD results

Based on lattice QCD-adjusted SU(2)f nonlocal Polyakov-Nambu-Jona-Lasinio (PNJL) models, we investigate how the location of the critical endpoint in the QCD phase diagram depends on the strenght of the vector meson coupling, as well as the Polyakov-loop (PL) potential and the form factors of the covariant model. The latter are constrained by lattice QCD data for the quark propagator. The strength of the vector coupling is adjusted such as to reproduce the slope of the pseudocritical temperature for the chiral phase transition at low chemical potential extracted recently from lattice QCD simulations. Our study supports the existence of a critical endpoint in the QCD phase diagram albeit the constraint for the vector coupling shifts its location to lower temperatures and higher baryochemical potentials than in the case without it.     

Anomalous quark-gluon chromomagnetic interaction and high-energy ρ-meson electroproduction

It is shown that existence of a large anomalous chromomagnetic moment of quark induced by nonperturbative structure of QCD leads to the additional contribution to exclusive ρ-meson electroproduction off proton target. The contribution coming from new type of quark-gluon interaction to the ρ-meson production cross section for both transversal and longitudinal polarization of virtual photon is found. Such nonperturbative contribution together with conventional perturbative two-gluon exchange allows us to describe the experimental data at low Q ² for transversal polarization. However, in the longitudinal polarization case there is still some discrepancy with the data. The possible source of this deviation is discussed.