Gluonic Distribution in the Constituent Quark and Nucleon Induced by the Instantons

Abstract Instanton effects can give large contribution to strong interacting processes, especially at the energy scale where perturbative QCD is no longer valid. However instanton contribution to the gluon contribution in constituent quark and nucleon has never been calculated before. Based on both the constituent quark picture and the instanton model for QCD vacuum, we calculate the unpolarized and polarized gluon distributions in the constituent quark and in the nucleon for the first time. We find that the pion field plays an important role in producing both the unpolarized and the polarized gluon distributions.     

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.     

Low-energy dynamics in ultradegenerate QCD matter

We study the low-energy behavior of QCD Green functions in the limit that the baryon chemical potential is much larger than the QCD scale parameter LambdaQCD. We show that there is a systematic low-energy expansion in powers of (omega/m)(1/3), where omega is the energy and m is the screening scale. This expansion is valid even if the effective quark-gluon coupling g is not small. The expansion is purely perturbative in the magnetic regime |k| > k0. If the external momenta and energies satisfy |k| approximately k0, planar, Abelian ladder diagrams involving the full quark propagator have to be resummed but the corresponding Dyson-Schwinger equations are closed.     

Spontaneous generation of Nambu-Jona-Lasinio interaction in QCD involving two light quarks

Within QCD involving two light quarks, the possibility of a spontaneous generation of effective interaction leading to Nambu-Jona-Lasinio model is studied by using the Bogolyubov quasiaverage approach. The compensation equation for the form factor of this interaction is shown to have a nontrivial solution that leads to a theory involving two parameters: the average value of the low-energy constant α _s and a dimensional parameter f _π. All of the remaining parameters, including the current and constituent quark masses, the quark condensate, the pion mass, and the sigma-meson mass and width, are expressed in terms of the input parameters in satisfactory agreement with experimental phenomenology. The results obtained here give sufficient grounds to conclude that the proposed approach is applicable in low-energy hadron physics and that it can be used in dealing with other problems.     

Chiral extrapolation, renormalization, and the viability of the quark model

The relationship of the quark model to the known chiral properties of QCD is a long-standing problem in the interpretation of low-energy QCD. In particular, how can the pion be viewed as both a collective Goldstone-boson quasiparticle and as a valence-quark-antiquark bound state? A comparison of the many-body solution of a simplified model of QCD to the constituent-quark model demonstrates that the quark model is sufficiently flexible to describe meson hyperfine splitting provided proper renormalization conditions and correct degrees of freedom are employed consistently.     

Low-energy QCD and ultraviolet renormalons

We discuss the contribution of ultraviolet (UV) renormalons in QCD to two-point functions of quark current operators. This explicitly includes effects due to the exchange of one renormalon chain as well as two chains. It is shown that, when the external Euclidean momentum of the two-point functions becomes smaller than the scale AL associated with the Landau singularity of the QCD one-loop running coupling constant, the positions of the UV renormalons in the Borel plane become true singularities in the integration range of the Bore] transform. This introduces ambiguities in the evaluation of the corresponding two-point functions. The ambiguities associated with the leading UV renormalon singularity are of the same type as the contribution due to the inclusion of dimension d = 6 local operators in a low-energy effective Lagrangian valid at scales smaller than AL. We then discuss the inclusion of an infinite number of renormalon chains and argue that the previous ambiguity hints at a plausible approximation scheme for low-energy QCD, resulting in an effective Lagrangian similar to the one of the extended Nambu-Jona-Lasinio (ENJL) model of QCD at large N_c.     

Low-energy theorems and the Dirac operator spectral density in QCD

We discuss the spectral density of the massless Dirac operator at small eigenvalues and quark masses compatible with the restrictions imposed by the low-energy theorems in QCD. The sum rule for its derivative with respect to the quark mass is found.     

Hypothesis of Quark Binding by Condensation of Gluons in Hadrons

Hypothesis of quark binding through condensation of gluons inside hadrons is formulated in the context of a renormalization group procedure for effective particles (RGPEP) in the light-front (LF) Hamiltonian approach to QCD. At the momentum scales of relative motion of hadronic constituents that are comparable with Λ _QCD , the hypothetical boost-invariant constituent dynamics is identified using gauge symmetry. The resulting picture of mesons and baryons closely resembles constituent quark models with harmonic oscillator potentials, shares some features of AdS/QCD, and can be systematically studied using RGPEP in QCD.     

Baryon spectra and electroweak nucleon form factors in constituent quark models

We discuss the spectra of light and strange baryons as well as the electroweak structure of the nucleons as described by relativistic constituent quark models. Special attention is paid to the performance of different types of quark dynamics and to the role of relativistic effects. It is found that the concept of constituent quark models, set up in a covariant framework, represents a promising tool to deal with low-energy hadron phenomena.     

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.     

Functional approach to QCD finite-energy sum rules

A new method for the determination of the QCD condensates from low-energy hadronic data is proposed. It generalizes the usual QCD finite-energy sum rules, taking into account explicitely the truncation error of the high-energy QCD expansion. The method is applied to the e⁺e^– annihilation intoI= 1 hadrons, indicating a rather large domain for the values of the gluon and four quark condensates.     

Vacuum structure,chiral symmetry breaking and electric dipole moment of neutron

Considering a CP-violating QCD interaction, the electric dipole moment of neutron (EDMN) is estimated in a quark model of light mesons with a dynamical breaking of chiral symmetry through a non-trivial vacuum structure. Pion and kaon, being treated consistently within the model, yield to the constituent quark wave functions as well as the dynamical quark masses and thus determine the constituent quark field operators with respect to light quark flavors. Using the translationally invariant hadronic states and these constituent quark field operators, the EDMN estimated here remains well within the recent experimental bound ofD _n<11 × 10⁻²⁶ e-cm with the CP-violation parameter |ϑ|=10⁻⁸, which in fact accounts for a strong CP-violation.     

K-->pipi amplitudes from lattice QCD with a light charm quark

We compute the leading-order low-energy constants of the DeltaS=1 effective weak Hamiltonian in the quenched approximation of QCD with up, down, strange, and charm quarks degenerate and light. They are extracted by comparing the predictions of finite-volume chiral perturbation theory with lattice QCD computations of suitable correlation functions carried out with quark masses ranging from a few MeV up to half of the physical strange mass. We observe a DeltaI=1/2 enhancement in this corner of the parameter space of the theory. Although matching with the experimental result is not observed for the DeltaI=1/2 amplitude, our computation suggests large QCD contributions to the physical DeltaI=1/2 rule in the GIM limit, and represents the first step to quantify the role of the charm-quark mass in K-->pipi amplitudes. The use of fermions with an exact chiral symmetry is an essential ingredient in our computation.     

Hadron spectrum and infrared-finite behavior of QCD running coupling

We study the behavior of the QCD effective coupling α _s in the low-energy region by exploiting the conventional meson spectrum within a relativistic quantum-field model based on analytical confinement of quarks and gluons. The spectra of quark-antiquark and two-gluon bound states are defined by using a master equation similar to the ladder Bethe-Salpeter equation. A new, independent and specific infrared-finite behavior of QCD coupling is found below energy scale ∼1 GeV. Particularly, an infrared-fixed point is extracted at α _s (0) ≅ 0.757 for confinement scale Λ = 345 MeV. We provide a new analytic estimate of the lowest-state glueball mass. As applications, we also estimate masses of some intermediate and heavy mesons as well as the weak-decay constants of light mesons. By introducing only a minimal set of parameters (the quark masses m _f and Λ) we obtain results in reasonable agreement with recent experimental data in a wide range of energy scale ∼0.1–10 GeV. We demonstrate that global properties of some low-energy phenomena may be explained reasonably in the framework of a simple relativistic quantum-field model if one guesses correct symmetry structure of the quark-gluon interaction in the confinement region and uses simple forms of propagators in the hadronisation regime. The model may serve a reasonable framework to describe simultaneously different sectors in low-energy particle 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.     

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.     

Quark Mass Dependence of Nucleon Magnetic Moment and Charge Radii

Understanding hadron structure within the framework of QCD is an extremely challenging problem. Our purpose here is to explain the model-independent consequences of the approximated chiral symmetry of QCD for two famous results concerning the quark structure of the nucleon. We show that both the apparent success of the constituent quark model in reproducing the ratio of proton to neutron magnetic moments and the apparent success of the Foldy term in reproducing the observed charge radius of the neutron are coincidental. That is, a relatively small change of the current quark mass would spoil both results.