Mass spectra of higher states of quarkonia and decays for scalar-vector confining interaction

Recently, we have studied a flavour-independent potential for quark-antiquark systems of equal and unequal masses in which the confining interaction is scalar-vector admixture with dominant scalar interaction and the spin-dependent part of the potential has been obtained from the non-relativistic reduction of the Bethe-Salpeter kernel. This potential was found to explain the heavy-quark data well. In the present work we have obtained further affirmative tests of the model by calculating the mass spectra of higher levels as well as the confining contribution of the spin-orbit forces forL1 states of quarkonia. We have considered the annihilation processes and radiative transitions too. The former include leptonic decay, two-photon decay, two-gluon annihilation, three-photon decay and three-gluon annihilations.     

Charmed baryons in a relativistic quark model

We calculate mass spectra of charmed baryons within a relativistically covariant quark model based on the Bethe-Salpeter equation in instantaneous approximation. Interactions are given by a linearly rising three-body confinement potential and a flavor-dependent two-body force derived from QCD instanton effects. This model has already been successfully applied to the calculation of light flavor baryon spectra and is now extended to heavy baryons. Within the same framework we compare the results to those obtained with the more conventional one-gluon exchange potential.     

A general scheme for computation of instanton effects

A general approach to the computation of instanton effects without invoking an ad hoc cut-off on their size is illustrated here by the computation of instanton contributions to the static $\text{Q}$Q potential and vacuum polarization. Our results suggest that the instanton effects are much smaller than perturbative effects in the region where both may be reliably computed.     

Resummation of large logarithms in the heavy-quark effects on the parton distributions inside the virtual photon

We discuss the resummation of the large logarithmic terms appearing in the heavy-quark effects on parton distribution functions inside the virtual photon. We incorporate heavy-quark mass effects by changing the initial condition of the leading-order DGLAP evolution equation. In a certain kinematical limit, we recover the logarithmic terms of the next-to-leading order heavy-quark effects obtained in the previous work. This method enables us to resum the large logarithmic terms due to heavy-quark mass effects on the parton distributions in the virtual photon. We numerically calculate parton distributions using the formulae derived in this work, and we discuss the property of the resummed heavy-quark effects.     

Nonperturbative contribution to the quark form factor within the instanton model

The nonperturbative effects in the quark form factor are considered in the Wilson loop formalism, within the framework of the instanton liquid model. For the integration path corresponding to this form factor, the explicit expression for the vacuum expectation value of the Wilson operator is found to the leading order. It is shown that the instantons produce the power-like corrections to the perturbative result, which are comparable in magnitude with the perturbative part at the scale of order of the inverse average instanton size. It is demonstrated that the instanton contributions to the quark form factor are exponentiated to high orders in the small instanton density parameter.Received: 30 September 2002, Published online: 22 October 2003PACS: 12.38.-t Quantum chromodynamics - 11.15.Tk Other nonperturbative techniques     

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     

Vacuum decay and the effective action at finite temperature

The problem of vacuum decay at finite temperature is discussed. It is shown that, when the unstable minimum in the potential arises via quantum effects, the corrections to the kinetic terms cannot be ignored since they are singular. This means that previous adaptations of the instanton method to realistic models are suspect. We also discuss alternative methods of calculations which may be able to avoid the problem.     

Information on the QCD phase transition and the vacuum permeability from the interquark potential

A method for the calculation of the interquark potential resulting from the instanton induced phase transition in the QCD vacuum is described and it is shown that good agreement is obtained with successful phenomenological potentials for parameter values close to those expected from naive instanton calculations.     

On the possibility of the dual Meissner effect induced by instantons

The classical Yang-Mills equation of motion is numerically investigated in the Lorentz gauge for a SU(2) gauge group. The color-electric field of two point-like charges is studied in the “empty” vacuum and in a state with an instanton present. The major effect for a fixed orientation of the instanton is that the color-electric field lines are expelled or attracted from the instanton region depending on the orientation of the instanton. If over the orientations of the instanton is averaged, this effect drops out. In this case of a random instanton orientation, we find that the external color-electric field is expelled from the instanton core. The origin of this effect is discussed. Received: 5 September 1997 / Published online: 23 February 1998     

Charge confinement and vacuum structure in the 1 + 1 dimensional Higgs model

We demonstrate that the 1 + 1 dimensional Higgs model is equivalent to the massive sine-Gordon model, and hence to the massive Schwinger model in a special case. We do this by deriving a dual Lagrangian which embodies instanton effects. Based on this equivalence, we discuss charge confinement and vacuum structure in the Lagrangian formalism.     

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.     

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.     

False vacuum decay in a brane world cosmological model

The false vacuum decay in a brane world model is studied in this work. We investigate the vacuum decay via the Coleman-de Luccia instanton, derive explicit approximative expressions for the Coleman-de Luccia instanton which is close to a Hawking-Moss instanton and compare the results with those already obtained within Einstein's theory of relativity.     

Toward the quantitative theory of the instanton liquid (II).: The SU(2) gluodynamics

In this paper we construct trial functions for the field configurations and study the interaction of pseudoparticles. Then we perform numerical simulations of the effective theory, integrating over collective coordinates. The main qualitative features of the phenomenological instanton liquid model are confirmed. We have evaluated their density in vacuum, as well as the instantonic contribution to the gluon condensate, to the static potential between quarks and to some correlation functions.     

An analysis of transverse fluctuations in multidimensional tunneling

We examine the asymptotic behaviour of the ground state tunnel-splitting of the multidimensional double well, with non-quadratic minima, where instanton techniques are inapplicable. We apply the recently developed path decomposition expansion for two model problems; the important effects of the transverse degrees of freedom are explored. In particular we discuss tunneling in the presences of a vacuum valley, which describes features exhibited in SU(2) gauge theories in a finite volume.     

Statistical mechanics of Coulomb gases as quantum theory on Riemann surfaces

Statistical mechanics of a 1D multivalent Coulomb gas can be mapped onto non-Hermitian quantum mechanics. We use this example to develop the instanton calculus on Riemann surfaces. Borrowing from the formalism developed in the context of the Seiberg-Witten duality, we treat momentum and coordinate as complex variables. Constant-energy manifolds are given by Riemann surfaces of genus g ≥ 1. The actions along principal cycles on these surfaces obey the ordinary differential equation in the moduli space of the Riemann surface known as the Picard-Fuchs equation. We derive and solve the Picard-Fuchs equations for Coulomb gases of various charge content. Analysis of monodromies of these solutions around their singular points yields semiclassical spectra as well as instanton effects such as the Bloch bandwidth. Both are shown to be in perfect agreement with numerical simulations.     

Nonlocal Nambu–Jona-Lasinio model and chiral chemical potential

We derive the critical temperature in a nonlocal Nambu–Jona-Lasinio model with the presence of a chiral chemical potential. The model we consider uses a form factor derived from recent studies of the gluon propagator in Yang–Mills theory and has the property to fit in excellent way the form factor arising from the instanton liquid picture for the vacuum of the theory. Nambu–Jona-Lasinio model is derived form quantum chromodynamics providing all the constants of the theory without any need for fits. We show that the critical temperature in this case always exists and increases as the square of the chiral chemical potential. The expression we obtain for the critical temperature depends on the mass gap that naturally arises from Yang–Mills theory at low-energy as also confirmed by lattice computations.     

Extracting muon momentum scale corrections for hadron collider experiments

The quark condensate is calculated within the world-line effective-action formalism, by using for the Wilson loop an ansatz provided by the stochastic vacuum model. Starting with the relation between the quark and the gluon condensates in the heavy-quark limit, we diminish the current quark mass down to the value of the inverse vacuum correlation length, finding in this way a 64?% decrease in the absolute value of the quark condensate. In particular, we find that the conventional formula for the heavy-quark condensate cannot be applied to the c-quark, and that the corrections to this formula can reach 23?% even in the case of the b-quark. We also demonstrate that, for an exponential parametrization of the two-point correlation function of gluonic field strengths, the quark condensate does not depend on the non-confining non-perturbative interactions of the stochastic background Yang?CMills fields.     

Instanton effects in supersymmetric gauge theories

We investigate how in supersymmetric gauge theories non-perturbative effects are able to generate non-trivial vacuum properties otherwise forbidden by perturbative non-renormalization theorems. This conclusion can be reliably drawn since the constancy of certain Green functions — due to supersymmetry (SUSY) — allows one to connect vacuum-dominated large distances with short-distance behaviour which is reliably computed by instanton methods. In all the cases we discuss (without matter, with massive or massless matter in real representations and, finally, with matter in complex representations) instanton calculations imply the occurrence of a variety of condensates. For the pure SUSY gauge theory, a gluino condensate induces the spontaneous breaking of Z_2N. For massive super-quantum chromodynamics (SQCD) we find a peculiar mass dependence of matter condensates whose origin is traced to mass singularities of non-zero mode instanton contributions. These contributions force the massless limit of SQCD to differ from the strictly massless case, in which the spontaneous breaking of chiral symmetries is induced. Inconsistency with an anomaly equation forces either infinite matter condensates or spontaneous SUSY breaking in the massless cases. For non-constant Green functions, instantons are shown to provide new calculable short-distance singularities of an obvious non-perturbative nature.