Variational study of vacuum wave functional in QCD

We develop a variational method in order to study non-perturbative structure of the vacuum wave functional in QCD. To retain gauge invariance, we employ a vacuum test functional motivated by the structure of perturbation theory. The resultant integral equation contains only renormalizable logarithmic divergences and is reliable in the weak coupling region. We find that this equation contains a non-perturbative solution besides the perturbative one, and the energy in the former state is lower. Further it is shown that the gluon condensation <G _μv ^a2 > calculated using this non-perturbative solution agrees with the result of several authors.     

Elastic diffraction and non-perturbative gluons

Zeitschrift für Physik C Particles and Fields - We consider a simple model for the propagator of a non-perturbative gluon and derive the rules determining its coupling to perturbative gluons...     

Perturbative versus condensate effects in super-heavy quarkonia

The perturbative and non-perturbative corrections to the Balmer spectrum in super-heavy quarkonia are compared. The leading perturbative contribution is due to the asymptotic freedom correction to the Coulomb potential, and vanishes extremely slowly with increasing quark mass m. We compare different “optimal” choices for the scale at which α_s should be evaluated for use in the Balmer formula. The leading non-perturbative correction, which is thought to be due to the presence of a gluon condensate, only becomes appreaciable for states having a size larger than about 0.1 fm. At this scale α_s is already so large that it becomes very difficult to distinguish the non-perturbative corrections from the higher-order perturbative ones.     

Equilibration in quark gluon plasma

The hydrodynamic expansion rate of quark gluon plasma (QGP) is evaluated and compared with the scattering rate of quarks and gluons within the system. Partonic scattering rates evaluated within the ambit of perturbative Quantum Choromodynamics (pQCD) are found to be smaller than the expansion rate evaluated with ideal equation of state (EoS) for the QGP. This indicate that during the space-time evolution the system remains out of equilibrium. Enhancement of pQCD cross sections and a more realistic EoS keep the partons closer to the equilibrium.     

Non-perturbative effects for the Quark-Gluon Plasma equation of state

The non-perturbative effects for the Quark-Gluon Plasma (QGP) equation of state (EoS) are considered. The modifications of the bag model EoS are constructed to satisfy the main qualitative features observed for the QGP EoS in the lattice QCD calculations. A quantitative comparison with the lattice results is done for the SU(3) gluon plasma and for the QGP with dynamical quarks. Our analysis advocates a negative value of the bag constant B.     

On the Use of the Running Coupling Constant α<Subscript>s</Subscript> in Calculations of Radiative Energy Losses of Fast Partons in a Quark–Gluon Plasma

The introduction of the running coupling constant α_s for a gluon emission vertex in calculations of radiative energy losses of partons in a quark–gluon plasma is discussed. It is argued that the virtuality scale for the running coupling constant α_s for induced emission of gluons is determined by the square of the transverse momentum of an emitted gluon rather than by the square of the invariant mass of the final two-parton state often used in the literature.     

Quark-Gluon Interactions at High Temperature and Large Distances

Continuum fourdimensional Quantum Chromodynamics (QCD) including quarks in the regime of high temperature and large distances (the HT regime) is studied to all perturbative orders. The imaginary time (τ) formalism is used. Then, as shown in previous works, QCD is described by a new generating functional Z_HT, in which quark fields retain their dependences on τ, while gluon and ghost fields are τ-independent. The invariance of Z_HT under BRST transformations in the HT regime is exhibited: it closed quark and electric gluon loops in the HT regime are obtained. The electric mass terms in Z_HT. Infinite sets of non-abelian Ward identities for the closed quark and electric gluon loops in the HT regime are obtained. The electric mass terms in Z_HT are shown to be infrared finite. We prove to all perturbative orders that one can regard as subdominant, and, hence, neglect consistently the contributions of :i) all closed electric gluon loops, ii) all closed quark loops with three or more vertices in diagrams having an even number of electric gluons (or none) in the external lines. In the HT regime, the axial anomalies are obtained: their expressions in terms of τ-independent gluon fields are similar to those for zero temperature. A non-trivial renormalization group (RG) equation in the HT regime, specifically due to the quark-gluon interaction, is presented. A positive beta function is obtained, and it is argued that interactions are not weak in that regime. The RG and the perturbative analysis to all orders appear to indicate that quarks and gluons may be confined in the HT regime (and, in particular in the Early Universe), due to the infrared divergent magnetic gluon sector. Other possibilities are also discussed.     

Light 0- Meson Solution of Bethe-Salpeter Equation Involving the Vacuum Condensates in QCD

We dkcuss the Bethe-Salpeter equation involving the vacuum condensates in QCD in the backgrouud fields. The bound state equation for the light 0^- meson (π and K) is solved in the ladder approximation of single gluon exchange, where the gluon propagator is calculated in tree level of a gluon condensate and a quark condensate. The kernel is divided into two parts: perturbative and non-pert,urbative. The non-perturbative part is determined by the vacuum condensate. Pseudo-scalar meson spectrum and decay constants are in good agreement with data.     

Transport equations and QCD collective modes in a self-consistent covariant background gauge

Following an interpretation of high-temperature instabilities of perturbative QCD, a self-consistent covariant background gauge quantization is proposed. Non-perturbative classically gauge invariant gluon, ghost, and quark equations of motion for coupled one- and two-point functions are derived in binary collision approximation (RPA). A stability analysis is described to determine coloured and colourless collective modes. Preliminary results indicate non-perturbative behaviour of the quark-gluon plasma involving self-consistent classical background fields. It leads to mass generation for gluons as well as for collective modes.     

Gluon recombination and shadowing at small values of x

We determine the recombination probabilities for gluons to go into gluons or into quarks in a low-density limit. A modified Altarelli-Parisi equation expressing this recombination is given. We find recombination is very small compared to normal evolution in all interesting circumstances except that of nuclear shadowing. Thus, for evolution above Q₀ ≈ 2 GeV, the gluon density remains far below saturation except at unusually small values of x.     

Numerical calculation of the momentum-space gluon propagator in quenched,reduced QCD3

A recently developed method of momentum-space Monte Carlo is applied to compute the momentum-space gluon propagator in quenched, reduced, continuum QCD₃ in axial gauge. There is some evidence that the gluon propagator D_μν(p) is finite as p → 0, which might indicate the existence of a non-perturbative gluon mass.     

Baryon spectrum and the forces between quarks

We study the effect of confinement on gluon bremsstrahlung. A natural infrared cutoff emerges both at small gluon momenta and at small angles. If the confinement potential is of the linear “string” type, the cutoff is controlled by the tension parameter and is thus about 1GeV for the transverse momentum of a hard gluon relative to its parent quark. We propose that this confinement effect may remove the necessity for introducing ad hoc cutoffs by a large “intrinsic partonp _T ” in phenomenological applications of perturbative QCD.     

Factorization and infrared properties of non-perturbative contributions to DIS structure functions

In this paper we present a new derivation of QCD factorization. We deduce the k _T and collinear factorizations for the DIS structure functions by consecutive reductions of a more general theoretical construction. We begin by studying the amplitude of forward Compton scattering off a hadron target, representing this amplitude as a set of convolutions of two blobs connected by the simplest, two-parton intermediate states. Each blob in the convolutions can contain both the perturbative and non-perturbative contributions. We formulate conditions for separating the perturbative and non-perturbative contributions and attributing them to the different blobs. After that the convolutions correspond to QCD factorization. Then we reduce this totally unintegrated (basic) factorization first to k _T -factorization and finally to collinear factorization. In order to yield a finite expression for the Compton amplitude, the integration over the loop momentum in the basic factorization must be free of both ultraviolet and infrared singularities. This obvious mathematical requirement leads to theoretical restrictions on the non-perturbative contributions (parton distributions) to the Compton amplitude and the DIS structure functions related to the Compton amplitude through the Optical Theorem. In particular, our analysis excludes the use of the singular factors x ^−a (with a>0) in the fits for the quark and gluon distributions because such factors contradict the integrability of the basic convolutions for the Compton amplitude. This restriction is valid for all DIS structure functions in the framework of both k _T -factorization and collinear factorization if we attribute the perturbative contributions only to the upper blob. The restrictions on the non-perturbative contributions obtained in the present paper can easily be extended to other QCD processes where the factorization is exploited.     

Non-linear BFKL dynamics: Color screening vs. gluon fusion

A feasible mechanism of unitarization of amplitudes of deep inelastic scattering at small values of Bjorken x is the gluon fusion. However, its efficiency depends crucially on the vacuum color screening effect which accompanies the multiplication and the diffusion of BFKL gluons from small to large distances. From the fits to lattice data on field strength correlators the propagation length of perturbative gluons is R _c ? (0.2–0.3) fm. The probability to find a perturbative gluon with short propagation length at large distances is suppressed exponentially. It changes the pattern of (dif)fusion dramatically. The magnitude of the fusion effect appears to be controlled by the new dimensionless parameter ～ R _c ² /8B, with the diffraction cone slope B standing for the characteristic size of the interaction region. It should slowly ∝ 1/lnQ ₂ decrease at large Q ². Smallness of the ratio R _c ² /8B makes the non-linear effects rather weak even at lowest Bjorken x available at HERA. We report the results of our studies of the non-linear BFKL equation which has been generalized to incorporate the running coupling and the screening radius, R _c as the infrared regulator.     

Analytic approach to the approximate solution of the independent DGLAP evolution equations with respect to the hard-Pomeron behavior

We show that it is possible to use hard-Pomeron behavior to the gluon distribution and singlet structure function at low x. We derive a second-order independent differential equation for the gluon distribution and the singlet structure function. In this approach, both singlet quarks and gluons have the same high-energy behavior at small x. These equations are derived from the next-to-leading order DGLAP evolution equations. All results can be consistently described in the framework of perturbative QCD, which shows an increase of gluon distribution and singlet structure functions as x decreases.     

On the chromo-electric permittivity and Debye screening in hot QCD

We study the response functions (chromo-electric susceptibilities) for an interacting quark-gluon plasma. The interaction effects have been encoded in the effective fugacities for quasi-partons which are extracted self-consistently from the two equations of state for hot QCD. The first one is the fully perturbative O(g ⁵) EOS and the second one, which is O(g ⁶ln(1/g)) , incorporates some non-perturbative effects. We find that the response function shows large deviations from the ideal behavior. We further determine the temperature dependence of the Debye mass by fixing the effective coupling constant Q² which appears in the transport equation. We show that our formalism naturally yields the leading-order HTL expression for the Debye mass if we employ the ideal EOS. Employing the Debye mass, we estimate the dissociation temperatures for various charmonium and bottomonium bound states. These results are consistent with the current theoretical studies.     

Studying gluon properties experimentally

We argue in this paper the following. (i) A large part of what is observed in high-energy hadron reactions may be rather directly interpretable in terms of gluon interactions. Since gluons do not interact directly with leptons and photons this could be a valuable way to study them experimentally. Earlier work in this direction is briefly summarized. We suggest how several quantities can be reinterpreted in terms of gluon interactions; the rise in σ_tot, and the more rapid increase of multiplicity with energy at very high energies, are particularly fruitful to examine. The possibility of interpreting inclusive polarization data in terms of gluon spin properties is considered. Most importantly, we propose that if certain of our predictions on central region particle ratios are correct, then the gluon distribution as a function of x may be measurable at energies in the ISABELLE range. (ii) The structure of gluon jets in mass, multiplicity and momentum is discussed; we suggest that gluon jets will be quite different from quark jets, with more of the energy of the gluon jet going into mass, so hard gluon jets may not exist.     

High energy evolution of soft gluon cascades

In this paper we derive an evolution equation for the gluon density in soft gluon cascades emitted from any colored source, in the leading logarithmic approximation of perturbative QCD. We show that this equation has the same form as the BFKL equation in the forward case. An explicit expression for the total cascade wavefunction involving an arbitrary number of soft gluons is obtained. Renormalization of the colored source wavefunction turns out to be responsible for the reggeization of the source. Laboratoire de Physique Théorique: Unité mixte 8627 du CNRS.     

Angular distribution of energy in jets

The transverse momentum distribution of heavy C-even resonances produced in hadron collisions probes, according to QCD, the spatial spread of color charge in gluons. An all-orders calculation of the effective doubly logarithmic gluon form factor is supported by recent data on χ (3.5) production. We predict a very wide p_t distribution of C-even b$\text{b}$ resonances associated with ?.