Power law running of the effective gluon mass

The dynamically generated effective gluon mass is known to depend non-trivially on the momentum, decreasing sufficiently fast in the deep ultraviolet, in order for the renormalizability of QCD to be preserved. General arguments based on the analogy with the constituent quark masses, as well as explicit calculations using the operator-product expansion, suggest that the gluon mass falls off as the inverse square of the momentum, relating it to the gauge-invariant gluon condensate of dimension four. In this article we demonstrate that the power law running of the effective gluon mass is indeed dynamically realized at the level of the non-perturbative Schwinger-Dyson equation. We study a gauge-invariant non-linear integral equation involving the gluon self-energy, and establish the conditions necessary for the existence of infrared finite solutions, described in terms of a momentum-dependent gluon mass. Assuming a simplified form for the gluon propagator, we derive a secondary integral equation that controls the running of the mass in the deep ultraviolet. Depending on the values chosen for certain parameters entering into the Ansatz for the fully dressed three-gluon vertex, this latter equation yields either logarithmic solutions, familiar from previous linear studies, or a new type of solutions, displaying power law running. In addition, it furnishes a non-trivial integral constraint, which restricts significantly (but does not determine fully) the running of the mass in the intermediate and infrared regimes. The numerical analysis presented is in complete agreement with the analytic results obtained, showing clearly the appearance of the two types of momentum dependence, well-separated in the relevant space of parameters. Several technical improvements, various open issues, and possible future directions, are briefly discussed.     

On dynamical gluon mass generation

The effective gluon propagator constructed with the pinch technique is governed by a Schwinger-Dyson equation with special structure and gauge properties, that can be deduced from the correspondence with the background field method. Most importantly the non-perturbative gluon self-energy is transverse order-by-order in the dressed loop expansion, and separately for gluonic and ghost contributions, a property which allows for a meanigfull truncation. A linearized version of the truncated Schwinger-Dyson equation is derived, using a vertex that satisfies the required Ward identity and contains massless poles. The resulting integral equation, subject to a properly regularized constraint, is solved numerically, and the main features of the solutions are briefly discussed.     

A QCD sum rule study of the light scalar mesons

We examine the interpretation of the light scalar meson nonet as bound states of the scalar diquark and the scalar antidiquark using the QCD sum rule approach. Our results are obtained by means of the operator product expansion (OPE) including operators up to dimension 8. They show no evidence of the coupling of the tetraquark states to the light scalar meson nonet.     

Aspects of quark mass generation on a torus

In this paper we report on recent results for the quark propagator on a compact manifold. The corresponding Dyson-Schwinger equations on a torus are solved on volumes similar to the ones used in lattice calculations. The quark-gluon interaction is fixed such that the lattice results are reproduced. We discuss both the effects in the infinite volume/continuum limit as well as effects when the volume is small.     

Dynamical chiral-symmetry breaking at T = 0 and T ≠ 0 in the Schwinger-Dyson equation with lattice QCD data

Dynamical chiral-symmetry breaking (DCSB) in QCD is investigated in the Schwinger-Dyson (SD) formalism based on lattice QCD data. From the quenched lattice data for the quark propagator in the Landau gauge, we extract the SD integral kernel function, the product of the quark-gluon vertex and the polarization factor in the gluon propagator, in an Ansatz-independent manner. We find that the SD kernel function exhibits the characteristic behavior of nonperturbative physics, such as infrared vanishing and strong enhancement at the intermediate-energy region around p 0.6GeV. The infrared and intermediate energy region (0.4GeV < p < 1.5GeV) is found to be most relevant for DCSB from analysis on the relation between the SD kernel and the quark mass function. We apply the lattice-QCD-based SD equation to thermal QCD, and calculate the quark mass function at the finite temperature. Spontaneously broken chiral symmetry is found to be restored at high temperature above 110 MeV.     

Constraints on the IR behaviour of gluon and ghost propagator from Ward-Slavnov-Taylor identities

We consider the constraints of the Slavnov-Taylor identity of the IR behaviour of gluon and ghost propagators and their compatibility with solutions of the ghost Dyson-Schwinger equation and with the lattice picture.     

Molecular dynamics simulation for the baryon-quark phase transition at finite baryon density

We study the baryon-quark phase transition in the molecular dynamics (MD) of the quark degrees of freedom at finite baryon density. The baryon state at low baryon density, and the deconfined quark state at high baryon density are reproduced. We investigate the equations of state of matters with different u-d-s compositions. It is found that the baryon-quark transition is sensitive to the quark width.     

Casimir scaling, glueballs, and hybrid gluelumps

Assuming that the Casimir scaling hypothesis is well verified in QCD, masses of glueballs and hybrid gluelumps (gluon attached to a point-like cˉ pair) are computed within the framework of the rotating string formalism. In our model, two gluons are attached by an adjoint string in a glueball, while the gluon and the colour octet cˉ pair are attached by two fundamental strings in a hybrid gluelump. Masses for such exotic hadrons are computed with very few free parameters. These predictions can serve as a guide for experimental searches. In particular, the ground-state glueballs lie on a Regge trajectory and the lightest 2⁺⁺ state has a mass compatible with some experimental candidates.     

Pion-mass dependence of three-nucleon observables

We use an effective field theory (EFT) which contains only short-range interactions to study the dependence of a variety of three-nucleon observables on the pion mass. The pion-mass dependence of input quantities in our “pionless” EFT is obtained from a recent chiral EFT calculation. To the order we work at, these quantities are the ¹ S ₀ scattering length and effective range, the deuteron binding energy, the ³ S ₁ effective range, and the binding energy of one three-nucleon bound state. The chiral EFT input we use has the inverse ³ S ₁ and ¹ S ₀ scattering lengths vanishing at m _π ^crit = 197.8577 MeV. At this “critical” pion mass, the triton has infinitely many excited states with an accumulation point at the three-nucleon threshold. We compute the binding energies of these states up to next-to-next-to-leading order in the pionless EFT and study the convergence pattern of the EFT in the vicinity of the critical pion mass. Furthermore, we use the pionless EFT to predict how doublet and quartet nd scattering lengths depend on m _π in the region between the physical pion mass and m _π = m _π ^crit .     

QCD at high baryon density in a random matrix model

A high-density diquark phase seems to be a generic feature of QCD. If so it should also be reproduced by random matrix models. We discuss a specific one in which the random matrix elements of the Dirac operator are supplemented by a finite chemical potential and by non-random elements which model the formation of instanton-anti-instanton molecules. Comparing our results to those found in a previous investigation by Vanderheyden and Jackson we find additional support for our starting assumption, namely that the existence of a high-density diquark phase is common to all QCD-like model. Received: 20 February 2001 / Accepted: 24 April 2001     

Hadron spectroscopy and structure from AdS/CFT

The AdS/CFT correspondence between conformal field theory and string states in an extended space-time has provided new insights into not only hadron spectra, but also their light-front wave functions. We show that there is an exact correspondence between the fifth-dimensional coordinate of anti-de Sitter space z and a specific impact variable ζ which measures the separation of the constituents within the hadron in ordinary space-time. This connection allows one to predict the form of the light-front wave functions of mesons and baryons, the fundamental entities which encode hadron properties and scattering amplitudes. A new relativistic Schr?dinger light-front equation is found which reproduces the results obtained using the fifth-dimensional theory. Since they are complete and orthonormal, the AdS/CFT model wave functions can be used as an initial ansatz for a variational treatment or as a basis for the diagonalization of the light-front QCD Hamiltonian. A number of applications of light-front wave functions are also discussed.     

Retardation effects in the rotating string model

A new method to study the retardation effects in mesons is presented. It is based on a generalized rotating string model, in which a nonzero value of the relative time between the quark and the antiquark is allowed. This approach leads to a retardation term in the Hamiltonian which behaves as a perturbation of the nonretarded Hamiltonian and preserves the Regge trajectories for light mesons. The straight-line ansatz is used to describe the string, and the relevance of this approximation is tested. It is shown that the string is actually curved because of retardation, but this bending does not bring a relevant contribution to the energy spectrum of the model.     

Large momenta fluctuations of charm quarks in the Quark-Gluon Plasma<Superscript>⋆</Superscript>

We show that large fluctuations of D-mesons kinetic-energy (or momentum) distributions might be a signature of a phase transition to the Quark-Gluon Plasma (QGP). In particular, a jump in the variance of the momenta or kinetic energy, as a function of a control parameter (temperature or Fermi energy at finite baryon densities) might be a signature for a first-order phase transition to the QGP. This behavior is completely consistent with the order parameter defined for a system of interacting quarks both at zero temperature (and finite baryon densities) or at finite temperatures which shows a jump in correspondence with a first-order phase transition to the QGP. The J/Ψ displays exactly the same behavior of the order parameter and of the variance of the D-mesons. We discuss implications for relativistic heavy-ion collisions within the framework of a transport model and possible hints for experimental search.     

Effective potential between two gluons from the scalar glueball

Starting from the 0⁺⁺ glueball mass and wave function computed from lattice QCD, we compute the local potential between two constituent gluons. Since the properties of constituent gluons are still a matter of research, we allow for them to be either massless, or massive with a mass around 0.7GeV. Both pictures are actually used in the literature. When the gluons are massless, the corresponding local potential is shown to be compatible with a Cornell form, that is a linear confinement plus a short-range Coulomb part, with standard values for the flux tube energy density and for the strong coupling constant. When the gluons are massive, the confining potential is a saturating one, commonly used to simulate string-breaking effects. These results fill a gap between lattice QCD and phenomenological models: The picture of the scalar glueball as a bound state of two constituent gluons interacting via a phenomenological potential is shown to emerge from pure gauge lattice QCD computations. Moreover, we show that the allowed potential shape is constrained by the mass of the constituent gluons.     

A remark on the large difference between the glueball mass and T<Subscript>c</Subscript> in quenched QCD

The lattice QCD studies indicate that the critical temperature T _c ≃ 260-280 MeV of the deconfinement phase transition in quenched QCD is considerably smaller than the lowest-lying glueball mass m _G ≃ 1500-1700 MeV, i.e., T _c ≪ m _G. As a consequence of this large difference, the thermal excitation of the glueball in the confinement phase is strongly suppressed by the statistical factor e ^-mG/Tc ≃ 0.00207 even near T ≃ T _c. We consider its physical implication, and argue the abnormal feature of the deconfinement phase transition in quenched QCD from the statistical viewpoint. To appreciate this, we demonstrate a statistical argument of the QCD phase transition using the recent lattice QCD data. From the phenomenological relation between T _c and the glueball mass, the deconfinement transition is found to take place in quenched QCD before a reasonable amount of glueballs is thermally excited. In this way, quenched QCD reveals a question “what is the trigger of the deconfinement phase transition ?” Received: 18 November 2002 / Accepted: 4 February 2003 / Published online: 29 April 2003     

Excited flux tube from q¯g hybrid mesons

In the framework of quark models, hybrid mesons are either seen as two-body qˉ systems with an excited flux tube connecting the quark to the antiquark or as three-body qˉg systems including a constituent gluon. In this work we show that, starting from the three-body wave function of the qˉg hybrid meson in which the gluonic degrees of freedom are averaged, the excited flux tube picture emerges as an equivalent qˉ potential. This equivalence between the excited flux tube and the constituent-gluon approach is confirmed for heavy hybrid mesons but, for the first time, it is shown to hold in the light sector too, provided the contribution of the quark dynamics is correctly taken into account.     

Baryonic masses based on the NJL model

We employ the Nambu-Jona-Lasinio model to determine the vacuum pressure on the quarks in a baryon and hence their density inside. Then we estimate the baryonic masses by implementing the local density approximation for the mean-field quark energies obtained in a uniform and isotropic system. We obtain a fair agreement with the experimental masses. Received: 27 September 2002 / Accepted: 4 October 2002 / Published online: 4 February 2003 RID="a" ID="a"e-mail: giacosa@tphys.physik.uni-tuebingen.de Communicated by A. Molinari     

A new application of the Gürsey and Radicati mass formula

We study the spin- and flavour-dependent SU(6) violations in the baryon spectrum by means of a Gürsey-Radicati mass formula. The average energy of each SU(6) multiplet is described using the SU(6)-invariant interaction given by a hypercentral potential containing a linear and a hyper-Coulomb term. We show that the nonstrange- and strange-baryon masses are, in general, fairly well reproduced and moreover that the Gürsey-Radicati formula holds in a satisfactory way also for the excited states up to 2 GeV.