Infrared gluon and ghost propagators from lattice QCD

We report on the infrared limit of the quenched lattice Landau gauge gluon and ghost propagators as well as the strong-coupling constant computed from large asymmetric lattices. The infrared lattice propagators are compared with the pure power law solutions from Dyson-Schwinger equations (DSE). For the gluon propagator, the lattice data is compatible with the DSE solution. The preferred measured gluon exponent being ∼0.52, favouring a vanishing propagator at zero momentum. The lattice ghost propagator shows finite-volume effects and, for the volumes considered, the propagator does not follow a pure power law. Furthermore, the strong-coupling constant is computed and its infrared behaviour investigated.     

WChPT analysis of twisted mass lattice data

We perform a Wilson Chiral Perturbation Theory (WChPT) analysis of quenched twisted mass lattice data. The data were generated by two independent groups with three different choices for the critical mass. For one choice, the so-called pion mass definition, one observes a strong curvature for small quark masses in various mesonic observables (“bending phenomenon”). Performing a combined fit to the next-to-leading (NLO) expressions, we find that WChPT describes the data very well and the fits provide very reasonable values for the low-energy parameters.     

Hadron structure on the lattice and in the continuum

Hadron structure physics has in recent years reached a level of precision which allows for a change of perspective. Model-based arguments are often quite unreliable. However, meanwhile they can be more and more replaced by controlled and systematic QCD approaches. The story of the strange electric form factor, which provided much of the motivation for the PAVI Conference series provides a typical example to illustrate this statement. However, high-precision theory is technically very challenging and progress is, therefore, unpleasantly slow. This fact and the present status in general is illustrated by a few typical examples.     

Search for the Θ1540) in lattice QCD

We report on a study of the pentaquark Θ⁺(1540), using a variety of different interpolating fields. We use chirally improved fermions in combination with Jacobi-smeared quark sources to improve the signal and get reliable results even for small quark masses. The results of our quenched calculations, which have been done on a 12³×24 lattice with a lattice spacing of a = 0.148fm, do not provide any evidence for the existence of a Θ⁺ with positive parity. We do observe, however, a signal compatible with nucleon-kaon scattering state. For the negative parity the results are inconclusive, due to the potential mixture with nucleon-kaon and N^*-kaon scattering states.     

Understanding nucleon structure using lattice simulations

This review focuses on the discussion of three key results of nucleon structure calculations on the lattice. These three results are the quark contribution to the nucleon spin, J_q, the nucleon-Δ transition form factors, and the nucleon axial coupling, g_A. The importance for phenomenology and experiment is discussed and the requirements for future simulations are pointed out.     

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.     

Transition Temperature of Two-Degenerate-Flavour QCD in the Chiral Limit

We present the results for the transition temperature of quantum chromodynamics （QCD） with two degenerate flavours （Nf = 2） of Wilson quarks. On lattice 8^3 × 4 with 4 representing the temporal extent, by using the Ferrenberg-Swendsen reweighting method, we determine the critical β = 6/g^2 where the transition occurs, g is the coupling constant. On lattice 8^2 × 20 × 4, by using the axial vector Ward-Takahashi identity, we calculate the current quark mass amq, a is the lattice spacing. Assuming the O（4） scaling, the critical β in the chiral limit is determined. We calculate the p meson mass amp at zero temperature on lattice 8^3 × 20. By using the experimental p meson mass to set the scale, we obtain 194（1） MeV for the transition temperature in the chiral limit.     

Field strength formulation,lattice Bianchi identities and perturbation theory for non-Abelian models

We develop an analytical approach for studying lattice gauge theories within the plaquette representation where the plaquette matrices play the role of the fundamental degrees of freedom. We start from the original Batrouni formulation and show how it can be modified in such a way that each non-Abelian Bianchi identity contains only two connectors instead of four. In addition, we include dynamical fermions in the plaquette formulation. Using this representation we construct the low-temperature perturbative expansion for U(1)$U(1)$ and SU(N)$\mathit{SU}(N)$ models and discuss its uniformity in the volume. The final aim of this study is to give a mathematical background for working with non-Abelian models in the plaquette formulation.     

Comparison of |Q|=1 and |Q|=2 gauge-field configurations on the lattice four-torus

It is known that exactly self-dual gauge-field configurations with topological charge |Q|=1 cannot exist on the untwisted continuum four-torus. We explore the manifestation of this remarkable fact on the lattice four-torus for SU(3) using advanced techniques for controlling lattice discretization errors, extending earlier work of De Forcrand et al. for SU(2). We identify three distinct signals for the instability of |Q|=1 configurations, and show that these signals manifest themselves early in the cooling process, long before the would-be instanton has shrunk to a size comparable to the lattice discretization threshold. These signals do not appear for the individual instantons which make up our |Q|=2 configurations. This indicates that these signals reflect the truly global nature of the instability, rather than the local discretization effects which cause the eventual disappearance of the would-be single instanton. Monte-Carlo generated SU(3) gauge-field configurations are cooled to the self-dual limit using an -improved gauge action chosen to have small but positive errors. This choice prevents lattice discretization errors from destroying instantons provided their size exceeds the dislocation threshold of the cooling algorithm. Lattice discretization errors are evaluated by comparing the -improved gauge-field action with an -improved action constructed from the square of an -improved lattice field-strength tensor, thus having different discretization errors. The number of action-density peaks, the instanton size, and the topological charge of configurations is monitored. We observe a fluctuation in the total topological charge of |Q|=1 configurations, and demonstrate that the onset of this unusual behavior corresponds with the disappearance of multiple-peaks in the action density. At the same time discretization errors are minimal.     

Lowest-lying tetra-quark hadrons in anisotropic lattice QCD

We present a detailed study of the lowest-lying hadrons in quenched improved anisotropic lattice QCD. Using the π π and diquark–antidiquark local and smeared operators, we attempt to isolate the signal for I(J ^P )=0(0⁺),2(0⁺) and 1(1⁺) states in two flavour QCD. In the chiral limit of the light-quark mass region, the lowest scalar 4q state is found to have a mass, m _4q ^I=0=927(12) MeV, which is slightly lower than the experimentally observed f ₀(980). The results from our variational analysis do not indicate a signature of a tetraquark resonance in I=1 and I=2 channels. After the chiral extrapolation the lowest 1(1⁺) state is found to have a mass m _4q ^I=1=1358(28) MeV. We analysed the static 4q potential extracted from a tetraquark Wilson loop and illustrated the behaviour of the 4q state as a bound state, unbinding at some critical diquark separation. From our analysis we conclude that the scalar 4q system appears as a two-pion scattering state and that there is no spatially-localised 4q state in the light-quark mass region.     

Probing nucleon structure on the lattice

The QCDSF/UKQCD Collaboration has an ongoing program to calculate nucleon matrix elements with two flavours of dynamical O(a) improved Wilson fermions. Here we present recent results on the electromagnetic form factors, the quark momentum fraction 〈x〉 and the first three moments of the nucleon's spin-averaged and spin-dependent generalised parton distributions, including preliminary results with pion masses as low as 320MeV.     

Non-perturbative study of the light pseudoscalar masses in chiral dynamics

We perform a non-perturbative chiral study of the masses of the lightest pseudoscalar mesons. In the calculation of the self-energies we employ the S -wave meson-meson amplitudes taken from Unitary Chiral Perturbation Theory (UCHPT) that include the lightest nonet of scalar resonances. Values for the bare masses of pions and kaons are obtained, as well as an estimate of the mass of the η₈ . The former are found to dominate the physical pseudoscalar masses. We also match our results with the self-energies from Chiral Perturbation Theory (CHPT) to O(p ⁴) , and resum higher orders from our calculated self-energies. A robust relation between several O(p ⁴) CHPT counterterms is then obtained. By taking into account values determined from previous chiral phenomenological studies of m _s/ and 3L ₇ + L ^r ₈(M _ρ) , we determine a tighter region of favoured values for the O(p ⁴) CHPT counterterms 2L ^r ₆(M _ρ) - L ^r ₄(M _ρ) and 2L ^r ₈(M _ρ) - L ^r ₅(M _ρ) . This determination perfectly overlaps with the recent determinations to O(p ⁶) in CHPT. We warn about a likely reduction in the value of m _s/ by higher loop diagrams and that this is not systematically accounted for by present lattice extrapolations. We also provide a favoured interval of values for m _s/ and 3L ₇ + L ^r ₈(M _ρ) .     

Statistical properties at the spectrum edge of the QCD Dirac operator

The statistical properties of the spectrum of the staggered Dirac operator in an SU(2) lattice gauge theory are analyzed both in the bulk of the spectrum and at the spectrum edge. Two commonly used statistics, the number variance and the spectral rigidity, are investigated. While the spectral fluctuations at the edge are suppressed to the same extent as in the bulk, the spectra are more rigid at the edge. To study this effect, we introduce a microscopic unfolding procedure to separate the variation of the microscopic spectral density from the fluctuations. For the unfolded data, the number variance shows oscillations of the same kind as before unfolding, and the average spectral rigidity becomes larger than the one in the bulk. In addition, the short-range statistics at the origin is studied. The lattice data are compared to predictions of chiral random-matrix theory, and agreement with the chiral Gaussian Symplectic Ensemble is found. Received: 6 November 1997 / Revised version: 19 January 1998     

Exclusive electroproduction of pion pairs

We investigate electroproduction of pion pairs on the nucleon in the framework of QCD factorization for hard exclusive processes. We extend previous analyses by taking the hard-scattering coefficients at next-to-leading order in α_s . The dynamics of the produced pion pair is described by two-pion distribution amplitudes, for which we perform a detailed theoretical and phenomenological analysis. In particular, we obtain constraints on these quantities by comparing our results with measurements of angular observables that are sensitive to the interference between two-pion production in the isoscalar and isovector channels.     

The process p¯↦γπwithin the handbag approach

We analyse the exclusive channel pˉ↦γπ⁰, assuming handbag dominance. The soft parts are parametrized in terms of CGLN amplitudes for the qˉ↦γπ⁰ transition and form factors for the pˉ↦qˉ ones; the latter represent moments of Generalized Distribution Amplitudes. We present a combined fit to Fermilab data from E760 taking simultaneously into account information from other exclusive reactions, especially from pˉ↦γγ data. Overall a nicely consistent picture emerges, such that one can hope, that our theoretical analysis will be reliable also for the kinematics of GSI/FAIR, which, hopefully, will provide much more precise and complete data. Consequently, data from this facility should improve our knowledge both on the proton-antiproton distribution amplitudes and the pion production mechanism.     

The analysis of space–time structure in QCD vacuum II: Dynamics of polarization and absolute X-distribution

We propose a framework for quantitative evaluation of dynamical tendency for polarization in an arbitrary random variable that can be decomposed into a pair of orthogonal subspaces. The method uses measures based on comparisons of given dynamics to its counterpart with statistically independent components. The formalism of previously considered X-distributions is used to express the aforementioned comparisons, in effect putting the former approach on solid footing. Our analysis leads to the definition of a suitable correlation coefficient with clear statistical meaning. We apply the method to the dynamics induced by pure-glue lattice QCD in local left–right components of overlap Dirac eigenmodes. It is found that, in finite physical volume, there exists a non-zero physical scale in the spectrum of eigenvalues such that eigenmodes at smaller (fixed) eigenvalues exhibit convex X-distribution (positive correlation), while at larger eigenvalues the distribution is concave (negative correlation). This chiral polarization scale thus separates a regime where dynamics enhances chirality relative to statistical independence from a regime where it suppresses it, and gives an objective definition to the notion of “low” and “high” Dirac eigenmode. We propose to investigate whether the polarization scale remains non-zero in the infinite volume limit, in which case it would represent a new kind of low energy scale in QCD.     

Dimension-2 condensates, <Emphasis Type="Italic">ζ</Emphasis>-regularization and large- N<Subscript>c</Subscript> Regge models

Dimension-2 and -4 gluon condensates are re-analyzed in large-N_c Regge models with the ζ-function regularization which preserves the spectrum in any ˉq channel separately. We demonstrate that the signs and magnitudes of both condensates can be properly described within the framework.     

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.