H. Thacker

Low-dimensional long-range topological structure in the QCD vacuum☆

Abstract Lattice topological charge associated with Ginsparg-Wilson fermions exhibits generic topological stability over quantum ensemble of configurations contributing to the QCD path integral. Moreover, the underlying chiral symmetry leads to the suppression of ultraviolet noise in the associated topological charge densities (“chiral smoothing”). This provides a solid foundation for the direct study of the role of topological charge fluctuations in the physics of QCD vacuum. Using these tools it was recently demonstrated that: (a) there is a well-defined space-time structure (order) in topological charge density (defined through overlap fermions) for typical configurations contributing to QCD path integral; (b) this fundamental structure is low-dimensional, exhibiting sign-coherent behavior on subsets of dimension less than four and not less than one; (c) the structure has a long-range global character (spreading over maximal space-time distances) and is built around the locally one-dimensional network of strong fields (skeleton). In this talk we elaborate on certain aspects and implications of these results.

Light quarks, zero modes, and exceptional configurations

In continuum QCD, nontrivial gauge topologies give rise to zero eigenvalues of the massless Dirac operator. In lattice QCD with Wilson fermions, analogs of these zero modes appear as exactly real eigenvalues of the Wilson-Dirac operator, leading to poles in the quark propagator in the vicinity of the critical hopping parameter. It is shown that {open_quotes}exceptional configurations,{close_quotes} which arise in the quenched approximation at small quark mass, are the result of the fluctuation of the position of zero mode poles to subcritical values of hopping parameter on particular gauge configurations. We describe a procedure for correcting these lattice artifacts by first isolating the contribution of zero mode poles to the quark propagator and then shifting the subcritical poles to the critical point. This procedure defines a modified quenched approximation in which accurate calculations can be carried out for arbitrarily small quark masses. {copyright} {ital 1998} {ital The American Physical Society}

Properties of B-Mesons in Lattice QCD

The results of an extensive study of {ital B}-meson properties in quenched lattice QCD are presented. The studies are carried out in the static quark limit where the {ital b} quark is taken to be infinitely massive. Our computations rely on a multistate smearing method introduced previously, with smearing functions generated from a relativistic lattice quark model. Systematic errors arising from excited state contamination, finite volume effects, and the chiral extrapolation for the light quarks are estimated. We obtain continuum results for the mass splitting {ital M}{sub {ital B}{ital s}}{minus}{ital M}{sub {ital B}{ital u}}=86{plus_minus}12(stat){sub {minus}9}{sup +7}(syst) MeV, the ratio of decay constants {ital f}{sub {ital B}{ital s}}/{ital f}{sub {ital B}{ital u}}=1.22{plus_minus}0.04(stat){plus_minus}0.02(syst). For the {ital B}-meson decay constant we separately exhibit the sizable uncertainties in the extrapolation to the continuum limit ({ital a}{r_arrow}0) and higher-order perturbative matching. We obtain {ital f}{sub {ital B}}=188{plus_minus}23(stat){plus_minus}15(syst){sub {minus}0}{sup +26}(extrap){plus_minus}14(pert) MeV.

Evidence Against Instanton Dominance of Topological Charge Fluctuations in QCD

The low-lying eigenmodes of the Dirac operator associated with typical gauge field configurations in QCD encode, among other low-energy properties, the physics behind the solution to the U{sub A}(1) problem (i.e. the origin of the {eta}{prime} mass), the nature of spontaneous chiral symmetry breaking, and the physics of string-breaking, quark-antiquark pair production, and the OZI rule. Moreover, the space-time chiral structure of these eigenmodes reflects the space-time topological structure of the underlying gauge field. We present evidence from lattice QCD on the local chiral structure of low Dirac eigenmodes leading to the conclusion that topological charge fluctuations of the QCD vacuum are not instanton-dominated. The result supports Wittens arguments that topological charge is produced by confinement-related gauge fluctuations rather than instantons.

Inherently global nature of topological charge fluctuations in QCD

We have recently presented evidence that in configurations dominating the regularized pure-glue QCD path integral, the topological charge density constructed from the overlap Dirac operator organizes into an ordered space-time structure. It was pointed out that, among other properties, this structure exhibits two important features: it is low-dimensional and geometrically global, i.e., consisting of connected sign-coherent regions with local dimensions 1 <= d < 4, and spreading over arbitrarily large space-time distances. Here we show that the space-time structure responsible for the origin of topological susceptibility indeed exhibits global behavior. In particular, we show numerically that topological fluctuations are not saturated by localized concentrations of most intense topological charge density. To the contrary, the susceptibility saturates only after the space-time regions with most intense fields are included, such that geometrically global structure is already formed. We demonstrate this result both at the fundamental level (full topological density) and at low energy (effective density). The drastic mismatch between the point of fluctuation saturation (approximate to 50% of space-time at low energy) and that of global structure formation (< 4% of space-time at low energy) indicates that the ordered space-time structure in topological charge is inherently global and that topological charge fluctuations in QCD cannot be understood in terms of individual localized pieces. Description in terms of global brane-like objects should be sought instead. (c) 2005 Elsevier B.V. All rights reserved.

The negativity of the overlap-based topological charge density correlator in pure-glue QCD and the non-integrable nature of its contact part

We calculate the lattice two-point function of topological charge density in pure-glue QCD using the discretization of the operator based on the overlap Dirac matrix. Utilizing data at three lattice spacings it is shown that the continuum limit of the correlator complies with the requirement of non-positivity at non-zero distances. For our choice of the overlap operator and the Iwasaki gauge action we find that the size of the positive core is approximate to 2a (with a being the lattice spacing) sufficiently close to the continuum limit. This result confirms that the overlap-based topological charge density is a valid local operator over realistic backgrounds contributing to the QCD path integral, and is important for the consistency of recent results indicating the existence of a low-dimensional global brane-like topological structure in the QCD vacuum. We also confirm the divergent short-distance behavior of the correlator, and the non-integrable nature of the associated contact part. (c) 2005 Elsevier B.V. All rights reserved.

Local chirality of low lying Dirac eigenmodes and the instanton liquid model

The reasons for using low-lying Dirac eigenmodes to probe the local structure of topological charge fluctuations in QCD are discussed, and the interpretation of the local chiral orientation probability distribution in these modes (as compared with the instanton picture) is clarified. The results with overlap Dirac operator in Wilson gauge backgrounds at lattice spacings ranging from a{approx}0.04 fm to a{approx}0.12 fm are reported, and it is found that the size and density of local structures responsible for double-peaking of the distribution are in disagreement with the assumptions of the Instanton Liquid Model. We argue that our results suggest that vacuum fluctuations do not produce locally quantized (integer-valued) topological charge in QCD, contrary to the semiclassical picture.

Efficient algorithm for QCD with light dynamical quarks

A new approach to the inclusion of virtual quark effects in lattice QCD simulations is presented. Infrared modes which build in the chiral physics in the light quark mass limit are included exactly and in a gauge invariant way. At fixed physical volume the number of relevant infrared modes does not increase as the continuum limit is approached. The acceptance of our procedure does not decrease substantially in the limit of small quark masses. Two alternative approaches are discussed for including systematically the remaining ultraviolet modes. In particular, we present evidence that these modes are accurately described by an effective action involving only small Wilson loops. {copyright} {ital 1998} {ital The American Physical Society}

Chiral Lagrangian parameters for scalar and pseudoscalar mesons

The results of a high-statistics study of scalar and pseudoscalar meson propagators in quenched lattice QCD are presented. For two values of lattice spacing,

Lattice QCD, the quark model, and heavy-light wavefunctions

\ensuremath{\beta}=5.7(a\ensuremath{\approx}.18\mathrm{fm})