arXiv subjects
Publications and source records attributed to A. Alexandru.
We derive the classical continuum limit of the operator tr$_s σ_{μν} D^{ov}(x,x)$ with $D^{ov}$ being the overlap Dirac operator and show that it corresponds to the gauge field strength tensor $F_{μν}(x)$.
The glueball-to-vacuum matrix elements of local gluonic operators in scalar, tensor, and pseudoscalar channels are investigated numerically on several anisotropic lattices with the spatial lattice spacing ranging from 0.1fm - 0.2fm. These matrix elements are needed to predict the glueball branching ratios in $J/ψ$ radiative decays which will help identify the glueball states in experiments. Two types of improved local gluonic operators are constructed for a self-consistent check and the finite volume effects are studied. We find that lattice spacing dependence of our results is very weak and the continuum limits are reliably extrapolated, as a result of improvement of the lattice gauge action and local operators. We also give updated glueball masses with various quantum numbers.
We present the first study of the charmonium spectrum using overlap fermions, on quenched configurations. Simulations are performed on $16^3 \times 72$ lattices, with Wilson gauge action at $β$ = 6.3345. We demonstrate that we have discretization errors under control at about 5%. We obtain 88(4) MeV for hyperfine splitting using the $r_0$ scale, and 121(6) MeV using the ($1\bar{P}-1\bar{S}$) scale. This paper raises the possibility that the discrepancy between the lattice results and the experimental value for charmonium hyperfine splitting can be resolved using overlap fermions to simulate the charm quark on lattice.
Long-range order of a specific kind has recently been found directly in configurations dominating the regularized QCD path integral. In particular, a low-dimensional global structure was identified in typical space-time distributions of topological charge defined via the overlap Dirac matrix. The presence of the order has been concluded from the fact that the structure disappears after random permutation of position coordinates in measured densities. Here we complete the argument for the reality of this structure (namely the conjecture that its existence is a consequence of QCD dynamics and not an artifact of the overlap-based definition of lattice topological field) by showing that the structure ceases to exist after randomizing the space-time coordinates of the underlying gauge field. This implies that the long-range order present in the overlap-based topological density is indeed a manifestation of QCD vacuum, and that the notion of the fundamental structure (structure involving relevant features at all scales) is viable.
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 ~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.
We have recently presented evidence that in configurations dominating the regularized pure-glue QCD path integral, the topological charge density constructed from 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 that is 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 (~ 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.
We present preliminary results using overlap fermions for the charmonium spectrum, in particular for hyperfine splitting. Simulations are performed on $16^3 \times 72$ lattices, with Wilson gauge action at $β=6.3345$. Depending on how the scale is set, we obtain 104(5) MeV (using $1\bar{P}-1\bar{S}$) or 88(4) MeV (using $r_0$=0.5 fm) for the hyperfine splitting.
We present a quenched lattice QCD calculation of spin-1/2 five-quark states with $uudd\bar{s}$ quark content for both positive and negative parities. We do not observe any bound pentaquark state in these channels for either I = 0 or I =1. The states we found are consistent with KN scattering states which are checked to exhibit the expected volume dependence of the spectral weight. The results are based on overlap-fermion propagators on two lattices, 12^3 x 28 and 16^3 x 28, with the same lattice spacing of 0.2 fm, and pion mass as low as ~ 180 MeV.
By using the freedom of picking a representative we explore connections between the Tomboulis SO(3)xZ(2) form of the partition function and the SU(2) form. We are able to express the monopole and vortex observables of the former in terms of configurations of the latter. Also we can measure Tomboulis and projection vortex counters on the same configuration to search for correlations.
We study the configuration space of the Tomboulis $SO(3) \times Z(2)$ formulation with periodic boundary conditions. The dynamical variables are constrained by the required coincidence of Z(2) and SO(3) monopoles. Furthermore, there is an additional constraint coming from the boundary conditions. We propose an update algorithm that satisfies the constraints and is straightforward to implement.
We explore simulations on periodic lattices in the Tomboulis $SO(3) \times Z(2)$ formulation. We measure gauge invariant vortex counters for "thin", "thick" and "hybrid" vortex sheets in order to tag Wilson loops by the occurance of gauge invariant vortices linking them. We also measure projection vortex counters defined in the maximal center gauge for comparison.
We examine the occurance of Z(2) and SO(3) vorticies and monopole distributions in the neighborhood of Wilson loops. We use the Tomboulis formulation, equivalent to the Wilson action, in which the links are invariant under Z(2) transformations and new plaquette variables carry the Z(2) degrees of freedom. This gives new gauge invariant observables to help gain insight into the area law and structure of the flux tube.
We explore simulations on periodic lattices in the Tomboulis $SO(3)\times Z(2)$ formulation. The dynamical variables are constrained. We propose an update algorithm that satisfies the constraints and is straightforward to implement. We show how boundary conditions put constraints on the configuration space.
We study the configuration space of the Tomboulis $SO(3) \times Z(2)$ formulation with periodic boundary conditions. The dynamical variables are constrained by the required coincidence of Z(2) and SO(3) monopoles. We propose an update algorithm that satisfies the constraints and is straightforward to implement. We further prove that this it reaches all configurations. We show how the boundary conditions put constraints on the configuration space. We measure gauge invariant vortex counters for "thin", "thick" and "hybrid" vortex sheets. For comparison we also measure projection vortex counters defined in the maximal center gauge.