Describing charmonium correlation functions in Euclidean time

We present a detailed investigation of the quark mass-dependence of charmonium correlators in Euclidean-time obtained using potential model as well as the comparison with results on isotropic lattice calculations.     

On the short distance behavior of the critical Ising model perturbed by a magnetic field

We apply here a recently developed approach to compute the short distance corrections to scaling for the correlators of all primary operators of the critical two-dimensional Ising model in a magnetic field. The essence of the method is the fact that if one deals with OPE Wilson coefficients instead of correlators, all-order IR safe formulas can be obtained for the perturbative expansion with respect to the magnetic field. This approach yields in a natural way the expected fractional powers of the magnetic field, which are clearly absent in the naive perturbative expression for correlators. The technique of the Mellin transform has been used to compute the IR behavior of the regularized integrals. As a corollary of our results, by comparing the existing numerical data for the lattice model we give an estimate of the vacuum expectation value of the energy operator of the continuous theory.     

Unusual liquid state of hard-core bosons on the pyrochlore lattice

We study the physics of hard-core bosons with unfrustrated hopping (t) and nearest-neighbor repulsion (V) on the three dimensional pyrochlore lattice. At half-filling, we demonstrate that the small V/t superfluid state eventually becomes unstable at large enough V/t to an unusual insulating state which displays no broken lattice translation symmetry. Equal time and static density correlators in this insulator are well described by a mapping to electric field correlators in the Coulomb phase of a U(1) lattice gauge theory, allowing us to identify this insulator with a U(1) fractionalized Mott-insulating state. The possibility of observing this phase in suitably designed atom-trap experiments with ultracold atoms is also discussed, as are specific experimental signatures.     

Lattice calculation of the κ meson

We study the κ meson in 2+1 flavor QCD with sufficiently light u/d quarks. Using numerical simulations, we measure the point-to-point κ correlators in the "Asqtad" improved staggered fermion formulation. We then analyze these correlators using rooted staggered chiral perturbation theory (rSχPT), with particular attention paid to bubble contribution. After chiral extrapolation, we obtain the physical κ mass with 828±97 MeV, which is within the recent experimental value of 800-900 MeV. These numerical simulations are carried out with MILC 2+1 flavor gauge configurations at a lattice spacing of a ≈ 0.12 fm.     

Lattice calculation of the κ meson

We study the κ meson in 2+1 flavor QCD with sufficiently light u/d quarks. Using numerical simulations, we measure the point-to-point κ correlators in the "Asqtad" improved staggered fermion formulation. We then analyze these correlators using rooted staggered chiral perturbation theory (rSχPT), with particular attention paid to bubble contribution. After chiral extrapolation, we obtain the physical κ mass with 828±97 MeV, which is within the recent experimental value of 800-900 MeV. These numerical simulations are carried out with MILC 2+1 flavor gauge configurations at a lattice spacing of a ≈ 0.12 fm.     

Hadron correlators and the structure of the quark propagator

The structure of the quark propagator of QCD in a confining background is not known. We make an ansatz for it, as hinted by a particular mechanism for confinement, and analyze its implications in the meson and baryon correlators. We connect the various terms in the Källen-Lehmann representation of the quark propagator with appropriate combinations of hadron correlators, which may ultimately be calculated in lattice QCD. Furthermore, using the positivity of the path integral measure for vector like theories, we reanalyze some mass inequalities in our formalism. A curiosity of the analysis is that, the exotic components of the propagator (axial and tensor), produce terms in the hadron correlators which, if not vanishing in the gauge field integration, lead to violations of fundamental symmetries. The non observation of these violations implies restrictions in the space-time structure of the contributing gauge field configurations. In this way, lattice QCD can help us analyze the microscopic structure of the mechanisms for confinement.Supported in part by CICYT (AEN91-0234) and DGICYT grant (PB91-0119-C02-01)     

Conformal correlation functions,Frobenius algebras and triangulations

We formulate two-dimensional rational conformal field theory as a natural generalization of two-dimensional lattice topological field theory. To this end we lift various structures from complex vector spaces to modular tensor categories. The central ingredient is a special Frobenius algebra object A in the modular category that encodes the Moore–Seiberg data of the underlying chiral CFT. Just like for lattice TFTs, this algebra is itself not an observable quantity. Rather, Morita equivalent algebras give rise to equivalent theories. Morita equivalence also allows for a simple understanding of T-duality.We present a construction of correlators, based on a triangulation of the world sheet, that generalizes the one in lattice TFTs. These correlators are modular invariant and satisfy factorization rules. The construction works for arbitrary orientable world sheets, in particular, for surfaces with boundary. Boundary conditions correspond to representations of the algebra A. The partition functions on the torus and on the annulus provide modular invariants and NIM-reps of the fusion rules, respectively.     

Evidence for instanton-induced dynamics from lattice QCD

We perform a study of the nonperturbative dynamics of the light-quark sector of QCD, based on some recent results of lattice simulations with chiral fermions. We analyze some correlators that are designed to probe the Dirac structure of the quark-quark interaction at different scales. We show that, in the nonperturbative regime, such an interaction contains very large scalar and pseudoscalar components. We observe quantitative agreement between lattice QCD results and the predictions of the instanton liquid model. Moreover, we study how the quark-quark interaction is modified, when quark loops are suppressed. We observe a dramatic effect related to the loss of unitarity, which is naturally explained in the instanton picture. Such an effect cannot be explained in a Dyson-Schwinger equations (DSE) approach, if one assumes a vector quark-gluon coupling.     

Dimensionally reduced U(1)+Higgs theory in the broken phase

We apply dimensional reduction to the finite temperature U(1)+Higgs theory and study the properties of the reduced 3-dimensional theory in the broken phase using lattice Monte Carlo simulations. We compute analytically the scalar condensate in optimized 2-loop perturbation theory and the correlators in 1-loop perturbation theory. These quantities are also calculated numerically. The two results for the condensate agree well but a 25% difference is observed for the scalar correlator, indicating the need for optimized 2-loop perturbative results.     

Spectral functions at small energies and the electrical conductivity in hot quenched lattice QCD

In lattice QCD, the maximum entropy method can be used to reconstruct spectral functions from Euclidean correlators obtained in numerical simulations. We show that at finite temperature the most commonly used algorithm, employing Bryan's method, is inherently unstable at small energies and gives a modification that avoids this. We demonstrate this approach using the vector current-current correlator obtained in quenched QCD at finite temperature. Our first results indicate a small electrical conductivity above the deconfinement transition.     

The Infrared Behaviour of the Pure Yang–Mills Green Functions

We review the infrared properties of the pure Yang–Mills correlators and discuss recent results concerning the two classes of low-momentum solutions for them reported in literature, i.e. decoupling and scaling solutions. We will mainly focus on the Landau gauge and pay special attention to the results inferred from the analysis of the Dyson–Schwinger equations of the theory and from “quenched” lattice QCD. The results obtained from properly interplaying both approaches are strongly emphasized.     

Generating series for GUE correlators

We extend to the Toda lattice hierarchy the approach of Bertola et al. (Phys D Nonlinear Phenom 327:30–57, 2016; IMRN, 2016) to computation of logarithmic derivatives of tau-functions in terms of the so-called matrix resolvents of the corresponding difference Lax operator. As a particular application we obtain explicit generating series for connected GUE correlators. On this basis an efficient recursive procedure for computing the correlators in full genera is developed.     

Linking confinement to spectral properties of the dirac operator

We represent Polyakov loops and their correlators as spectral sums of eigenvalues and eigenmodes of the lattice Dirac operator. The deconfinement transition of pure gauge theory is characterized as a change in the response of moments of eigenvalues to varying the boundary conditions of the Dirac operator. We argue that the potential between static quarks is linked to spatial correlations of Dirac eigenvectors.     

Universal,finite-temperature,crossover functions of the quantum transition in the Ising chain in a transverse field

We consider finite-temperature properties of the Ising chain in a transverse field in the vicinity of its zero-temperature, second-order quantum phase transition. New universal crossover functions for static and dynamic correlators of the “spin” operator are obtained. The static results follow from an early lattice computation of McCoy, and a method of analytic continuation in the space of coupling constants. The dynamic results are in the “renormalized classical” region and follow from a proposed mapping of the quantum dynamics to the Glauber dynamics of a classical Ising chain.     

On the extraction of zero momentum form factors on the lattice

We propose a method to expand correlation functions with respect to the spatial components of external momenta. From the coefficients of the expansion it is possible to extract Lorentz-invariant form factors at zero spatial momentum transfer avoiding model dependent extrapolations. These objects can be profitably calculated on the lattice. We have explicitly checked the validity of the proposed procedure by considering two-point correlators with insertions of the axial current, the form factors of the semileptonic decay of pseudoscalar mesons, and the hadronic vacuum polarization tensor entering, for example, the lattice calculation of the anomalous magnetic moment of the muon.     

Direct Scaling Analysis of Localization in Single-Particle Quantum Systems on Graphs with Diagonal Disorder

We propose a simplified version of the Multi-Scale Analysis of Anderson models on a lattice and, more generally, on a countable graph with polynomially bounded growth of balls, with diagonal disorder represented by an IID or strongly mixing correlated potential. We apply the new scaling procedure to discrete Schr?dinger operators and obtain localization bounds on eigenfunctions and eigenfunction correlators in arbitrarily large finite subsets of the graph which imply the spectral and strong dynamical localization in the entire graph.     

Factorial correlators: angular scaling within QCD jets

Factorial correlators measure the amount of dynamical correlation in the multiplicity between two separated phase-space windows. We present the analytical derivation of factorial correlators for a QCD jet described at the double logarithmic (DL) accuracy. We obtain a new angular scaling property for properly normalized correlators between two solid-angle cells or two rings around the jet axis. Normalized QCD factorial correlators scale with the angular distance and are independent of the window size. Scaling violations are expected beyond the DL approximation, in particular from the subjet structure. Experimental tests are feasible, and thus would be welcome. Received: 12 January 2001 / Published online: 7 September 2001     

Analytic calculation of field-strength correlators

Field correlators are expressed using background-field formalism through the gluelump Green’s functions. The latter are obtained in the path-integral and Hamiltonian formalism. As a result, the behavior of field correlators is obtained at small and large distances for both perturbative and nonperturbative parts. The latter decay exponentially at large distances and are finite at x = 0, in agreement with OPE and lattice data. The text was submitted by the author in English.