David Lenkner

Improved stochastic estimation of quark propagation with Laplacian Heaviside smearing in lattice QCD

A new method of stochastically estimating the low-lying effects of quark propagation is proposed which allows accurate determinations of temporal correlations of single-hadron and multi-hadron operators in lattice QCD. The method is well suited for calculations in large volumes. Contributions involving quark propagation connecting hadron sink operators at the same final time can be handled in a straightforward manner, even for a large number of final time slices. The method exploits Laplacian Heaviside (LapH) smearing. ZN noise is introduced in a novel way, and variance reduction is achieved using judiciously-chosen noise dilution projectors. The method is tested using isoscalar mesons in the scalar, pseudoscalar, and vector channels, and using the two-pion system of total isospin I = 0,1,2 on large anisotropic 24 3 × 128 lattices with spatial spacing as � 0.12 fm and temporal spacing at � 0.034 fm for pion masses m� � 390 and 240 MeV.

Extended hadron and two-hadron operators of definite momentum for spectrum calculations in lattice QCD

Multi-hadron operators are crucial for reliably extracting the masses of excited states lying above multi-hadron thresholds in lattice QCD Monte Carlo calculations. The construction of multi-hadron operators with significant coupling to the lowest-lying multi-hadron states of interest involves combining single hadron operators of various momenta. The design and implementation of large sets of spatially-extended single-hadron operators of definite momentum and their combinations into two-hadron operators are described. The single hadron operators are all assemblages of gauge-covariantly-displaced, smeared quark fields. Group-theoretical projections onto the irreducible representations of the symmetry group of a cubic spatial lattice are used in all isospin channels. Tests of these operators on 24^3 x 128 and 32^3 x 256 anisotropic lattices using a stochastic method of treating the low-lying modes of quark propagation which exploits Laplacian Heaviside quark-field smearing are presented. The method provides reliable estimates of all needed correlations, even those that are particularly difficult to compute, such as eta eta -> eta eta in the scalar channel, which involves the subtraction of a large vacuum expectation value. A new glueball operator is introduced, and the evaluation of the mixing of this glueball operator with a quark-antiquark operator, pi-pi, and eta-eta operators is shown to be feasible.

The excited hadron spectrum in lattice QCD using a new method of estimating quark propagation

Progress in determining the spectrum of excited baryons and mesons in lattice QCD is described. Large sets of carefully‐designed hadron operators have been studied and their effectiveness in facilitating the extraction of excited‐state energies is demonstrated. A new method of stochastically estimating the low‐lying effects of quark propagation is proposed which will allow reliable determinations of temporal correlations of single‐hadron and multi‐hadron operators.

A novel method for evaluating correlation functions in lattice hadron spectroscopy

We describe a new approach for evaluating hadronic correlation functions which combines Laplacian-Heaviside quark smearing with a stochastic estimator of quark propagators. This method utilizes noise dilution in a new way to reduce the variance in correlators. The efficacy of the new algorithm is demonstrated on a number of systems, including disconnected diagrams and multi-hadron correlators, on a small lattice where comparisons with the results obtained with exactly determined quark propagators are possible. On larger lattice volumes, the use of exact propagators becomes prohibitively expensive, while the stochastic method is still computationally feasible.

Spectrum of excited states using the stochastic LapH method

Progress in computing the spectrum of excited baryons and mesons in lattice QCD is described. Our first results in the zero-momentum bosonic I=1, S=0, T1u+ symmetry sector of QCD using a correlation matrix of 56 operators are presented. In addition to a dozen spatially-extended meson operators, 44 two-meson operators are used, involving a wide variety of light isovector, isoscalar, and strange meson operators of varying relative momenta. All needed Wick contractions are efficiently evaluated using a stochastic method of treating the low-lying modes of quark propagation that exploits Laplacian Heaviside quark-field smearing. Level identification is discussed.

Excited-state hadron masses from lattice QCD

Progress in computing the spectrum of excited baryons and mesons in lattice QCD is described. Large sets of spatially-extended hadron operators are used. The need for multi-hadron operators in addition to single-hadron operators is emphasized, necessitating the use of a new stochastic method of treating the low-lying modes of quark propagation which exploits Laplacian Heaviside quark-field smearing. A new glueball operator is tested and computing the mixing of this glueball operator with a quark-antiquark operator and multiple two-pion operators is shown to be feasible.

Excited-State Hadrons Using the Stochastic LapH Method

Progress in computing the spectrum of excited baryons and mesons in lattice QCD is described. Large sets of spatially-extended hadron operators are used. The need for multi-hadron operators in addition to single-hadron operators is emphasized, necessitating the use of a new stochastic method of treating the low-lying modes of quark propagation which exploits Laplacian Heaviside quark-field smearing. A new glueball operator is tested and computing the mixing of this glueball operator with a quark-antiquark operator and multiple two-pion operators is shown to be feasible. Some of our initial results show warning signs about extracting high-lying resonance energies using only single-hadron operators.

Progress Report on Computing Excited‐State Hadron Masses in Lattice QCD

Our progress in computing the spectrum of excited baryons and mesons in lattice QCD is described. Sets of spatially‐extended hadron operators with a variety of different momenta are used. A new method of stochastically estimating the low‐lying effects of quark propagation is utilized which allows reliable determinations of temporal correlations of both single‐hadron and multi‐hadron operators. The method is tested on the isoscalar mesons in the scalar, pseudoscalar, and vector channels, and on the two‐pion system of total isospin I = 0,1,2.

Excited isovector mesons using the stochastic LapH method

The spectrum of excited isovector mesons is studied using a 32^3 x 256 anisotropic lattice with u,d quark masses set to give a pion mass near 240 MeV. Results in the bosonic isovector nonstrange symmetry channels of zero total momentum are presented using correlation matrices of unprecedented size. In addition to spatially-extended single-meson operators, large numbers of two-meson operators are used, involving a wide variety of light isovector, isoscalar, and strange meson operators of varying relative momenta. All needed Wick contractions are efficiently evaluated using a stochastic method of treating the low-lying modes of quark propagation that exploits Laplacian Heaviside quark-field smearing. Level identification is discussed.

The finite volume spectrum of excited states from lattice QCD simulations

We present results for the spectrum of excited mesons obtained from temporal correlations of spatially-extended single-hadron and multi-hadron operators computed in lattice QCD. The stochastic LapH algorithm is implemented on anisotropic, dynamical lattices for isovectors for pions of mass 390 MeV. A large correlation matrix with single-particle and two-particle probe operators is diagonalized to identify resonances. The masses of excited states in the I = 1,S = 0,T 1u channel as well as the mixing of single and multi-particle probe operators are presented.