A new method for computing all elements of the lattice quark propagator is proposed. The method combines the spectral decomposition of the propagator, computing the lowest eigenmodes exactly, with noisy estimators which are 'diluted', i.e. taken to have support only on a subset of time, space, spin or colour. We find that the errors are dramatically reduced compared to traditional noisy estimator techniques.Comment: 24 pages, 18 figure

The simulation of QCD on dynamical (Nf=2) anisotropic lattices is described. A method for nonperturbative renormalisation of the parameters in the anisotropic gauge and quark actions is presented. The precision with which this tuning can be carried out is determined in dynamical simulations on 8^3x48 and 8^3x80 lattices.Comment: 6 pages, 6 figures. Added plot of static quark potential. To be published in Phys.Rev.

We discuss a robust projection method for the extraction of excited-state masses of the nucleon from a matrix of correlation functions. To illustrate the algorithm in practice, we present results for the positive parity excited states of the nucleon in quenched QCD. Using eigenvectors obtained via the variational method, we construct an eigenstate-projected correlation function amenable to standard analysis techniques. The method displays its utility when comparing results from the fit of the projected correlation function with those obtained from the eigenvalues of the variational method. Standard nucleon interpolators are considered, with 2 × 2 and 3 × 3 correlation matrix analyses presented using various combinations of source-smeared, sink-smeared and smeared-smeared correlation functions. Using these new robust methods, we observe a systematic dependency of the extracted nucleon excited-state masses on source-and sink-smearing levels. To the best of our knowledge, this is the first clear indication that a correlation matrix of standard nucleon interpolators is insufficient to isolate the eigenstates of QCD.

We present results for the negative parity low-lying state of the nucleon, N 1 2 − (1535 MeV) S 11 , from a variational analysis method. The analysis is performed in quenched QCD with the FLIC fermion action. The principal focus of this paper is to explore the level ordering between the Roper (P 11 ) and the negative parity ground (S 11 ) states of the nucleon. Evidence of the physical level ordering is observed at light quark masses. A wide variety of smearedsmeared correlation functions are used to construct correlation matrices. A comprehensive correlation matrix analysis is performed to ensure an accurate isolation of the N 1 2 − state.

We present results for the first positive parity excited state of the nucleon, namely, the Roper resonance (N 1 2 + =1440 MeV) from a variational analysis technique. The analysis is performed for pion masses as low as 224 MeV in quenched QCD with the FLIC fermion action. A wide variety of smeared-smeared correlation functions are used to construct correlation matrices. This is done in order to find a suitable basis of operators for the variational analysis such that eigenstates of the QCD Hamiltonian may be isolated. A lower lying Roper state is observed that approaches the physical Roper state. To the best of our knowledge, the first time this state has been identified at light quark masses using a variational approach.

We present results for the spectrum of static-light mesons from N f = 2 lattice QCD. These results were obtained using all-to-all light quark propagators on an anisotropic lattice, yielding an improved signal resolution when compared to more conventional lattice techniques. With a light quark mass close to the strange quark, we have measured the splittings between the ground-state S-wave staticlight meson and higher excitations. We attempt to identify the quantum numbers of the excited states in the context of the reduced spatial symmetries of the lattice.

Positive-parity spin-1 2 excitations of the nucleon are explored in lattice QCD. The variational method is used in this investigation and several correlation matrices are employed. As our focus is on the utility and methodology of the variational approach, we work in the quenched approximation to QCD. Various sweeps of Gaussian fermion-field smearing are applied at the source and at the sink of 1 " 1 and 1 2 correlation functions to obtain a large basis of operators. Using several different approaches for constructing basis interpolators, we demonstrate how improving the basis can split what otherwise might be interpreted as a single state into multiple eigenstates. Consistency of the extracted excited energy states are explored over various dimensions of the correlation matrices. The use of large correlation matrices is emphasized for the reliable extraction of the excited eigenstates of QCD.

We compute charmonium spectral functions in 2-flavour QCD using the maximum entropy method and anisotropic lattices. We find that the S-waves (J/ψ and η c ) survive up to temperatures close to 2T c , while the P-waves (χ c0 and χ c1 ) melt away below 1.3T c .