First results with non-perturbative fermion improvement

We present initial results for light hadron masses and nucleon structure functions using a recent proposal for eliminating all $O(a)$ effects from Wilson fermion simulations in the quenched approximation. With initially limited statistics, we find a much more linear APE plot and a value of the axial coupling $g_A$ nearer to the experimental point than with comparable runs using unimproved Wilson fermions.Comment: 3 pages, 2 PostScript figures, LaTeX 2.09 with espcrc2.sty v2.6, amstex and epsf, talk presented at LATTICE96(phenomenology) by P. Stephenso

Resummation of Cactus Diagrams in Lattice QCD, to all Orders

We show how to perform a resummation, to all orders in perturbation theory, of a certain class of gauge invariant tadpole-like diagrams in Lattice QCD. These diagrams are often largely responsible for lattice artifacts. Our resummation leads to an improved perturbative expansion. Applied to a number of cases of interest, e.g. the lattice renormalization of some two-fermion operators, this expansion yields results remarkably close to corresponding nonperturbative estimates. We consider in our study both the Wilson and the clover action for fermions.Comment: LATTICE99(Improvement and Renormalization), 3 pages, LATeX with eps figures, uses espcrc2.sty. Corrected a statement regarding comparison with other methods. (We thank A. Kronfeld for bringing this point to our attention.

Quenching Effects in the Hadron Spectrum

Lattice QCD has generated a wealth of data in hadronic physics over the last two decades. Until relatively recently, most of this information has been within the "quenched approximation" where virtual quark--anti-quark pairs are neglected. This review presents a descriptive discussion of the effects of removing this approximation in the calculation of hadronic masses.Comment: To appear in "Lattice Hadron Physics", ed. A.C. Kalloniatis, D.B. Leinweber and A.G. William

Perturbative Renormalization of Improved Lattice Operators

We derive bases of improved operators for all bilinear quark currents up to spin two (including the operators measuring the first moment of DIS Structure Functions), and compute their one-loop renormalization constants for arbitrary coefficients of the improvement terms. We have thus control over O(a) corrections, and for a suitable choice of improvement coefficients we are only left with errors of O(a^2).Comment: 4 pages, LaTeX + 1 eps file + epscrc2.sty (included). Talk given to the Lattice 97 International Symposium, 22-26 July 1997, Edinburgh, UK. Minor changes in notatio

The Critical Hopping Parameter in O(a) improved Lattice QCD

We calculate the critical value of the hopping parameter, $\kappa_c$, in O(a) improved Lattice QCD, to two loops in perturbation theory. We employ the Sheikholeslami-Wohlert (clover) improved action for Wilson fermions. The quantity which we study is a typical case of a vacuum expectation value resulting in an additive renormalization; as such, it is characterized by a power (linear) divergence in the lattice spacing, and its calculation lies at the limits of applicability of perturbation theory. The dependence of our results on the number of colors $N$, the number of fermionic flavors $N_f$, and the clover parameter $c_{SW}$, is shown explicitly. We compare our results to non perturbative evaluations of $\kappa_c$ coming from Monte Carlo simulations.Comment: 11 pages, 2 EPS figures. The only change with respect to the original version is inclusion of the standard formulae for the gauge fixing and ghost parts of the action. Accepted for publication in Physical Review

SSOR Preconditioning of Improved Actions

We generalize local lexicographic SSOR preconditioning for the Sheikholeslami-Wohlert improved Wilson fermion action and the truncated perfect free fermion action. In our test implementation we achieve performance gains as known from SSOR preconditioning of the standard Wilson fermion action.Comment: 3 pages, Latex, 3 figures, Talk presented at Lattice'9

O(a)O(a) Improvement of Nucleon Matrix Elements

We report on preliminary results of a high statistics quenched lattice QCD calculation of nucleon matrix elements within the Symanzik improvement programme. Using the recently determined renormalisation constants from the Alpha Collaboration we present a fully non-pertubative calculation of the forward nucleon axial matrix element with $O(a)$ lattice artifacts completely removed. Runs are made at $\beta=6.0$ and $\beta=6.2$, in an attempt to check scaling and $O(a^2)$ effects. We shall also briefly describe results for $$, the matrix element of a higher derivative operator.Comment: 3 pages, Latex, 4 figures, epsf.sty and espcrc2.sty needed, Talk given at LATTICE97. Figure 4 correcte

Perturbative renormalization of bilinear quark and gluon operators

The renormalisation constants for local bilinear quark operators are calculated using the Sheikholeslami-Wohlert improved action. In addition we compute the renormalisation constant of the leading gluon operator for different group representations and discuss the mixing of the operators E^2 and B^2.Comment: 3 pages, poster contributed at Lattice96, St. Loui

Jump Markov Chains and Rejection-Free Metropolis Algorithms

We consider versions of the Metropolis algorithm which avoid the inefficiency of rejections. We first illustrate that a natural Uniform Selection Algorithm might not converge to the correct distribution. We then analyse the use of Markov jump chains which avoid successive repetitions of the same state. After exploring the properties of jump chains, we show how they can exploit parallelism in computer hardware to produce more efficient samples. We apply our results to the Metropolis algorithm, to Parallel Tempering, and to a two-dimensional ferromagnetic 4$\times$4 Ising model.Comment: 18 pages, 8 figure

Generalised Spin Projection for Fermion Actions

The majority of compute time doing lattice QCD is spent inverting the fermion matrix. The time that this takes increases with the condition number of the matrix. The FLIC(Fat Link Irrelevant Clover) action displays, among other properties, an improved condition number compared to standard actions and hence is of interest due to potential compute time savings. However, due to its two different link sets there is a factor of two cost in floating point multiplications compared to the Wilson action. An additional factor of two has been attributed due to the loss of the so-called spin projection trick. We show that any split-link action may be written in terms of spin projectors, reducing the additional cost to at most a factor of two. Also, we review an efficient means of evaluating the clover term, which is additional expense not present in the Wilson action.Comment: 4 page