Monte Carlo Quasi-Heatbath by approximate inversion

When sampling the distribution P(phi) ~ exp(-|A phi|^2), a global heatbath normally proceeds by solving the linear system A phi = eta, where eta is a normal Gaussian vector, exactly. This paper shows how to preserve the distribution P(phi) while solving the linear system with arbitrarily low accuracy. Generalizations are presented.Comment: 10 pages, 1 figure; typos corrected, reference added; version to appear in Phys. Rev.

Improving Stochastic Estimator Techniques for Disconnected Diagrams

Disconnected diagrams are expected to be sensitive to the inclusion of dynamical fermions. We present a feasibility study for the observation of such effects on the nucleonic matrix elements of the axial vector current, using SESAM full QCD vacuum configurations with Wilson fermions on $16^3\times 32$ lattices, at $\beta =5.6$. Starting from the standard methods developed by the Kentucky and Tsukuba groups, we investigate the improvement from various refinements thereof.Comment: One author added. Contribution to Lattice 1997, 3 pages LaTex, to appear in Nucl. Phys. B (Proc. Suppl.

Improved Upsilon Spectrum with Dynamical Wilson Fermions

We present results for the b \bar b spectrum obtained using an O(M_bv^6)-correct non-relativistic lattice QCD action, where M_b denotes the bare b-quark mass and v^2 is the mean squared quark velocity. Propagators are evaluated on SESAM's three sets of dynamical gauge configurations generated with two flavours of Wilson fermions at beta = 5.6. These results, the first of their kind obtained with dynamical Wilson fermions, are compared to a quenched analysis at equivalent lattice spacing, beta = 6.0. Using our three sea-quark values we perform the ``chiral'' extrapolation to m_eff = m_s/3, where m_s denotes the strange quark mass. The light quark mass dependence is found to be small in relation to the statistical errors. Comparing the full QCD result to our quenched simulation we find better agreement of our dynamical data with experimental results in the spin-independent sector but observe no unquenching effects in hyperfine-splittings. To pin down the systematic errors we have also compared quenched results in different ``tadpole'' schemes as well as using a lower order action. We find that spin-splittings with an O(M_bv^4) action are O(10%) higher compared to O(M_bv^6) results. Relative to the results obtained with the plaquette method the Landau gauge mean link tadpole scheme raises the spin splittings by about the same margin so that our two improvements are opposite in effect.Comment: 24 pages (latex file, Phys Rev D style file, uses epsf-style

A High Precision Study of the QQ(bar) Potential from Wilson Loops in the Regime of String Breaking

For lattice QCD with two sea quark flavours we compute the static quark antiquark potential V(R) in the regime where string breaking is expected. In order to increase statistics, we make full use of the lattice information by including all lattice vectors R to any possible lattice separation in the infrared regime. The corresponding paths between the lattice points are constructed by means of a generalized Bresenham algorithm as known from computer graphics. As a results we achieve a determination of the unquenched potential in the range .8 to 1.5 fm with hitherto unknown precision. Furthermore, we demonstrate some error reducing methods for the evaluation of the transition matrix element between two- and four-quark states.Comment: 6 pages, 7 figure

Finite Density Algorithm in Lattice QCD -- a Canonical Ensemble Approach

I will review the finite density algorithm for lattice QCD based on finite chemical potential and summarize the associated difficulties. I will propose a canonical ensemble approach which projects out the finite baryon number sector from the fermion determinant. For this algorithm to work, it requires an efficient method for calculating the fermion determinant and a Monte Carlo algorithm which accommodates unbiased estimate of the probability. I shall report on the progress made along this direction with the Pad\'{e} - Z$_2$ estimator of the determinant and its implementation in the newly developed Noisy Monte Carlo algorithm.Comment: Invited talk at Nankai Symposium on Mathematical Physics, Tianjin, Oct. 2001, 18 pages, 3 figures; expanded and references adde

Bottomonium from NRQCD with Dynamical Wilson Fermions

We present results for the b \bar b spectrum obtained using an O(M_bv^6)-correct non-relativistic lattice QCD action. Propagators are evaluated on SESAM's three sets of dynamical gauge configurations generated with two flavours of Wilson fermions at beta = 5.6. Compared to a quenched simulation at equivalent lattice spacing we find better agreement of our dynamical data with experimental results in the spin-independent sector but observe no unquenching effects in hyperfine-splittings. To pin down the systematic errors we have also compared quenched results in different ``tadpole'' schemes and used a lower order action.Comment: Talk presented at LATTICE'97, 3 pages, Late

On the low fermionic eigenmode dominance in QCD on the lattice

We demonstrate the utility of a spectral approximation to fermion loop operators using low-lying eigenmodes of the hermitian Dirac-Wilson matrix, Q. The investigation is based on a total of 400 full QCD vacuum configurations, with two degenerate flavors of dynamical Wilson fermions at beta =5.6, at two different sea quark masses. The spectral approach is highly competitive for accessing both topological charge and disconnected diagrams, on large lattices and small quark masses. We propose suitable partial summation techniques that provide sufficient saturation for estimating Tr Q^{-1}, which is related to the topological charge. In the effective mass plot of the eta' meson we achieved a consistent early plateau formation, by ground state projecting the connected piece of its propagator.Comment: 15 pages, 25 figures, citations adde

Moments of Structure Functions in Full QCD

Moments of the quark density distribution, moments of the quark helicity distribution, and the tensor charge are calculated in full QCD. Calculations of matrix elements of operators from the operator product expansion have been performed on $16^3 \times 32$ lattices for Wilson fermions at $\beta = 5.6$ using configurations from the SESAM collaboration and at $\beta = 5.5$ using configurations from SCRI. One-loop perturbative renormalization corrections are included. Selected results are compared with corresponding quenched calculations and with calculations using cooled configurations.Comment: Lattice 2000 (Hadronic Matrix Elements), 4 pages, 5 figure

An Estimate of alpha_S from Bottomonium in Unquenched QCD

We estimate the strong coupling constant from the perturbative expansion of the plaquette. The scale is set by the 2S-1S and 1P-1S splittings in bottomonium which are computed in NRQCD on dynamical gauge configurations with nf=2 degenerate Wilson quarks at intermediate masses. We have increased the statistics of our spectrum calculation in order to reliably extrapolate in the sea-quark mass. We find a value of alpha_MS(m_Z) = 0.1118(26) which is somewhat lower than previous estimates within NRQCD.Comment: LATTICE98(heavyqk

Flavour singlet pseudoscalar masses in N_f = 2 QCD

We perform a lattice mass analysis in the flavour singlet pseudoscalar channel on the SESAM and TXL full QCD vacuum configurations, with 2 active flavours of dynamical Wilson fermions at beta = 5.6. At our inverse lattice spacing, a^-1 = 2.3 GeV, we retrieve by a chiral extrapolation to the physical light quark masses the value m_eta' = 3.7(+8)(-4) m_pi. A crude extrapolation from (N_f = 3) phenomenology would suggest m_eta' \approx 5.1 m_pi for N_f = 2 QCD. we verify that the mass gap between the singlet state eta' and the pi flavour triplt state is due to gauge configurations with non-trivial topology.Comment: 8 pages, 10 figure