Path Integrals in Lattice Quantum Chromodynamics

I discuss the use of path integrals to study strong-interaction physics from first principles. The underlying theory is cast into path integrals which are evaluated numerically using Monte Carlo methods on a space-time lattice. Examples are given on progress related to nuclear physics.Comment: 6 pages, 5 figures. Talk given at the International Conference on Path Integrals - New Trends and Perspectives, 23-28 September 2007, Dresden, German

Excited Baryons and Chiral Symmetry Breaking of QCD

N* masses in the spin-1/2 and spin-3/2 sectors are computed using two non-perturbative methods: lattice QCD and QCD sum rules. States with both positive and negative parity are isolated via parity projection methods. The basic pattern of the mass splittings is consistent with experiments. The mass splitting within the same parity pair is directly linked to the chiral symmetry breaking QCD.Comment: contribution to Baryon 2002, 5 pages, 3 figure

Scattering phaseshift formulas for mesons and baryons in elongated boxes

We derive L\"{u}scher phaseshift formulas for two-particle states in boxes elongated in one of the dimensions. Such boxes offer a cost-effective way of varying the relative momentum of the particles. Boosted states in the elongated direction, which allow wider access to energies, are also considered. The formulas for the various scenarios (moving and zero-momentum states in cubic and elongated boxes) are compared and relations between them are clarified. The results are applicable to a wide set of meson-meson and meson-baryon elastic scattering processes, with the two-particle system having equal or unequal masses.Comment: 28 pages, 2 figures, 16 tables. Updated to match published versio

Neutron electric polarizability

We use the background field method to extract the "connected" piece of the neutron electric polarizability. We present results for quenched simulations using both clover and Wilson fermions and discuss our experience in extracting the mass shifts and the challenges we encountered when we lowered the quark mass. For the neutron we find that as the pion mass is lowered below 500\MeV, the polarizability starts rising in agreement with predictions from chiral perturbation theory. For our lowest pion mass, m_\pi=320\MeV, we find that \alpha_n = 3.8(1.3)\times 10^{-4}\fm^3, which is still only one third of the experimental value. We also present results for the neutral pion; we find that its polarizability turns negative for pion masses smaller than 500\MeV which is puzzling.Comment: 11 pages, 8 figures, presented at the XXVII International Symposium on Lattice Field Theory, July 26-31, 2009, Peking University, Beijing, Chin

EMMIX-uskew: An R Package for Fitting Mixtures of Multivariate Skew t-distributions via the EM Algorithm

This paper describes an algorithm for fitting finite mixtures of unrestricted Multivariate Skew t (FM-uMST) distributions. The package EMMIX-uskew implements a closed-form expectation-maximization (EM) algorithm for computing the maximum likelihood (ML) estimates of the parameters for the (unrestricted) FM-MST model in R. EMMIX-uskew also supports visualization of fitted contours in two and three dimensions, and random sample generation from a specified FM-uMST distribution. Finite mixtures of skew t-distributions have proven to be useful in modelling heterogeneous data with asymmetric and heavy tail behaviour, for example, datasets from flow cytometry. In recent years, various versions of mixtures with multivariate skew t (MST) distributions have been proposed. However, these models adopted some restricted characterizations of the component MST distributions so that the E-step of the EM algorithm can be evaluated in closed form. This paper focuses on mixtures with unrestricted MST components, and describes an iterative algorithm for the computation of the ML estimates of its model parameters. The usefulness of the proposed algorithm is demonstrated in three applications to real data sets. The first example illustrates the use of the main function fmmst in the package by fitting a MST distribution to a bivariate unimodal flow cytometric sample. The second example fits a mixture of MST distributions to the Australian Institute of Sport (AIS) data, and demonstrate that EMMIX-uskew can provide better clustering results than mixtures with restricted MST components. In the third example, EMMIX-uskew is applied to classify cells in a trivariate flow cytometric dataset. Comparisons with other available methods suggests that the EMMIX-uskew result achieved a lower misclassification rate with respect to the labels given by benchmark gating analysis

Light Hadron Spectroscopy on Coarse Lattices with O(a^2) Mean-Field Improved Actions

The masses and dispersions of light hadrons are calculated in lattice QCD using an O(a^2) tadpole-improved gluon action and an O(a^2) tadpole-improved next-nearest-neighbor fermion action originally proposed by Hamber and Wu. Two lattices of constant volume with lattice spacings of approximately 0.40 fm and 0.24 fm are considered. The results reveal some scaling violations at the coarser lattice spacing on the order of 5%. At the finer lattice spacing, the calculated mass ratios reproduce state-of-the-art results using unimproved actions. Good dispersion and rotational invariance up to momenta of pa ~ 1 are also found. The relative merit of alternative choices for improvement operators is assessed through close comparisons with other plaquette-based tadpole-improved actions.Comment: 17 page RevTeX manuscript. 7 Figures. This and related papers may also be obtained from http://www.physics.adelaide.edu.au/~dleinweb/Publications.htm