The Sigma Commutator from Lattice QCD

As a direct source of information on chiral symmetry breaking within QCD, the sigma commutator is of considerable importance. Since hadron structure is a non-perturbative problem, numerical calculations on a space-time lattice are currently the only rigorous approach. With recent advances in the calculation of hadron masses within full QCD, it is of interest to see whether the sigma commutator can be calculated directly from the dependence of the nucleon mass on the input quark mass. We show that, provided the correct chiral behaviour of QCD is respected in the extrapolation to realistic quark masses, one can indeed obtain a fairly reliable determination of the sigma commutator using present lattice data. For two-flavour dynamical fermion QCD the sigma commutator lies between 45 and 55 MeV based on recent data from CP-PACS and UKQCD.Comment: 4 pages, 3 figures, uses espcrc1.sty and epsfig.sty. Contribution to the proceedings of the International Conference on Quark Nuclear Physics held in Adelaide Feb. 200

Chiral Nonanalytic Behaviour: The Edinburgh Plot

The Edinburgh Plot is a scale independent way of presenting lattice QCD calculations over a wide range of quark masses. In this sense it is appealing as an indicator of how the approach to physical quark masses is progressing. The difficulty remains that even the most state of the art calculations are still at quark masses that are too heavy to apply dimensionally-regulated chiral perturbation theory. We present a method allowing predictions of the behaviour of the Edinburgh plot, in both the continuum, and on the lattice.Comment: 3 pages, 4 figures, Lattice2002(Spectrum

Baryon Mass Extrapolation

Consideration of the analytical properties of pion-induced baryon self-energies leads to new functional forms for the extrapolation of light baryon masses. These functional forms reproduce the leading non-analytic behavior of chiral perturbation theory, the correct heavy-quark limit and have the advantage of containing information on the extended structure of hadrons. The forms involve only three unknown parameters which may be optimized by fitting to present lattice data. Recent dynamical fermion results from CP-PACS and UK-QCD are extrapolated using these new functional forms. We also use these functions to probe the limit of the chiral perturbative regime and shed light on the applicability of chiral perturbation theory to the extrapolation of present lattice QCD results.Comment: LATTICE99 (QCD Spectrum and Quark Masses

Chiral Corrections to Baryon Masses Calculated within Lattice QCD

Consideration of the analytic properties of pion-induced baryon self energies leads to new functional forms for the extrapolation of light baryon masses. These functional forms reproduce the leading non-analytic behavior of chiral perturbation theory, the correct non-analytic behavior at the $N \pi$ threshold and the appropriate heavy-quark limit. They involve only three unknown parameters, which may be obtained by fitting lattice QCD data. Recent dynamical fermion results from CP-PACS and UKQCD are extrapolated using these new functional forms. We also use these functions to probe the limit of applicability of chiral perturbation theory.Comment: 4 pages, 2 figures, Contribution to the Proceedings of the 15th Particles and Nuclei International Conference (PANIC 99), Uppsala, Sweden, June 10-16, 199

Dynamical chiral symmetry breaking and a critical mass

On a bounded, measurable domain of non-negative current-quark mass, realistic models of QCD's gap equation can simultaneously admit two inequivalent dynamical chiral symmetry breaking (DCSB) solutions and a solution that is unambiguously connected with the realisation of chiral symmetry in the Wigner mode. The Wigner solution and one of the DCSB solutions are destabilised by a current-quark mass and both disappear when that mass exceeds a critical value. This critical value also bounds the domain on which the surviving DCSB solution possesses a chiral expansion. This value can therefore be viewed as an upper bound on the domain within which a perturbative expansion in the current-quark mass around the chiral limit is uniformly valid for physical quantities. For a pseudoscalar meson constituted of equal mass current-quarks, it corresponds to a mass m_{0^-}~0.45GeV. In our discussion we employ properties of the two DCSB solutions of the gap equation that enable a valid definition of in the presence of a nonzero current-mass. The behaviour of this condensate indicates that the essentially dynamical component of chiral symmetry breaking decreases with increasing current-quark mass.Comment: 9 pages, 7 figures. Minor wording change

A Radial Basis Function (RBF) Compact Finite Difference (FD) Scheme for Reaction-Diffusion Equations on Surfaces

We present a new high-order, local meshfree method for numerically solving reaction diffusion equations on smooth surfaces of codimension 1 embedded in ℝd. The novelty of the method is in the approximation of the Laplace-Beltrami operator for a given surface using Hermite radial basis function (RBF) interpolation over local node sets on the surface. This leads to compact (or implicit) RBF generated finite difference (RBF-FD) formulas for the Laplace-Beltrami operator, which gives rise to sparse differentiation matrices. The method only requires a set of (scattered) nodes on the surface and an approximation to the surface normal vectors at these nodes. Additionally, the method is based on Cartesian coordinates and thus does not suffer from any coordinate singularities. We also present an algorithm for selecting the nodes used to construct the compact RBF-FD formulas that can guarantee the resulting differentiation matrices have desirable stability properties. The improved accuracy and computational cost that can be achieved with this method over the standard (explicit) RBF-FD method are demonstrated with a series of numerical examples. We also illustrate the flexibility and general applicability of the method by solving two different reaction-diffusion equations on surfaces that are defined implicitly and only by point clouds

Chiral Extrapolation: An Analogy with Effective Field Theory

We draw an analogy between the chiral extrapolation of lattice QCD calculations from large to small quark masses and the interpolation between the large mass (weak field) and small mass (strong field) limits of the Euler--Heisenberg QED effective action. In the latter case, where the exact answer is known, a simple extrapolation of a form analogous to those proposed for the QCD applications is shown to be surprisingly accurate over the entire parameter range.Comment: 6 pp, revtex, 3 figs; minor changes -- version to appear in PL

Performance of a multi-disciplinary emergency department observation protocol for acetaminophen overdose.

The availability of 20-h N-acetylcysteine (NAC) infusion for low-risk acetaminophen (APAP) overdose enabled our center to implement an Emergency Department observation unit (OU) protocol as an alternative to hospitalization. Our objective was to evaluate our early experience with this protocol. This retrospective cohort study included all patients treated for low-risk APAP overdose in our academic hospital between 2006 and 2011. Cases were identified using OU and pharmacy records. Successful OU discharge was defined as disposition with no inpatient admission. Differences in medians with 95 % confidence intervals were used for comparisons. One hundred ninety-six patients received NAC for APAP overdose with a mean age of 35 years (SD 14); 73 % were white, and 43 % were male. Twenty (10 %) received care in the OU; 3/20(15 %) met criteria for inclusion in the OU protocol and 13/20(65 %) were discharged successfully. Out of the 196 patients, 10 met criteria for inclusion in the OU protocol but instead received care in the inpatient setting. The median total length of stay from presentation to ED discharge was 41 h for all patients treated in the OU, compared to 68 h for ten patients who met criteria for inclusion in the OU protocol but who were admitted (difference 27 h, 95 % CI 18-72 h). ED observation for APAP overdose can be a viable alternative to inpatient admission. Most patients were successfully discharged from the OU. This evaluation identified both over- and under-utilization of the OU. OU treatment resulted in shorter median length of stay than inpatient admission