Heavy Dynamical Fermions in Lattice QCD

It is expected that the only effect of heavy dynamical fermions in QCD is to renormalize the gauge coupling. We derive a simple expression for the shift in the gauge coupling induced by $N_f$ flavors of heavy fermions. We compare this formula to the shift in the gauge coupling at which the confinement-deconfinement phase transition occurs (at fixed lattice size) from numerical simulations as a function of quark mass and $N_f$. We find remarkable agreement with our expression down to a fairly light quark mass. However, simulations with eight heavy flavors and two light flavors show that the eight flavors do more than just shift the gauge coupling. We observe confinement-deconfinement transitions at $\beta=0$ induced by a large number of heavy quarks. We comment on the relevance of our results to contemporary simulations of QCD which include dynamical fermions.Comment: COLO-HEP-311, 26 pages and 6 postscript figures; file is a shar file and all macros are (hopefully) include

QCD Thermodynamics at Nt=8N_t=8 and 12

We present results from studies of high temperature QCD with two flavors of Kogut-Susskind quarks on $16^3\times 8$ lattices at a quark mass of $am_q=0.00625$ and on $24^3\times 12$ lattices at quark masses $am_q=0.008$ and 0.016. The value of the crossover temperature is consistent with that obtained on coarser lattices and/or at larger quark masses. Results are presented for the chiral order parameter and for the baryon number susceptibility.Comment: 3-pages, uuencoded compressed postscript file, contribution to Lattice'94 conferenc

An adaptive pseudo-spectral method for reaction diffusion problems

The spectral interpolation error was considered for both the Chebyshev pseudo-spectral and Galerkin approximations. A family of functionals I sub r (u), with the property that the maximum norm of the error is bounded by I sub r (u)/J sub r, where r is an integer and J is the degree of the polynomial approximation, was developed. These functionals are used in the adaptive procedure whereby the problem is dynamically transformed to minimize I sub r (u). The number of collocation points is then chosen to maintain a prescribed error bound. The method is illustrated by various examples from combustion problems in one and two dimensions

The Traveling Salesman Problem: Low-Dimensionality Implies a Polynomial Time Approximation Scheme

The Traveling Salesman Problem (TSP) is among the most famous NP-hard optimization problems. We design for this problem a randomized polynomial-time algorithm that computes a (1+eps)-approximation to the optimal tour, for any fixed eps>0, in TSP instances that form an arbitrary metric space with bounded intrinsic dimension. The celebrated results of Arora (A-98) and Mitchell (M-99) prove that the above result holds in the special case of TSP in a fixed-dimensional Euclidean space. Thus, our algorithm demonstrates that the algorithmic tractability of metric TSP depends on the dimensionality of the space and not on its specific geometry. This result resolves a problem that has been open since the quasi-polynomial time algorithm of Talwar (T-04)

The role of heavy fermions

Heavy dynamical fermions with masses around the cut-off do not change the low energy physics apart from a finite renormalization of the gauge coupling. In this paper we study how light the heavy fermions have to be to cause more than this trivial renormalization.Comment: uuencoded 3 page postscript contribution to Lattice 93, COLO-HEP-33

A Compton-thin Solution for the Suzaku X-ray Spectrum of the Seyfert 2 Galaxy Mkn 3

Mkn 3 is a Seyfert 2 galaxy that is widely regarded as an exemplary Compton-thick AGN. We study the Suzaku X-ray spectrum using models of the X-ray reprocessor that self-consistently account for the Fe K$\alpha$ fluorescent emission line and the associated Compton-scattered, or reflection, continuum. We find a solution in which the average global column density, $0.234^{+0.012}_{-0.010} \times 10^{24} \ \rm cm^{-2}$, is very different to the line-of-sight column density, $0.902^{+0.012}_{-0.013} \times 10^{24} \ \rm cm^{-2}$. The global column density is $\sim 5$ times smaller than that required for the matter distribution to be Compton-thick. Our model accounts for the profiles of the Fe K$\alpha$ and Fe K$\beta$ lines, and the Fe K edge remarkably well, with a solar abundance of Fe. The matter distribution could consist of a clumpy medium with a line-of-sight column density higher than the global average. A uniform, spherically-symmetric distribution alone cannot simultaneously produce the correct fluorescent line spectrum and reflection continuum. Previous works on Mkn 3, and other AGN, that assumed a reflection continuum from matter with an infinite column density could therefore lead to erroneous or "puzzling" conclusions if the matter out of the line-of-sight is really Compton-thin. Whereas studies of samples of AGN have generally only probed the line-of-sight column density, with simplistic, one-dimensional models, it is important now to establish the global column densities in AGN. It is the global properties that affect the energy budget in terms of reprocessing of X-rays into infrared emission, and that constrain population synthesis models of the cosmic X-ray background.Comment: Accepted by MNRAS, 23 pages, 6 figures, 4 table

Deepwater Drilling: Law, Policy, and Economics of Firm Organization and Safety

Although the causes of the Deepwater Horizon spill are not yet conclusively identified, significant attention has focused on the safety-related policies and practices—often referred to as the safety culture—of BP and other firms involved in drilling the well. This paper defines and characterizes the economic and policy forces that affect safety culture and identifies reasons why those forces may or may not be adequate or effective from the public’s perspective. Two potential justifications for policy intervention are that: a) not all of the social costs of a spill may be internalized by a firm; and b) there may be principal-agency problems within the firm, which could be reduced by external monitoring. The paper discusses five policies that could increase safety culture and monitoring: liability, financial responsibility (a requirement that a firm’s assets exceed a threshold), government oversight, mandatory private insurance, and risk-based drilling fees. We find that although each policy has a positive effect on safety culture, there are important differences and interactions that must be considered. In particular, the latter three provide external monitoring. Furthermore, raising liability caps without mandating insurance or raising financial responsibility requirements could have a small effect on the safety culture of small firms that would declare bankruptcy in the event of a large spill. The paper concludes with policy recommendations for promoting stronger safety culture in offshore drilling; our preferred approach would be to set a liability cap for each well equal to the worst-case social costs of a spill, and to require insurance up to the cap.Deepwater Horizon, BP oil spill, safety culture, government policy, liability caps, financial responsibility, insurance

Lattice QCD Production on Commodity Clusters at Fermilab

We describe the construction and results to date of Fermilab's three Myrinet-networked lattice QCD production clusters (an 80-node dual Pentium III cluster, a 48-node dual Xeon cluster, and a 128-node dual Xeon cluster). We examine a number of aspects of performance of the MILC lattice QCD code running on these clusters.Comment: Talk from the 2003 Computing in High Energy and Nuclear Physics (CHEP03), La Jolla, Ca, USA, March 2003, 6 pages, LaTeX, 8 eps figures. PSN TUIT00

Two-Flavor Staggered Fermion Thermodynamics at N_t = 12

We present results of an ongoing study of the nature of the high temperature crossover in QCD with two light fermion flavors. These results are obtained with the conventional staggered fermion action at the smallest lattice spacing to date---approximately 0.1 fm. Of particular interest are a study of the temperature of the crossover a determination of the induced baryon charge and baryon susceptibility, the scalar susceptibility, and the chiral order parameter, used to test models of critical behavior associated with chiral symmetry restoration. From our new data and published results for N_t = 4, 6, and 8, we determine the QCD magnetic equation of state from the chiral order parameter using O(4) and mean field critical exponents and compare it with the corresponding equation of state obtained from an O(4) spin model and mean field theory. We also present a scaling analysis of the Polyakov loop, suggesting a temperature dependent ``constituent quark free energy.''Comment: LaTeX 25 pages, 15 Postscript figure