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

The beta function and equation of state for QCD with two flavors of quarks

We measure the pressure and energy density of two flavor QCD in a wide range of quark masses and temperatures. The pressure is obtained from an integral over the average plaquette or psi-bar-psi. We measure the QCD beta function, including the anomalous dimension of the quark mass, in new Monte Carlo simulations and from results in the literature. We use it to find the interaction measure, E-3p, yielding non-perturbative values for both the energy density E and the pressure p. uuencoded compressed PostScript file Revised version should work on more PostScript printers.Comment: 24 page

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

Scaling of Pseudo-Critical Couplings in Two-Flavour QCD

We study the scaling behaviour of the pseudo-critical couplings for the chiral phase transition in two-flavour QCD. We show that all existing results from lattice simulations on lattices with temporal extent $N_\tau = 4$, 6 and 8 can be mapped onto a universal scaling curve. The relevant combination of critical exponents, $\beta\delta$, is consistent with the scaling behaviour expected for a second order phase transition with $O(4)$ exponents. At present, scaling according to the $O(2)$ symmetry group can, however, not be ruled out.Comment: 8 pages, NSF-ITP 93-12

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)

Quark number susceptibilities, strangeness and dynamical confinement

We report first results on the strange quark number susceptibility, chi_s, over a large range of temperatures, mainly in the plasma phase of QCD. Chi_s jumps across the phase transition temperature, T_c, and grows rapidly with temperature above but close to T_c. For all quark masses and susceptibilities in the entire temperature range studied, we found significant departures from ideal-gas values. We also observed a strong correlation between these quantities and the susceptibility in the scalar/pseudo-scalar channel, supporting ideas of ``dynamical confinement'' in the high temperature phase of the QCD plasma.Comment: 4 pages, 4 figure

Potential model calculations and predictions for heavy quarkonium

We investigate the spectroscopy and decays of the charmonium and upsilon systems in a potential model consisting of a relativistic kinetic energy term, a linear confining term including its scalar and vector relativistic corrections and the complete perturbative one-loop quantum chromodynamic short distance potential. The masses and wave functions of the various states are obtained using a variational technique, which allows us to compare the results for both perturbative and nonperturbative treatments of the potential. As well as comparing the mass spectra, radiative widths and leptonic widths with the available data, we include a discussion of the errors on the parameters contained in the potential, the effect of mixing on the leptonic widths, the Lorentz nature of the confining potential and the possible $c\bar{c}$ interpretation of recently discovered charmonium-like states.Comment: Physical Review published versio

Pressure and non-linear susceptibilities in QCD at finite chemical potentials

When the free energy density of QCD is expanded in a series in the chemical potential, mu, the Taylor coefficients are the non-linear quark number susceptibilities. We show that these depend on the prescription for putting chemical potential on the lattice, making all extrapolations in chemical potential prescription dependent at finite lattice spacing. To put bounds on the prescription dependence, we investigate the magnitude of the non-linear susceptibilities over a range of temperature, T, in QCD with two degenerate flavours of light dynamical quarks at lattice spacing 1/4T. The prescription dependence is removed in quenched QCD through a continuum extrapolation, and the dependence of the pressure, P, on mu is obtained.Comment: 15 pages, 2 figures. Data on chi_uuuu added, discussion enhance