A Phenomenological Treatment of Chiral Symmetry Restoration and Deconfinement

A phenomenological expression for the thermodynamic potential of gluons and quarks is constructed which incorporates the features of deconfinement and chiral symmetry restoration known from lattice simulations. The thermodynamic potential is a function of the Polyakov loop and chiral condensate expectation values. The gluonic sector uses a successful model for pure (SU(N_c)) gauge theories in which the Polyakov loop eigenvalues are the fundamental order parameters for deconfinement. The quark sector is given by a Nambu-Jona-Lasinio model in which a constant background (A_0) field couples the chiral condensate to the Polyakov loop. We consider the case of (N_f = 2) in detail. For two massless quarks, we find a second order chiral phase transition. Confinement effects push the transition to higher temperatures, but the entropy associated with the gluonic sector acts in the opposite direction. For light mass quarks, only a rapid crossover occurs. For sufficiently heavy quarks, a first order deconfinement transition emerges. This simplest model has one adjustable parameter, which can be set from the chiral transition temperature for light quarks. It predicts all thermodynamic quantities as well as the behavior of the chiral condensate and the Polyakov loop over a wide range of temperatures.Comment: 3 pages, 4 eps figures, Lattice 2002 conference contribution, Lattice2002(nonzerot

Wilson Polynomials and the Lorentz Transformation Properties of the Parity Operator

The parity operator for a parity-symmetric quantum field theory transforms as an infinite sum of irreducible representations of the homogeneous Lorentz group. These representations are connected with Wilson polynomials

Flavor Relationships Among Muscles of the Beef Chuck and Round

Flavor relationships among muscles and causes of liver-like off-flavor of six muscles from each of 30 beef carcasses were evaluated by a trained sensory panel. The infraspinatus (flat iron) was lowest in sour, metallic, and oxidized flavors and highest in fatty flavor. The vastus lateralis (knuckle side) had the most intense off-flavor and was among the highest for sour and oxidized. Heme iron concentration and pH were lowly related to off-flavor. Of 18 muscles from three carcasses, 16 were high in liver-like off-flavor. These data suggest liver-like off-flavor is related to something that impacts the entire animal

Complete High Temperature Expansions for One-Loop Finite Temperature Effects

We develop exact, simple closed form expressions for partition functions associated with relativistic bosons and fermions in odd spatial dimensions. These expressions, valid at high temperature, include the effects of a non-trivial Polyakov loop and generalize well-known high temperature expansions. The key technical point is the proof of a set of Bessel function identities which resum low temperature expansions into high temperature expansions. The complete expressions for these partition functions can be used to obtain one-loop finite temperature contributions to effective potentials, and thus free energies and pressures.Comment: 9 pages, RevTeX, no figures. To be published in Phys. Rev D. v2 has revised introduction and conclusions, plus a few typographical errors are corrected; v3 corrects one typ

Flavor Relationships Among Muscles of the Beef Chuck and Round

Flavor relationships among muscles and causes of liver-like off-flavor of six muscles from each of 30 beef carcasses were evaluated by a trained sensory panel. The infraspinatus (flat iron) was lowest in sour, metallic, and oxidized flavors and highest in fatty flavor. The vastus lateralis (knuckle side) had the most intense off-flavor and was among the highest for sour and oxidized. Heme iron concentration and pH were lowly related to off-flavor. Of 18 muscles from three carcasses, 16 were high in liver-like off-flavor. These data suggest liver-like off-flavor is related to something that impacts the entire animal

The Finite Temperature SU(2) Savvidy Model with a Non-trivial Polyakov Loop

We calculate the complete one-loop effective potential for SU(2) gauge bosons at temperature T as a function of two variables: phi, the angle associated with a non-trivial Polyakov loop, and H, a constant background chromomagnetic field. Using techniques broadly applicable to finite temperature field theories, we develop both low and high temperature expansions. At low temperatures, the real part of the effective potential V_R indicates a rich phase structure, with a discontinuous alternation between confined (phi=pi) and deconfined phases (phi=0). The background field H moves slowly upward from its zero-temperature value as T increases, in such a way that sqrt(gH)/(pi T) is approximately an integer. Beyond a certain temperature on the order of sqrt(gH), the deconfined phase is always preferred. At high temperatures, where asymptotic freedom applies, the deconfined phase phi=0 is always preferred, and sqrt(gH) is of order g^2(T)T. The imaginary part of the effective potential is non-zero at the global minimum of V_R for all temperatures. A non-perturbative magnetic screening mass of the form M_m = cg^2(T)T with a sufficiently large coefficient c removes this instability at high temperature, leading to a stable high-temperature phase with phi=0 and H=0, characteristic of a weakly-interacting gas of gauge particles. The value of M_m obtained is comparable with lattice estimates.Comment: 28 pages, 5 eps figures; RevTeX 3 with graphic

Gluon Quasiparticles and the Polyakov Loop

A synthesis of Polyakov loop models of the deconfinement transition and quasiparticle models of gluon plasma thermodynamics leads to a class of models in which gluon quasiparticles move in a non-trivial Polyakov loop background. These models are successful candidates for explaining both critical behavior and the equation of state for the SU(3) gauge theory at temperatures above the deconfinement temperature T_c. Polyakov loops effects are most important at intermediate temperatures from T_c up to roughly 2.5 T_c, while quasiparticle mass effects provide the dominant correction to blackbody behavior at higher temperatures.Comment: 6 pages, 7 eps figures, revtex

Flavor Relationships among Muscles form the Beef Chuck and Round

This research compared off-flavor notes and the relationship of pH and heme-iron content to off-flavor for different beef muscles. After grading, knuckles and shoulder clods were removed from 16 USDA Choice and 14 USDA Select beef carcasses, vacuum- packaged, and aged for 7 d. The rectus femoris (REC), vastus medalis (VAM), vastus lateralis (VAL), teres major (TER), infraspinatus (INF), and triceps brachii-long head (TRI) were separated, cut into steaks, and frozen (−16°C). Sensory analysis was conducted using a trained taste panel, with steaks grilled to an internal temperature of 65°C. Heme-iron concentration and pH were determined. The INF had lower (P \u3c 0.05) off-flavor intensity ratings and less frequent sour flavor than the other muscles, and the VAL had the most intense (P \u3c 0.05) off-flavor ratings and among the greatest frequency of sour, charred, and oxidized flavors. The frequencies of liver-like, bloody, and rancid flavors were not affected by muscle type. Heme-iron concentration did not differ among muscles. Three USDA Select carcasses had intense off-flavor in the muscles. Liver-like flavor was highly negatively correlated with off-flavor intensity for each of the muscles tested. Muscles rated a 5 or below (on an 8-point rating scale, where 1 = extremely intense off-flavor and 8 = no off-flavor) in off-flavor intensity and identified as liver-like by 30% or more of the panelists were grouped together and compared to normal muscles. Those in the liver-flavored group were less frequently identified as charred, probably because the liver-like flavor was so intense. There were no differences between the 2 groups for sour, metallic, bloody, oxidized, or fatty off-flavor notes. Regression equations containing the linear and quadratic functions of heme-iron concentration, muscle pH, and their interaction were established for the frequency of off-flavor notes within each muscle. The REC, TER, VAL, and VAM showed a relationship between pH, heme iron, and off-flavor intensity (P \u3c 0.05). Liver-like flavor was explained partially by pH and heme iron in the REC, VAM, and VAL (R2 = 0.45 to 0.55; P \u3c 0.05). Few other significant relationships were found. Heme iron and pH were unrelated to metallic, oxidized, or rancid flavors for any of the muscles tested. These data suggest that liver-like off-flavors are specific to individual animals, and that pH and heme iron are not strongly related to off-flavor notes

Phenomenological Equations of State for the Quark-Gluon Plasma

Two phenomenological models describing an SU(N) quark-gluon plasma are presented. The first is obtained from high temperature expansions of the free energy of a massive gluon, while the second is derived by demanding color neutrality over a certain length scale. Each model has a single free parameter, exhibits behavior similar to lattice simulations over the range T_d - 5T_d, and has the correct blackbody behavior for large temperatures. The N = 2 deconfinement transition is second order in both models, while N = 3,4, and 5 are first order. Both models appear to have a smooth large-N limit. For N >= 4, it is shown that the trace of the Polyakov loop is insufficient to characterize the phase structure; the free energy is best described using the eigenvalues of the Polyakov loop. In both models, the confined phase is characterized by a mutual repulsion of Polyakov loop eigenvalues that makes the Polyakov loop expectation value zero. In the deconfined phase, the rotation of the eigenvalues in the complex plane towards 1 is responsible for the approach to the blackbody limit over the range T_d - 5T_d. The addition of massless quarks in SU(3) breaks Z(3) symmetry weakly and eliminates the deconfining phase transition. In contrast, a first-order phase transition persists with sufficiently heavy quarks.Comment: 22 pages, RevTeX, 9 eps file