Renormalization in Self-Consistent Approximation schemes at Finite Temperature III: Global Symmetries

We investigate the symmetry properties for Baym's $\Phi$-derivable schemes. We show that in general the solutions of the dynamical equations of motion, derived from approximations of the $\Phi$-functional, do not fulfill the Ward-Takahashi identities of the symmetry of the underlying classical action, although the conservation laws for the expectation values of the corresponding Noether currents are fulfilled exactly for the approximation. Further we prove that one can define an effective action functional in terms of the self-consistent propagators which is invariant under the operation of the same symmetry group representation as the classical action. The requirements for this theorem to hold true are the same as for perturbative approximations: The symmetry has to be realized linearly on the fields and it must be free of anomalies, i.e., there should exist a symmetry conserving regularization scheme. In addition, if the theory is renormalizable in Dyson's narrow sense, it can be renormalized with counter terms which do not violate the symmetry.Comment: 32 papges, 3 figures, uses ReVTeX 4, V2: Added one more reference, V3: Corrected some typos, added two more sections about the large-N expansio

Chiral symmetry restoration in linear sigma models with different numbers of quark flavors

Chiral symmetry restoration at nonzero temperature is studied in the framework of the O(4) linear sigma model and the U(N_f)_r x U(N_f)_l linear sigma model with N_f=2,3, and 4 quark flavors. We investigate the temperature dependence of the masses of the scalar and pseudoscalar mesons, and the non-strange, strange, and charm condensates within the Hartree approximation as derived from the Cornwall-Jackiw-Tomboulis formalism. We find that the masses of the non-strange and strange mesons at nonzero temperature depend sensitively on the particular symmetry of the model and the number of light quark flavors N_f. On the other hand, due to the large charm quark mass, neither do charmed mesons significantly affect the properties of the other mesons, nor do their masses change appreciably in the temperature range around the chiral symmetry restoration temperature. In the chiral limit, the transition temperatures for chiral symmetry restoration are surprisingly close to those found in lattice QCD.Comment: 28 pages, 8 figure

Heavy-Quark Diffusion, Flow and Recombination at RHIC

We discuss recent developments in assessing heavy-quark interaction in the Quark-Gluon Plasma (QGP). While induced gluon radiation is expected to be the main energy-loss mechanism for fast-moving quarks, we focus on elastic scattering which prevails toward lower energies, evaluating both perturbative (gluon-exchange) and nonperturbative (resonance formation) interactions in the QGP. The latter are treated within an effective model for D- and B-meson resonances above T_c as motivated by current QCD lattice calculations. Pertinent diffusion and drag constants, following from a Fokker-Planck equation, are implemented into an expanding fireball model for Au-Au collisions at RHIC using relativistic Langevin simulations. Heavy quarks are hadronized in a combined fragmentation and coalescence framework, and resulting electron-decay spectra are compared to recent RHIC data. A reasonable description of both nuclear suppression factors and elliptic flow up to momenta of ~5 GeV supports the notion of a strongly interacting QGP created at RHIC. Consequences and further tests of the proposed resonance interactions are discussed.Comment: 8 pages, 14 figures, contribution to the proceedings for the "International Conference on Strangeness in Quark Matter 2006

Choice Functions and Hard Choices

A hard choice is a situation in which an agent is unable to make a justifiable choice from a given menu of alternatives. Our objective is to present a systematic treatment of the axiomatic structure of such situations. To do so, we draw on and contribute to the study of choice functions that can be indecisive, i.e., that may fail to select a non-empty set for some menus. In this more general framework, we present new characterizations of two well-known choice rules, the maximally dominant choice rule and the top-cycle choice rule. Together with existing results, this yields an understanding of the circumstances in which hard choices arise

Heavy Flavor Production at STAR

e present measurements on $D^0$ meson production via direct reconstruction of its hadronic decay channel $D^0\to K\pi$ in minimum bias $d$+Au and Au+Au collisions at $\sqrt{s_{NN}}$=200 GeV with $p_T$ up to $\sim$3 GeV/$c$. Non-photonic electron spectra from the charm semi-leptonic decays are analyzed from the same data set as well as in $p$+$p$ collision at $\sqrt{s}$=200 GeV using the STAR Time-of-Flight (TOF) and Barrel EMC (BEMC) detectors, respectively. Results of the charm-decayed single muon (prompt muon) spectra are also presented at low $p_T$ in Au+Au collisions measured by the TOF detector. The charm production total cross-section per nucleon-nucleon collision is measured to be 1.26$\pm$0.09(stat.)$\pm$0.23(sys.) mb in minimum bias Au+Au collisions, which is consistent with the $N_{bin}$ scaling compared to 1.4$\pm0.2\pm$0.4 mb in minimum bias $d$+Au collisions, and supports the idea that charm quarks should be produced mostly via parton fusion at early stage in relativistic heavy-ion collisions. A Blast-Wave model fit to the low $p_T$ ($<2$ GeV/c) non-photonic electrons, prompt muons and $D^0$ spectra shows that charm hadrons may kinetically freeze-out earlier than light hadrons with a smaller collective velocity. The nuclear modification factors ($R_{AA}$) of the non-photonic electrons in central Au+Au collisions are significantly below unity at $p_T>\sim$2 GeV/$c$, which indicates a significant amount of energy loss for heavy quarks in Au+Au collisions. The charm transverse momentum distribution must have been modified by the hot and dense matter created in central Au+Au collisions at RHIC.Comment: 7 pages, 4 figures, proceedings for the Strange Quark Matter 2006 conferenc

Large-space shell-model calculations for light nuclei

An effective two-body interaction is constructed from a new Reid-like $NN$ potential for a large no-core space consisting of six major shells and is used to generate the shell-model properties for light nuclei from $A$=2 to 6. (For practical reasons, the model space is partially truncated for $A$=6.) Binding energies and other physical observables are calculated and compare favorably with experiment.Comment: prepared using LaTex, 21 manuscript pages, no figure

Hard gluon damping in hot QCD

The gluon collisional width in hot QCD plasmas is discussed with emphasis on temperatures near $T_c$, where the coupling is large. Considering its effect on the entropy, which is known from lattice calculations, it is argued that the width, which in the perturbative limit is given by $\gamma \sim g^2 \ln(1/g) T$, should be sizeable at intermediate temperatures but has to be small close to $T_c$. Implications of these results for several phenomenologically relevant quantities, such as the energy loss of hard jets, are pointed out.Comment: uses RevTex and graphic

The O(N) linear sigma model at finite temperature beyond the Hartree approximation

We study the O(N) linear sigma model with spontaneous symmetry breaking, using a Hartree-like ansatz with a classical field and variational masses. We go beyond the Hartree approximation by including the two-loop contribution, the sunset diagram, using the 2PPI expansion. We have computed numerically the effective potential at finite temperature. We find a phase transition of second order, while it is first order in the Hartree approximation. We also discuss some implications of the fact that in this order, the decay of the sigma into two pions affects the thermal diagrams.Comment: 22 pages, 14 figures. v2: minor corrections, some more references. v3: added new set of data, new appendix. Submitted to Phys.Rev.