An effective chiral Hadron-Quark Equation of State

We construct an effective model for the QCD equation of state, taking into account chiral symmetry restoration as well as the deconfinement phase transition. The correct asymptotic degrees of freedom at the high and low temperature limits are included (quarks $\leftrightarrow$ hadrons). The model shows a rapid crossover for both order parameters, as is expected from lattice calculations. We then compare the thermodynamic properties of the model at $\mu_B=0$ which turn out to be in qualitative agreement with lattice data, while apparent quantitative differences can be attributed to hadronic contributions and excluded volume corrections. Furthermore we discuss the effects of a repulsive vector type quark interaction at finite baryon number densities on the resulting phase diagram of the model. Our current model is able to reproduce a first-order liquid gas phase transition as expected, but does not show any signs of a first order deconfinement or chiral phase transition. Both transitions rather appear as a very wide crossover in which heavily medium modified hadron coexist with free quarks.Comment: 19 pages, 13 figures Version accepted by J. Phys.

The Free Energy of High Temperature QED to Order e5e^{5} From Effective Field Theory

Massless quantum electrodynamics is studied at high temperature and zero chemical potential. We compute the Debye screening mass to order $e^{4}$ and the free energy to order $e^{5}$} by an effective field theory approach, recently developed by Braaten and Nieto. Our results are in agreement with calculations done in resummed perturbation theory. This method makes it possible to separate contributions to the free energy from different momentum scales (order $T$ and $eT$) and provides an economical alternative to computations in the full theory which involves the dressing of internal propagators.Comment: 10 pages Latex, 6 figure

Active restoration initiates high quality forest succession in a deforested landscape in Amazonia.

Amazonia is well known for its high natural regeneration capacity; for this reason, passive restoration is normally recommended for the recovery of its degraded forests. However, highly deforested landscapes in southern Amazonia require active restoration. Since restoration methods can shape the quality and speed of early forest recovery, this study aimed to verify how active restoration pushes sites stably covered with exotic grasses towards forest recovery. We evaluated early forest succession at active restoration sites, i.e., soil plowing, direct seeding of pioneer species, and seedling stock planting at low density. We analyzed forest structure, diversity, and species composition in two age classes, 0.5–3.5 and 4.5–7.5 years old. As reference, we evaluated sites able to naturally regenerate in the same region. We sampled 36 active restoration and 31 natural regeneration sites along the Madeira River, southern Amazonia. Active restoration triggered succession to similar or higher levels of forest structure than sites where natural regeneration was taking place. The most dominant species did not overlap between active restoration and natural regeneration sites. The overall composition of species was different between the two restoration methods. Dominant species and size class distribution show that active restoration is performing successfully. Soil preparation combined with a high availability of seeds of pioneer trees resulted in a high stem density and basal area of facilitative pioneer trees. Planted seedlings added species diversity and increased density of large trees. Interventions to increase the odds of natural regeneration can be effective for non-regenerating sites in resilient landscapes

Interactions between U(1)U(1) Cosmic Strings: An Analytical Study

We derive analytic expressions for the interaction energy between two general $U(1)$ cosmic strings as the function of their relative orientation and the ratio of the coupling constants in the model. The results are relevant to the statistic description of strings away from critical coupling and shed some light on the mechanisms involved in string formation and the evolution of string networks.Comment: 31 pages,REVTEX, Imperial/TP/93-94/3

SQM 2006: Theory Summary and Perspectives

In this write-up of my SQM 2006 Theory Summary talk I focus on a selection of key contributions which I consider to have a large impact on the current status of the field of strangeness physics or which may have the potential to significantly advance strangeness -- or in general flavor physics -- in the near future.Comment: 16 pages, 4 figures, SQM 2006 proceedings. Revised version containing two modifications to the transport theory sectio

Baryon Washout, Electroweak Phase Transition, and Perturbation Theory

We analyze the conventional perturbative treatment of sphaleron-induced baryon number washout relevant for electroweak baryogenesis and show that it is not gauge-independent due to the failure of consistently implementing the Nielsen identities order-by-order in perturbation theory. We provide a gauge-independent criterion for baryon number preservation in place of the conventional (gauge-dependent) criterion needed for successful electroweak baryogenesis. We also review the arguments leading to the preservation criterion and analyze several sources of theoretical uncertainties in obtaining a numerical bound. In various beyond the standard model scenarios, a realistic perturbative treatment will likely require knowledge of the complete two-loop finite temperature effective potential and the one-loop sphaleron rate.Comment: 25 pages, 9 figures; v2 minor typos correcte

Dynamical renormalization group approach to transport in ultrarelativistic plasmas: the electrical conductivity in high temperature QED

The DC electrical conductivity of an ultrarelativistic QED plasma is studied in real time by implementing the dynamical renormalization group. The conductivity is obtained from the realtime dependence of a dissipative kernel related to the retarded photon polarization. Pinch singularities in the imaginary part of the polarization are manifest as growing secular terms that in the perturbative expansion of this kernel. The leading secular terms are studied explicitly and it is shown that they are insensitive to the anomalous damping of hard fermions as a result of a cancellation between self-energy and vertex corrections. The resummation of the secular terms via the dynamical renormalization group leads directly to a renormalization group equation in real time, which is the Boltzmann equation for the (gauge invariant) fermion distribution function. A direct correspondence between the perturbative expansion and the linearized Boltzmann equation is established, allowing a direct identification of the self energy and vertex contributions to the collision term.We obtain a Fokker-Planck equation in momentum space that describes the dynamics of the departure from equilibrium to leading logarithmic order in the coupling.This determines that the transport time scale is given by t_{tr}=(24 pi)/[e^4 T \ln(1/e)}]. The solution of the Fokker-Planck equation approaches asymptotically the steady- state solution as sim e^{-t/(4.038 t_{tr})}.The steady-state solution leads to the conductivity sigma = 15.698 T/[e^2 ln(1/e)] to leading logarithmic order. We discuss the contributions beyond leading logarithms as well as beyond the Boltzmann equation. The dynamical renormalization group provides a link between linear response in quantum field theory and kinetic theory.Comment: LaTex, 48 pages, 14 .ps figures, final version to appear in Phys. Rev.

Dynamical Renormalization Group Approach to Quantum Kinetics in Scalar and Gauge Theories

We derive quantum kinetic equations from a quantum field theory implementing a diagrammatic perturbative expansion improved by a resummation via the dynamical renormalization group. The method begins by obtaining the equation of motion of the distribution function in perturbation theory. The solution of this equation of motion reveals secular terms that grow in time, the dynamical renormalization group resums these secular terms in real time and leads directly to the quantum kinetic equation. We used this method to study the relaxation in a cool gas of pions and sigma mesons in the O(4) chiral linear sigma model. We obtain in relaxation time approximation the pion and sigma meson relaxation rates. We also find that in large momentum limit emission and absorption of massless pions result in threshold infrared divergence in sigma meson relaxation rate and lead to a crossover behavior in relaxation. We then study the relaxation of charged quasiparticles in scalar electrodynamics (SQED). While longitudinal, Debye screened photons lead to purely exponential relaxation, transverse photons, only dynamically screened by Landau damping lead to anomalous relaxation, thus leading to a crossover between two different relaxational regimes. We emphasize that infrared divergent damping rates are indicative of non-exponential relaxation and the dynamical renormalization group reveals the correct relaxation directly in real time. Finally we also show that this method provides a natural framework to interpret and resolve the issue of pinch singularities out of equilibrium and establish a direct correspondence between pinch singularities and secular terms. We argue that this method is particularly well suited to study quantum kinetics and transport in gauge theories.Comment: RevTeX, 40 pages, 4 eps figures, published versio

Real and imaginary-time QQˉQ\bar{Q} correlators in a thermal medium

We investigate the behavior of a pair of heavy fermions, denoted by $Q$ and $\bar{Q}$, in a hot/dense medium. Although we have in mind the situation where $Q$ and $\bar{Q}$ denote heavy quarks, our treatment will be limited to simplified models, which bear only some general similarities with QCD. We study in particular the limiting case where the mass of the heavy fermions is infinite. Then a number of results can be derived exactly: a Schr\"odinger equation can be established for the correlator of the heavy quarks; the interaction effects exponentiate, leading to a simple instantaneous effective potential for this Schr\"odinger equation. We consider simple models for the medium in which the $Q\bar Q$ pair propagates. In the case where the medium is a plasma of photons and light charged fermions, an imaginary part develops in this effective potential. We discuss the physical interpretation of this imaginary part in terms of the collisions between the heavy particles and the light fermions of the medium; the same collisions also determine the damping rate of the heavy fermions. Finally we study the connection between the real-time propagator of the heavy fermion pair and its Euclidean counterpart, and show that the real part of the potential entering the Schr\"odinger equation for the real-time propagator is the free energy calculated in the imaginary-time formalism.Comment: 32 pages, 8 figure