Renormalization Group Summation and the Free Energy of Hot QCD

Using an approach developed in the context of zero-temperature QCD to systematically sum higher order effects whose form is fixed by the renormalization group equation, we sum to all orders the leading log (LL) and next-to-leading log (NLL) contributions to the thermodynamic free energy in hot QCD. While the result varies considerably less with changes in the renormalization scale than does the purely perturbative result, a novel ambiguity arises which reflects the strong scheme dependence of thermal perturbation theory.Comment: 7 pages REVTEX4, 2 figures; v2: typos correcte

Solution to the 3-loop Φ\Phi-derivable Approximation for Scalar Thermodynamics

We solve the 3-loop $\Phi$-derivable approximation to the thermodynamics of the massless $\phi^4$ field theory by reducing it to a 1-parameter variational problem. The thermodynamic potential is expanded in powers of $g^2$ and $m/T$, where $g$ is the coupling constant, $m$ is a variational mass parameter, and $T$ is the temperature. There are ultraviolet divergences beginning at 6th order in $g$ that cannot be removed by renormalization. However the finite thermodynamic potential obtained by truncating after terms of 5th order in $g$ and $m/T$ defines a stable approximation to the thermodynamic functions.Comment: 4 pages, 1 figur

Two-loop HTL Thermodynamics with Quarks

We calculate the quark contribution to the free energy of a hot quark-gluon plasma to two-loop order using hard-thermal-loop (HTL) perturbation theory. All ultraviolet divergences can be absorbed into renormalizations of the vacuum energy and the HTL quark and gluon mass parameters. The quark and gluon HTL mass parameters are determined self-consistently by a variational prescription. Combining the quark contribution with the two-loop HTL perturbation theory free energy for pure-glue we obtain the total two-loop QCD free energy. Comparisons are made with lattice estimates of the free energy for N_f=2 and with exact numerical results obtained in the large-N_f limit.Comment: 33 pages, 6 figure

Quasi-Particle Description of Strongly Interacting Matter: Towards a Foundation

We confront our quasi-particle model for the equation of state of strongly interacting matter with recent first-principle QCD calculations. In particular, we test its applicability at finite baryon densities by comparing with Taylor expansion coefficients of the pressure for two quark flavours. We outline a chain of approximations starting from the Phi-functional approach to QCD which motivates the quasi-particle picture.Comment: Aug 2006. 6 pp. Invited Talk given at Hot Quarks 2006, Villasimius, Sardinia, Italy, 15-20 May 200

Electronic Structure and Heavy Fermion Behavior in LiV_2O_4

First principles density functional calculations of the electronic and magnetic properties of spinel-structure LiV$_{2}$O$_{4}$ have been performed using the full potential linearized augmented planewave method. The calculations show that the electronic structure near the Fermi energy consists of a manifold of 12 bands derived from V $t_{2g}$ states, weakly hybridized with O p states. While the total width of this active manifold is approximately 2 eV, it may be roughly decomposed into two groups: high velocity bands and flatter bands, although these mix in density functional calculations. The flat bands, which are the more atomic-like lead to a high density of states and magnetic instability of local moment character. The value of the on-site exchange energy is sensitive to the exact exchange correlation parameterization used in the calculations, but is much larger than the interaction between neighboring spins, reflecting the weak coupling of the magnetic system with the high velocity bands. A scenario for the observed heavy fermion behavior is discussed in which conduction electrons in the dispersive bands are weakly scattered by local moments associated with strongly correlated electrons in the heavy bands.This is analogous to that in conventional Kondo type heavy fermions, but is unusual in that both the local moments and conduction electrons come from the same d-manifold.Comment: 6 Revtex pages, Postscript figs embedded. Revision: figure 4 replaced with a better version, showing the band character explicitel

The pressure of QCD at finite temperatures and chemical potentials

The perturbative expansion of the pressure of hot QCD is computed here to order g^6ln(g) in the presence of finite quark chemical potentials. In this process all two- and three-loop one-particle irreducible vacuum diagrams of the theory are evaluated at arbitrary T and mu, and these results are then used to analytically verify the outcome of an old order g^4 calculation of Freedman and McLerran for the zero-temperature pressure. The results for the pressure and the different quark number susceptibilities at high T are compared with recent lattice simulations showing excellent agreement especially for the chemical potential dependent part of the pressure.Comment: 35 pages, 6 figures; text revised, one figure replace

Thermodynamics of Large-N_f QCD at Finite Chemical Potential

We extend the previously obtained results for the thermodynamic potential of hot QCD in the limit of large number of fermions to non-vanishing chemical potential. We give exact results for the thermal pressure in the entire range of temperature and chemical potential for which the presence of a Landau pole is negligible numerically. In addition we compute linear and non-linear quark susceptibilities at zero chemical potential, and the entropy at small temperatures. We compare with the available perturbative results and determine their range of applicability. Our numerical accuracy is sufficiently high to check and verify existing results, including the recent perturbative results by Vuorinen on quark number susceptibilities and the older results by Freedman and McLerran on the pressure at zero temperature and high chemical potential. We also obtain a number of perturbative coefficients at sixth order in the coupling that have not yet been calculated analytically. In the case of both non-zero temperature and non-zero chemical potential, we investigate the range of validity of a scaling behaviour noticed recently in lattice calculations by Fodor, Katz, and Szabo at moderately large chemical potential and find that it breaks down rather abruptly at $\mu_q \gtrsim \pi T$, which points to a presumably generic obstruction for extrapolating data from small to large chemical potential. At sufficiently small temperatures $T \ll \mu_q$, we find dominating non-Fermi-liquid contributions to the interaction part of the entropy, which exhibits strong nonlinearity in the temperature and an excess over the free-theory value.Comment: 18 pages, 7 figures, JHEP style; v2: several updates, rewritten and extended sect. 3.4 covering now "Entropy at small temperatures and non-Fermi-liquid behaviour"; v3: additional remarks at the end of sect. 3.4; v4: minor corrections and additions (version to appear in JHEP

Deriving the dependence structure of portfolio credit derivatives using evolutionary algorithms

Even if the correct modeling of default dependence is essential for the valuation of portfolio credit derivatives, for the pricing of synthetic CDOs a one-factor Gaussian copula model with constant and equal pairwise correlations for all assets in the reference portfolio has become the standard market model. If this model were a reflection of market opinion, there wouldn't be the implied correlation smile that is observed in the market. The purpose of this paper is to derive a cor-relation structure from observed CDO tranche spreads. The correlation structure is chosen such that all tranche spreads of the traded CDO can be reproduced. This implied correlation structure can then be used to price off-market tranches with the same underlying as the traded CDO. Using this approach we can significantly reduce the risk to misprice off-market derivatives. Due to the complexity of the optimization problem we apply Evolutionary Algorithms

Resummations of free energy at high temperature

We discuss resummation strategies for free energy in quantum field theories at nonzero temperatures T. We point out that resummations should be performed for the short- and long-distance parts separately in order to avoid spurious interference effects and double-counting. We then discuss and perform Pade resummations of these two parts for QCD at high T. The resummed results are almost invariant under variation of the renormalization and factorization scales. We perform the analysis also in the case of the massless scalar $\phi^4$ theory.Comment: 16 pages, revtex4, 15 eps-figures; minor typographic errors corrected; the version as it appears in Phys.Rev.

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