782 research outputs found
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 -derivable Approximation for Scalar Thermodynamics
We solve the 3-loop -derivable approximation to the thermodynamics of
the massless field theory by reducing it to a 1-parameter variational
problem. The thermodynamic potential is expanded in powers of and ,
where is the coupling constant, is a variational mass parameter, and
is the temperature. There are ultraviolet divergences beginning at 6th
order in that cannot be removed by renormalization. However the finite
thermodynamic potential obtained by truncating after terms of 5th order in
and 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 LiVO 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 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 , which points to a
presumably generic obstruction for extrapolating data from small to large
chemical potential. At sufficiently small temperatures , 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
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 , 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 , should be sizeable at intermediate temperatures but has to be small close
to . 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
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