9 research outputs found
Kaon condensation in CFL quark matter, the Goldstone theorem, and the 2PI Hartree approximation
At very high densities, QCD is in the color-flavor-locked phase, which is a
color-superconducting phase. The diquark condensates break chiral symmetry in
the same way as it is broken in vacuum QCD and gives rise to an octet of
pseudo-Goldstone bosons and a superfluid mode. The lightest of these are the
charged and neutral kaons. For energies below the superconducting gap, the
kaons are described by an -symmetric effective scalar field
theory with chemical potentials. We use this effective theory to study
Bose-condensation of kaons and their properties as functions of the temperature
and the chemical potentials. We use the 2-particle irreducible effective action
formalism in the Hartree approximation. The renormalization of the gap
equations and the effective potential is studied in detail and we show that the
counterterms are independent of temperature and chemical potentials. We
determine the phase diagram and the medium-dependent quasiparticle masses. It
is shown that the Goldstone theorem is satisfied to a very good approximation.Comment: Talk given at the 9th Quark Confinement and the Hadron Spectrum
conference (QCHS9), Madrid, Spain, 30 Aug-3 Sep 201
Hard-thermal-loop QCD Thermodynamics
Naively resummed perturbative approximations to the thermodynamic functions
of QCD do not converge at phenomenologically relevant temperatures. Here we
review recent results of a three-loop hard-thermal-loop perturbation theory
calculation of the thermodynamic functions of a quark-gluon plasma for general
N_c and N_f. We show comparisons of our recent results with lattice data from
both the hotQCD and Wuppertal-Budapest groups. We demonstrate that the
three-loop hard-thermal-loop perturbation result for QCD thermodynamics agrees
with lattice data down to temperatures T ~ 2 T_c.Comment: 8 pages, 2 figures; Talk given at the Symposium on "High Energy
Strong Interactions", Aug. 9-13, 2010, Yukawa Institute for Theoretical
Physics, Kyoto, Japan; submitted to Prog. Theor. Phys. Supp
The QCD trace anomaly
In this brief report we compare the predictions of a recent
next-to-next-to-leading order hard-thermal-loop perturbation theory (HTLpt)
calculation of the QCD trace anomaly to available lattice data. We focus on the
trace anomaly scaled by T^2 in two cases: N_f=0 and N_f=3. When using the
canonical value of mu = 2 pi T for the renormalization scale, we find that for
Yang-Mills theory (N_f=0) agreement between HTLpt and lattice data for the
T^2-scaled trace anomaly begins at temperatures on the order of 8 T_c while
when including quarks (N_f=3) agreement begins already at temperatures above 2
T_c. In both cases we find that at very high temperatures the T^2-scaled trace
anomaly increases with temperature in accordance with the predictions of HTLpt.Comment: 12 pages, 4 figures; v3 published versio
Pressure to order in -theory at weak coupling
We calculate the pressure of massless -theory to order
at weak coupling. The contributions to the pressure arise from the hard
momentum scale of order and the soft momentum scale of order .
Effective field theory methods and dimensional reduction are used to separate
the contributions from the two momentum scales: The hard contribution can be
calculated as a power series in using naive perturbation theory with bare
propagators. The soft contribution can be calculated using an effective theory
in three dimensions, whose coefficients are power series in . This
contribution is a power series in starting at order . The calculation
of the hard part to order involves a complicated four-loop sum-integral
that was recently calculated by Gynther, Laine, Schr\"oder, Torrero, and
Vuorinen. The calculation of the soft part requires calculating the mass
parameter in the effective theory to order and the evaluation of
five-loop vacuum diagrams in three dimensions. This gives the free energy
correct up to order . The coefficients of the effective theory satisfy a
set of renormalization group equations that can be used to sum up leading and
subleading logarithms of . We use the solutions to these equations to
obtain a result for the free energy which is correct to order .
Finally, we investigate the convergence of the perturbative series.Comment: 29 pages and 12 figs. New version: we have pushed the calculations to
g^8*log(g) using the renormalization group to sum up log(g) from higher
orders. Published in JHE
NNLO hard-thermal-loop thermodynamics for QCD
We calculate the thermodynamic functions of a quark-gluon plasma for general
N_c and N_f to three-loop order using hard-thermal-loop perturbation theory. At
this order, all the ultraviolet divergences can be absorbed into
renormalizations of the vacuum, the HTL mass parameters, and the strong
coupling constant.We show that at three loops, the results for the pressure and
trace anomaly are in very good agreement with recent lattice data down to
temperatures T~2T_c.Comment: 8 pages, 2 fig
Three-loop HTL QCD thermodynamics
The hard-thermal-loop perturbation theory (HTLpt) framework is used to
calculate the thermodynamic functions of a quark-gluon plasma to three-loop
order. This is the highest order accessible by finite temperature perturbation
theory applied to a non-Abelian gauge theory before the high-temperature
infrared catastrophe. All ultraviolet divergences are eliminated by
renormalization of the vacuum, the HTL mass parameters, and the strong coupling
constant. After choosing a prescription for the mass parameters, the three-loop
results for the pressure and trace anomaly are found to be in very good
agreement with recent lattice data down to , which are
temperatures accessible by current and forthcoming heavy-ion collision
experiments.Comment: 27 pages, 11 figures; corresponds with published version in JHE