Lars E. Leganger

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 T ~ 2 − 3Tc, which are temperatures accessible by current and forthcoming heavy-ion collision experiments.

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{sup 2} in two cases: N{sub f}=0 and N{sub f}=3. When using the canonical value of {mu}=2{pi}T for the renormalization scale, we find that for Yang-Mills theory (N{sub f}=0) agreement between HTLpt and lattice data for the T{sup 2}-scaled trace anomaly begins at temperatures on the order of 8T{sub c}, while treating the subtracted piece as an interaction term when including quarks (N{sub f}=3) agreement begins already at temperatures above 2T{sub c}. In both cases we find that at very high temperatures the T{sup 2}-scaled trace anomaly increases with temperature in accordance with the predictions of HTLpt.

Hard-Thermal-Loop QCD Thermodynamics

Naively resummed perturbative approximations to the thermodynamic functionsof QCD do not converge at phenomenologically relevant temperatures. Here wereview recent results of a three-loop hard-thermal-loop perturbation theorycalculation of the thermodynamic functions of a quark-gluon plasma for generalN_c and N_f. We show comparisons of our recent results with lattice data fromboth the hotQCD and Wuppertal-Budapest groups. We demonstrate that thethree-loop hard-thermal-loop perturbation result for QCD thermodynamics agreeswith lattice data down to temperatures T ~ 2 T_c.

Kaon condensation in the color–flavor-locked phase of quark matter, the Goldstone theorem, and the 2PI Hartree approximation

Abstract 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 O ( 2 ) × O ( 2 ) -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. The effects of imposing electric charge neutrality is examined as well.

Pressure to order

We calculate the pressure of massless 4-theory to order g8log (g) at weak coupling. The contributions to the pressure arise from the hard momentum scale of order T and the soft momentum scale of order gT. 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 g2 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 g2. This contribution is a power series in g starting at order g3. The calculation of the hard part to order g6 involves a complicated four-loop sum-integral that was recently calculated by Gynther, Laine, Schroder, Torrero, and Vuorinen. The calculation of the soft part requires calculating the mass parameter in the effective theory to order g6 and the evaluation of five-loop vacuum diagrams in three dimensions. This gives the free energy correct up to order g7. 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 T/gT. We use the solutions to these equations to obtain a result for the free energy which is correct to order g8log (g). Finally, we investigate the convergence of the perturbative series.

g^8*log(g)

We calculate the pressure of massless 4-theory to order g8log (g) at weak coupling. The contributions to the pressure arise from the hard momentum scale of order T and the soft momentum scale of order gT. 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 g2 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 g2. This contribution is a power series in g starting at order g3. The calculation of the hard part to order g6 involves a complicated four-loop sum-integral that was recently calculated by Gynther, Laine, Schroder, Torrero, and Vuorinen. The calculation of the soft part requires calculating the mass parameter in the effective theory to order g6 and the evaluation of five-loop vacuum diagrams in three dimensions. This gives the free energy correct up to order g7. 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 T/gT. We use the solutions to these equations to obtain a result for the free energy which is correct to order g8log (g). Finally, we investigate the convergence of the perturbative series.

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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 O(2)×O(2)‐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 s...

\phi^4

The decay modes of the type

-theory at weak coupling

B \to \pi \, D

Pressure to order g(8) log g of massless phi(4) theory at weak coupling

are dynamically different. For the case