Abstract
We calculate all those QCD $N$-point functions which are relevant for a three-loop QCD thermodynamics calculation with finite quark masses within the hard the thermal loop approximation. Using the effective quark propagator, we also calculate second order quark and baryon number susceptibilities within the hard thermal loop approximation and compare the results with available lattice data.
Highlights
It is an experimental fact that colored quarks and gluons are confined to hadrons by the strong interaction
The reason why deconfined matter is expected to be encountered at high energy densities is related to the asymptotic freedom of quantum chromodynamics (QCD), i.e., the fact that the value of the strong coupling constant decreases logarithmically as a function of the energy scale
In most thermodynamic calculations applying the perturbation theory, either the temperature or the chemical potentials are assumed to be the dominant energy scale in the system and, in particular, much larger than the QCD scale or any quark masses. Questionable whether the latter is necessarily a good approximation at the lowest temperatures and densities where the hard thermal loop perturbation theory (HTLPT) results are typically applied; the strange quark mass is after all of the order of 100 MeV, which is certainly not negligible at the temperatures reached in the Relativistic Heavy Ion Collider (RHIC) and Large Hadron Collider (LHC) heavy-ion experiments
Summary
It is an experimental fact that colored quarks and gluons are confined to hadrons by the strong interaction. Relevance for most practical applications, the value of the strong coupling constant is not small, and it turns out that, e.g., for bulk thermodynamic quantities, a strict expansion in the QCD coupling constant converges only at astronomically high temperatures and chemical potentials The source of this problem has been readily identified as the infrared sector of the theory, i.e., contributions from soft gluonic momenta of the order of the Debye mass or smaller. In most thermodynamic calculations applying the perturbation theory, either the temperature or the chemical potentials are assumed to be the dominant energy scale in the system and, in particular, much larger than the QCD scale or any quark masses It is, questionable whether the latter is necessarily a good approximation at the lowest temperatures and densities where the HTLPT results are typically applied; the strange quark mass is after all of the order of 100 MeV, which is certainly not negligible at the temperatures reached in the RHIC and LHC heavy-ion experiments. In the Appendix, we discuss the HTL effective gluon propagator and gluon dispersion relations including finite quark masses
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