Abstract
Using only global symmetries of QCD, we set up an effective model of quarks at finite temperature near the crossover, including all possible terms up to dimension-6. We first treat this in mean field theory. Then we investigate low-energy fluctuations around it up to one-loop order in fermions below the crossover. Static correlation functions of pions and the crossover temperature, both measured on the lattice, completely suffice to fix all parameters of the theory. We examine predictions of this theory, including those for thermodynamic quantities. The results are encouraging.
Highlights
Effective field theories (EFTs) are good ways of organizing the computation of low-energy or long-distance effects in a quantum field theory
QCD at very low temperature, T, seems to be well described by an EFT which describes the dynamics of pions [1,2]
Using the methods of the Appendix, we find that the free energy density in the mean field theory (MFT), using dimensional regularization, is
Summary
Effective field theories (EFTs) are good ways of organizing the computation of low-energy or long-distance effects in a quantum field theory. At very high temperature it seems to be possible to understand longdistance phenomena qualitatively in an effective weakcoupling expansion [3]. These rely on a separation of scales T ≫ gT ≫ g2T, where g is the gauge coupling at momentum scale of order T. The finite temperature crossover from a chiral symmetry broken hadronic state to a symmetry restored quark-gluon state occurs here. It is the range of temperatures which seems to be most relevant for experiments using heavy-ion collisions. VI; it is possible to read this section before the rest of the paper
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