Effective field theory for thermal QCD with 2 + 1 flavors

We write a long-distance effective field theory (EFT) for QCD at finite temperature just below the crossover temperature T c o . The low energy constants of this EFT are obtained from lattice measurements of the screening mass of pions at two temperatures for N f = 2 + 1 using lattice results obtained at physical values of pion and Kaon masses, and N f = 2 where the lattice simulations were performed with a heavier pion mass. The EFT gives good predictions for other static pion properties for N f = 2 , where lattice results are available. We show the corresponding predictions for N f = 2 + 1 , where they are not yet measured. We demonstrate that EFT gives excellent predictions for the phase diagram in N f = 2 + 1 . The predictions for the pressure are investigated, and predictions are also given for a Wick-rotated real-time quantity called the kinetic mass.