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Thermodynamics and quark condensates of three-flavor QCD at low temperature

We use three-flavor chiral perturbation theory ($χ$PT) to calculate the pressure, light and $s$-quark condensates of QCD in the confined phase at finite temperature to ${\cal O}(p^6)$ in the low-energy expansion. We also include electromagnetic effects to order $e^2$, where the electromagnetic coupling $e$ counts as order $p$. Our results for the pressure and the condensates suggest that $χ$PT converges very well for temperatures up to approximately 150 MeV. We combine $χ$PT and the Hadron Resonance Gas (HRG) model by adding heavier baryons and mesons. Our results are compared with lattice simulations an d the agreement is very good for temperatures below {170} MeV, in contrast to the results from $χ$PT which agree with the lattice only up to $T\approx120$ MeV. Our value for the chiral crossover temperature is 160.1 MeV, which compares favorably to the lattice result of $157.3$ MeV.