The quark condensate |〈0|¯qq|0〉 | is an order parameter of spontaneous chiral symmetry breaking in QCD. With increasing temperature and baryon density it decreases. For low T this effect can be systematically calculated in ChPT and the estimate Tc ≃ 190 MeV for the critical temperature has been found. This is remarkably consistent with Tc = (192 ± 8) MeV  obtained in QCD lattice simulations (modulo still persisting disputes between different lattice groups ). The density dependence of the quark condensate can be extracted by exploiting the Feynman-Hellmann theorem with respect to the quark mass term mq ¯qq. The leading linear term in the density ρ introduces the nucleon sigma-term σN = 〈N|mq ¯qq|N 〉 = mq ∂MN/∂mq = (45 ± 8) MeV. Corrections beyond it arise from the NN-interactions. Because of the Goldstone boson nature of the pion, m2 π ∼ mq, the pion-exchange dynamics in nuclear matter plays a particularly important role. Altogether, one has for the ratio of the in-medium to the vacuum chiral quark condensate: 〈¯qq〉(ρ) ρ = 1 − 〈0|¯qq|0 〉 f2 π σN m 2
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