We analyze chiral restoration within the $O(N+1)/O(N)$ nonlinear sigma model for large $N$ as an effective theory for low-energy QCD at finite temperature $T$. The free energy is constructed diagrammatically to $\mathcal{O}(T{M}^3)$ in the pion mass expansion, which allows us to derive the quark condensate and the scalar susceptibility in the chiral limit. At this order, we do not have to deal with renormalization, either from divergences from mass tadpoles or from those of higher order loop contributions. Our results for the critical behavior are consistent with expectations from lattice analysis and with previous works where the susceptibility is saturated by the thermal $f_0(500)$ pole.

• Received 3 October 2016

DOI:https://doi.org/10.1103/PhysRevD.94.116008