Topological susceptibility at zero and finite temperature in the Nambu-Jona-Lasinio model

We consider the three flavor Nambu-Jona-Lasinio model with the 't Hooft interaction incorporating the U(1)_A anomaly. In order to set the coupling strength of the 't Hooft term, we employ the topological susceptibility $\chi$ instead of the eta' meson mass. The value for $\chi$ is taken from lattice simulations. We also calculate $\chi$ at finite temperature within the model. Comparing it with the lattice data, we extract information about the behavior of the U(1)_A anomaly at finite temperature. We conclude that within the present framework, the effective restoration of the U(1)_A symmetry does not necessarily take place even at high temperature where the chiral symmetry is restored.