Theta dependence of the vacuum energy density in chiral effective Lagrangian models at finite temperature, above Tc

In this work, extending a previous study at zero temperature (T=0), we perform a systematic study of the modifications to the QCD vacuum energy density εvac in the finite-temperature case, above the chiral transition at Tc, caused by a nonzero value of the parameter θ, using two different effective Lagrangian models which implement the U(1) axial anomaly of the fundamental theory and which are both well defined also above Tc. In particular, we derive (and critically compare) the expressions for the topological susceptibility χ and for the second cumulant c4 starting from the θ dependence of εvac(θ) in the two models