Study of the theta dependence of the vacuum energy density in chiral effective Lagrangian models at zero temperature

We perform a systematic study of the modifications to the QCD vacuum energy density ϵvac in the zero-temperature case (T=0) caused by a small, but nonzero, value of the parameter θ, using different effective Lagrangian models which include the flavor-singlet meson field and implement the U(1) axial anomaly of the fundamental theory. In particular, we derive the expressions for the topological susceptibility χ and for the second cumulant c4 starting from the θ dependence of ϵvac(θ) in the various models that we have considered. Moreover, we evaluate numerically our results, so as to compare them with each other, with the predictions of the chiral effective Lagrangian and, finally, also with the available lattice data