Field theoretical approach to the study of theta dependence in Yang-Mills theories on the lattice

We discuss the extension of the field theoretical approach, already used in the lattice determination of the topological susceptibility, to the computation of further terms in the expansion of the ground state energy $F(\theta)$ around $\theta = 0$ in SU(N) Yang-Mills theories. In particular we determine the fourth order term in the expansion for SU(3) pure gauge theory and compare our results with previous cooling determinations. In the last part of the paper we make some considerations about the nature of the ultraviolet fluctuations responsible for the renormalization of the lattice topological charge correlation functions; in particular we propose and test an ansatz which leads to improved estimates of the fourth and higher order terms in the expansion of F(\theta).