θ Dependence in SU (3) Yang-Mills theory from analytic continuation

We investigate the topological properties of the SU(3) pure gauge theory by performing numerical simulations at imaginary values of the θ parameter. By monitoring the dependence of various cumulants of the topological charge distribution on the imaginary part of θ and exploiting analytic continuation, we determine the free energy density up to the sixth order in θ, f(θ,T)=f(0,T)+12χ(T)θ2(1+b2(T)θ2+b4(T)θ4+O(θ6)). That permits us to achieve determinations with improved accuracy, in particular for the higher-order terms, with control over the continuum and the infinite-volume extrapolations. We obtain b2=-0.0216(15) and |b4|4×10-4.