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 theta parameter. By monitoring the dependence of various cumulants of the topological charge distribution on the imaginary part of theta and exploiting analytic continuation, we determine the free energy density up to the sixth order in theta, f(theta, T) = f(0, T) + 1/2 chi(T)theta(2)(1+ b(2)(T)theta(2) + b(4)(T)theta(4) + O(theta(6))). 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 b(2) = -0.0216(15) and vertical bar b(4)vertical bar less than or similar to 4 x 10(-4).