The θ-dependence of the Yang-Mills spectrum from analytic continuation

We study the θ-dependence of the string tension and of the lightest glueball mass in four-dimensional SU(N) Yang-Mills theories. More precisely, we focus on the coefficients parametrizing the Oθ² dependence of these quantities, which we investigate by means of numerical simulations of the lattice-discretized theory, carried out using imaginary values of the θ parameter. Topological freezing at large N is avoided using the Parallel Tempering on Boundary Conditions algorithm. We provide controlled continuum extrapolations of such coefficients in the N = 3 case, and we report the results obtained on two fairly fine lattice spacings for N = 6.