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 𝒪(θ^2) 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. 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.