The topological susceptibility slope $\chi^\prime$ of the pure-gauge SU(3) Yang-Mills theory

We determine the pure-gauge $\mathrm{SU}(3)$ topological susceptibility slope $\chi^\prime$, related to the next-to-leading-order term of the momentum expansion of the topological charge density 2-point correlator, from numerical lattice Monte Carlo simulations. Our strategy consists in performing a double-limit extrapolation: first we take the continuum limit at fixed smoothing radius, then we take the zero-smoothing-radius limit. Our final result is $\chi^\prime = [17.1(2.1)~\mathrm{MeV}]^2$. We also discuss a theoretical argument to predict its value in the large-$N$ limit, which turns out to be remarkably close to the obtained $N=3$ lattice result.