The topological susceptibility slope ${\chi }^{\mathrm{\prime }}$ in the large-$N$ limit

This paper presents the first non-perturbative lattice determination of the Yang–Mills topological susceptibility slope ${\chi }^{\mathrm{\prime }}$ in the large-$N$ limit. This quantity represents the $\mathcal{O}(p^2)$ term of the momentum expansion of the topological charge density two-point correlator, and has important theoretical and phenomenological implications for strong interactions. This calculation is based on a novel algorithm that avoids topological freezing at large $N$ on fine lattices, and on a novel method to reliably compute ${\chi }^{\mathrm{\prime }}$ on the lattice. The results of this study are relevant for the description of the proton spin in deep inelastic scattering experiments via the Shore–Veneziano formula.