The topological susceptibility and excess kurtosis in SU(3) Yang-Mills theory

Abstract: We determine the topological susceptibility and the excess kurtosis of $SU(3)$ pure gauge theory in four space-time dimensions. The result is based on high-statistics studies at seven lattice spacings and in seven physical volumes, allowing for a controlled continuum and infinite volume extrapolation. We use a gluonic topological charge measurement, with gradient flow smoothing in the operator. Two complementary smoothing strategies are used (one keeps the flow time fixed in lattice units, one in physical units). Our data support a recent claim that both strategies yield a universal continuum limit; we find $\chi_\mathrm{top}^{1/4}r_0=0.4769(14)(11)$ or $\chi_\mathrm{top}^{1/4}=197.8(0.7)(2.7)\,\mathrm{MeV}$.