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arXiv · 1510.08826

Non-Gaussianity of the topological charge distribution in $\mathrm{SU}(3)$ Yang-Mills theory

Marco Cè
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Abstract

In Yang-Mills theory, the cumulants of the naïve lattice discretization of the topological charge evolved with the Yang-Mills gradient flow coincide, in the continuum limit, with those of the universal definition. We sketch in these proceedings the main points of the proof. By implementing the gradient-flow definition in numerical simulations, we report the results of a precise computation of the second and the fourth cumulant of the $\mathrm{SU}(3)$ Yang-Mills theory topological charge distribution, in order to measure the deviation from Gaussianity. A range of high-statistics Monte Carlo simulations with different lattice volumes and spacings is used to extrapolate the results to the continuum limit with confidence by keeping finite-volume effects negligible with respect to the statistical errors. Our best result for the topological susceptibility is $t_0^2χ=6.67(7)\times 10^{-4}$, while for the ratio between the fourth and the second cumulant we obtain $R=0.233(45)$.

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Marco Cè. 2015-10-29. Non-Gaussianity of the topological charge distribution in $\mathrm{SU}(3)$ Yang-Mills theory. https://doi.org/10.22323/1.251.0318

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