The Topological Susceptibility of QCD at High Temperatures

Two of the most challenging problems in modern physics are the origin of dark matter and the strong CP problem. The latter means the non-observation of the violation of the combined particle-antiparticle and parity (CP) symmetries by the strong interaction which is conceptually allowed. Both problems - although prima facie disparate - could be simultaneously solved by the Peccei-Quinn mechanism. This results in a new particle, the axion. Despite strong experimental efforts, the discovery of the axion is yet to come, making precise theoretical predictions of its properties, especially its mass, highly valuable. The axion's properties are closely related to the topological structure of the vacuum of quantum chromodynamics (QCD). The QCD vacuum exhibits topologically non-trivial fluctuations of the gauge fields with the most important fluctuations being instantons. These topological fluctuations are quantified by the topological susceptibility that controls the axion mass and therefore is - especially at high temperatures - an important input for axion cosmology. Since topological effects are inherently non-perturbative, lattice QCD is particularly suitable for precisely determining the topological susceptibility. However, lattice simulations become extremely challenging at high temperatures because the topological susceptibility is very suppressed. In this work, we develop and establish a novel method based on a combination of gradient flow and reweighting that artificially enhances the number of instantons and therefore allows to determine the topological susceptibility at high temperatures. For computational simplicity, we content ourselves to pure SU(3) Yang-Mills theory for developing the method, but it is explicitly designed to be applicable also in full QCD. In particular, we provide a discretization of the instanton that allows for an analysis of the lattice-spacing effects on a lattice study of the topological susceptibility. We then present the reweighting method that is eventually used to determine the topological susceptibility up to 2 GeV in pure SU(3) Yang-Mills theory which constitutes the first direct determination of the topological susceptibility at such high temperatures.