Finite - Temperature topological Susceptibility of QCD with heavy Quarks

The axion is a very interesting hypothetical particle, as it is not only an ideal dark matter candidate, but also dynamically, i.e., “naturally”, solves the strong CP problem - the discrepancy between the theoretically allowed violation of the combined particle-antiparticle exchange and spatial flip-symmetry in QCD on the one hand and its experimentally observed (nearly perfect) conservation on the other hand. “Hypothetical particle” means here that, despite significant experimental effort, the axion has until now avoided experimental detection. Therefore, precise theoretical predictions about its properties, especially its mass, are required. Furthermore, the investigation of cosmology with axions has shown that the cosmological history of axions depends critically on the temperature-dependent axion mass in the temperature range between 400 and 1100 MeV, where very little is known about the axion mass so far. The axion, and especially its mass, are directly linked to the topological properties of QCD. The QCD vacuum allows for topologically non-trivial, local configurations, which do not play a role in perturbation theory, but have non-perturbative effects on the quarks and gluons. At zero temperature, these configurations are called instantons and for finite T they are called calorons. The strength of these instanton/caloron effects, i.e., the strength of the quark-gluon system’s response to such a topological background, is determined by the topological susceptibility χtop. In turn, the axion mass is proportional to the square root of χtop. Using lattice QCD, the main model for accessing non-perturbative QCD effects, to obtain χtop becomes very challenging at high temperatures as 400 MeV < T < 1100 MeV, because the topological susceptibility is strongly suppressed at high T and since the bottom quark is not heavy enough to ignore at such temperatures, while so far only 2+1+1, but no 2+1+1+1 (including a dynamical bottom quark) lattice simulations exist. Therefore, we estimate the effect of the bottom quark on χtop at high temperatures by computing the ration between the 4-quark χtop (available from lattice QCD) and the 4+1-quark χtop in the caloron gas approximation. We do this by computing small-mass and large-mass expansions of the finite-mass and -temperature fermionic fluctuation determinant and connecting them with a Padé approximant. Together with the lattice QCD results, this allows for predictions for χtop with a bottom quark at arbitrary temperatures.