Higher topological charge and the QCD vacuum

Abstract

It is shown that gauge field configurations with higher topological charge modify the structure of the QCD vacuum, which is reflected in its dependence on the CP-violating topological phase θ. To explore this, topological susceptibilities and the production of axion dark matter are studied here. The formers characterize the topological charge distribution and are therefore sensitive probes of the topological structure of QCD. The latter depends on the effective potential of axions, which is determined by the θ dependence of QCD. The production of cold dark matter through the vacuum realignment mechanism of axions can, therefore, be affected by higher topological charge effects. This is discussed qualitatively in the deconfined phase at high temperatures, where a description based on a dilute gas of instantons with arbitrary topological charge is valid. As a result, topological susceptibilities exhibit a characteristic temperature dependence due to anharmonic modifications of the θ dependence. Furthermore, multi-instanton effects give rise to a topological mechanism to increase the amount of axion dark matter.

Phase Transitions in Particle Physics

“…Although this simple prediction has been customarily used in several computations due to its simplicity and due to the lack of more reliable results, it is expected (and confirmed by numerical simulations) that the DIGA result is not reliable for temperatures close to the crossover and even up to the few GeV region, where deviations from perturbative calculations are still pronounced and non-perturbative effects are still not completely negligible. Corrections to the DIGA due to multi-instanton contribution can be computed systematically [486]. However, since the temperature-dependence of m a (T ) in this temperature range is needed to accurately compute axion cosmology [487], it has been pointed out in the literature that an independent and fully non-perturbative computation of χ(T ) from lattice simulations would be needed to obtain full control on m a (T ) [488,489].…”