Multi-instanton contributions to anomalous quark interactions

In quantum chromodynamics (QCD), the role which topologically nontrivial configurations play in splitting the singlet pseudo-Goldstone meson, the η′, from the octet is familiar. In addition, such configurations contribute to other processes which violate the axial U(1)A symmetry. While the nature of topological fluctuations in the vacuum is still unsettled, at temperatures above that for the chiral phase transition, they can be described by a dilute gas of instantons. We show that instantons of arbitrary topological charge Q generate anomalous interactions between 2Nf|Q| quarks, which for Q=1 make the η′ heavy. For two flavors we compute an anomalous quartic meson coupling and discuss its implications for the phenomenology of the chiral phase transition. A dilute instanton gas suggests that for cold, dense quarks, instantons do not evaporate until very high densities, when the baryon chemical potential is ≳2 GeV.