The Myriad Uses of Instantons

TL;DR

This paper explores the role of instantons in quantum chromodynamics, showing how they generate interactions affecting meson masses and phase transition phenomenology, especially at high temperatures and densities.

Contribution

It provides a detailed analysis of instanton effects across different topological charges and their implications for meson properties and the chiral phase transition.

Findings

Instantons of arbitrary topological charge generate anomalous quark interactions.

For Q=1, instantons contribute to making the $ ext{η}^ ext{'}$ meson heavy.

Instantons persist at high densities until baryon chemical potential exceeds ~2 GeV.

Abstract

In quantum chromodynamics (QCD), the role which topologically non-trivial configurations play in splitting the singlet pseudo-Goldstone meson, the $\eta^\prime$, 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 confined phase is still unsettled, at temperatures well 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 $2 N_f |Q|$ quarks, which for $Q = 1$ make the $\eta^\prime$ 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 $\gtrsim 2$ GeV.