U_A(1) problems and gluon topology: Anomalous symmetry in QCD - Graham Shore (Hidden Symmetries and Higgs Phenomena. Proceedings,Zuoz 1998, 1998)
Many of the distinctive and subtle features of the dynamics in the UA(1) channel in QCD can be related to gluon topology, more precisely to the topological susceptibility χ(k^2) = i \int d^4x e^ikx⟨0|T Q(x) Q(0)|0⟩, where Q = α_s trGμνG ̃μν is the gluon topological charge density. The link is the UA(1) axial (ABJ) anomaly. In this lecture, we describe the anomalous UA(1) chiral Ward identities in a functional formalism and show how two apparently unrelated ‘UA(1) problems’ – the mass of the η′ and the violation of the Ellis- Jaffe sum rule in polarised deep-inelastic scattering – can be explained in terms of the gluon topological susceptibility. They are related through a UA(1) extension of the Goldberger- Treiman formula, which is derived here for QCD with both massless and massive quarks.