The U(1)_A Anomaly and QCD Phenomenology

Abstract

The role of the $U(1)_A$ anomaly in QCD phenomenology is reviewed, focusing on the relation between quark dynamics and gluon topology. Topics covered include a generalisation of the Witten-Veneziano formula for the mass of the $\eta'$, the determination of pseudoscalar meson decay constants, radiative pseudoscalar decays and the $U(1)_A$ Goldberger-Treiman relation. Sum rules are derived for the proton and photon structure functions $g_1^p$ and $g_1^\c$ measured in polarised deep-inelastic scattering. The first moment sum rule for $g_1^p$ (the `proton spin' problem) is confronted with new data from COMPASS and HERMES on the deuteron structure function and shown to be quantitatively explained in terms of topological charge screening. Proposals for experiments on semi-inclusive DIS and polarised two-photon physics at future $ep$ and high-luminosity $e^+ e^-$ colliders are discussed.