Pseudoscalar meson decay constants and couplings, the Witten-Veneziano formula beyond large Nc, and the topological susceptibility

The QCD formulae for the radiative decays η,η′→γγ, and the corresponding Dashen-Gell-Mann-Oakes-Renner relations, differ from conventional PCAC results due to the gluonic U(1)A axial anomaly. This introduces a critical dependence on the gluon topological susceptibility. In this paper, we revisit our earlier theoretical analysis of radiative pseudoscalar decays and the DGMOR relations and extract explicit experimental values for the decay constants. This is our main result. The flavour singlet DGMOR relation is the generalisation of the Witten-Veneziano formula beyond large Nc, so we are able to give a quantitative assessment of the realisation of the 1/Nc expansion in the U(1)A sector of QCD. Applications to other aspects of η′ physics, including the relation with the first moment sum rule for the polarised photon structure function g1γ, are highlighted. The U(1)A Goldberger-Treiman relation is extended to accommodate SU(3) flavour breaking and the implications of a more precise measurement of the η and η′-nucleon couplings are discussed. A comparison with the existing literature on pseudoscalar meson decay constants using large-Nc chiral Lagrangians is also made.