Pseudoscalar meson decay constants and couplings, the Witten–Veneziano formula beyond large image, and the topological susceptibility Original Research Article

The QCD formulae for the radiative decays image, and the corresponding Dashen–Gell-Mann–Oakes–Renner relations, differ from conventional PCAC results due to the gluonic image 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 image, so we are able to give a quantitative assessment of the realisation of the image expansion in the image sector of QCD. Applications to other aspects of image physics, including the relation with the first moment sum rule for the polarised photon structure function image, are highlighted. The image Goldberger–Treiman relation is extended to accommodate image flavour breaking and the implications of a more precise measurement of the η and image-nucleon couplings are discussed. A comparison with the existing literature on pseudoscalar meson decay constants using large-image chiral Lagrangians is also made.