  The QCD formulae for the radiative decays $\eta,\eta'\to\c\c$, 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 $N_c$, so we are able to give a quantitative assessment of the
realisation of the $1/N_c$ expansion in the $U(1)_A$ sector of QCD.
Applications to other aspects of $\eta'$ physics, including the relation with
the first moment sum rule for the polarised photon structure function $g_1^\c$,
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 $\eta$ and $\eta'$-nucleon couplings are discussed. A
comparison with the existing literature on pseudoscalar meson decay constants
using large-$N_c$ chiral Lagrangians is also made.
