  We present results for the $\eta$ and $\eta^\prime$ masses and their four
independent decay constants at the physical point as well as their anomalous
gluonic matrix elements $a_{\eta^{(\prime)}}$. The chiral and continuum limit
extrapolation is performed on twenty-one $N_f = 2+1$ Coordinated Lattice
Simulations (CLS) ensembles with non-perturbatively improved Wilson fermions at
four different lattice spacings and along two trajectories in the quark mass
plane, including one ensemble very close to physical quark masses. For the
first time the decay constants are determined directly from the axialvector
matrix elements without model assumptions. This allows us to study their QCD
scale dependence and to determine all low-energy constants contributing at
next-to-leading order in large-$N_c$ ChPT at a well defined QCD renormalization
scale. We also discuss higher excited states in the $1400\,\mathrm{MeV}$
region.
