Short study of the eta-eta' system in the two mixing angle scheme

A two mixing angle description of the pseudoscalar decay constants associated to the $\eta$-$\eta^\prime$ system is used to parametrize the theoretical amplitudes of the radiative decays $(\eta,\eta^\prime)\to\gamma\gamma$ and the coupling constants $g_{V(\eta,\eta^\prime)\gamma}$ with $V=\rho,\omega,\phi$. The parametrization is performed in both the ``octet-singlet'' basis and the ``quark-flavour'' basis. An excellent agreement with the most recent experimental data is achieved. Our analysis reveals that at the present experimental accuracy the two mixing angles differ significantly in the former basis but not in the latter, in accordance with the expectations of large $N_c$ Chiral Perturbation Theory where the difference between the two mixing angles are due to a $SU(3)_f$-breaking effect and a violation of the OZI rule respectively.