We propose a new η -${\mathrm{\eta }}^{\prime }$ mixing scheme where we start from the quark flavor basis and assume that the decay constants in that basis follow the pattern of particle state mixing. On exploiting the divergences of the axial vector currents — which embody the axial vector anomaly — all basic parameters are fixed to first order of flavor symmetry breaking. That approach naturally leads to a mass matrix, quadratic in the masses, with specified elements. We also test our mixing scheme against experiment and determine corrections to the first order values of the basic parameters from phenomenology. Finally, we generalize the mixing scheme to include the ${\eta }_c.$ Again the divergences of the axial vector currents fix the mass matrix and, hence, mixing angles and the charm content of the η and ${\mathrm{\eta }}^{\prime }$.

• Received 27 February 1998

DOI:https://doi.org/10.1103/PhysRevD.58.114006