$η-η^\prime$ mixing and the next-to-leading-order power correction

Abstract

The next-to-leading-order $O(1/Q^4)$ power correction for $ηγ$ and $η^\primeγ$ form factors are evaluated and employed to explore the $η-η^\prime$ mixing. The parameters of the two mixing angle scheme are extracted from the data for form factors, two photon decay widths and radiative $J/ψ$ decays. The $χ^2$ analysis gives the result: $f_{η_1}=(1.16\pm0.06)f_π, f_{η_8}=(1.33\pm0.23)f_π, θ_1=-9^\circ\pm 3^\circ, θ_8=-21.3^\circ\pm 2.3^\circ$, where $f_{η_{1(8)}}$ and $θ_{1(8)}$ are the decay constants and the mixing angles for the singlet (octet) state. In addition, we arrive at a stringent range for $f_{η^\prime}^c:-10$ MeV$\le f_{η^\prime}^c\le -4$ MeV.