$\eta -{\eta }^{\prime }$ mixing and the next-to-leading-order power correction

Abstract

The next-to-leading-order $O(1/Q^4)$ power correction for $\eta \gamma$ and ${\eta }^{\prime }\gamma$ form factors are evaluated and employed to explore the $\eta -{\eta }^{\prime }$ mixing. The parameters of the two mixing angle scheme are extracted from the data for form factors, two photon decay widths and radiative $J/\psi$ decays. The ${\chi }^2$ analysis gives the result: $f_{{\eta }_1}=(1.16\pm 0.06)f_{\pi },f_{{\eta }_8}=(1.33\pm 0.23)f_{\pi },{\theta }_1=-9^{\circ }\pm 3^{\circ },{\theta }_8=-21.3^{\circ }\pm 2.3^{\circ }$, where $f_{{\eta }_{1(8)}}$ and ${\theta }_{1(8)}$ are the decay constants and the mixing angles for the singlet (octet) state. In addition, we arrive at a stringent range for $f_{{\eta }^{\prime }}^c:-10$ MeV$\le f_{{\eta }^{\prime }}^c\le -4$ MeV.

Comments: 23 pages, 9 figures, To be publshied in Phys. Rev. D