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

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

2002-04-23

arxiv.org/abs/hep-ph/0204264v1

Phys.Rev. D65 (2002) 094019

Physics

High Energy Physics

High Energy Physics - Phenomenology

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

Scientific paper

10.1103/PhysRevD.65.094019

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: $f_{\eta_1}=(1.16\pm0.06)f_\pi, f_{\eta_8}=(1.33\pm0.23)f_\pi, \theta_1=-9^\circ\pm 3^\circ, \theta_8=-21.3^\circ\pm 2.3^\circ$, 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.

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