Determination of the η and η′ mixing angle from the pseudoscalar transition form factors

Abstract

The possible range of the η– $\eta^{\prime}$ mixing angle is determined from the transition form factors Fηγ(Q2) and $F_{\eta^{\prime}\gamma}(Q^2)$ with the help of up-to-date experimental data. For this purpose, the quark-flavor mixing scheme is adopted and the pseudoscalar transition form factors are calculated in the framework of light-cone pQCD, in which the transverse-momentum corrections and the contributions beyond the leading Fock state have been carefully taken into consideration. We construct a phenomenological expression to estimate the contributions to the form factors beyond the leading Fock state, based on their asymptotic behavior at Q2→0 and $Q^2\to\infty$ . By taking the quark-flavor mixing scheme, our results lead to $\phi={38.0}^{\circ}\pm{1.0}^{\circ}\pm{2.0}^{\circ}$ , where the first error comes from the experimental uncertainty and the second error from the uncertainties of the parameters of the wavefunction. The possible intrinsic charm component in η and $\eta^{\prime}$ is discussed, and our present analysis also disfavors a large intrinsic charm component in η and $\eta^{\prime}$ , e.g. $|f^c_{\eta^{\prime}}|\le{50}\,\text{MeV}$ .