Determination of the $\eta$ and ${\eta }^{\prime }$ Mixing Angle from the Pseudoscalar Transition Form Factors

Abstract

The possible range of $\eta -{\eta }^{\prime }$ mixing angle is determined from the transition form factors $F_{\eta \gamma }(Q^2)$ and $F_{{\eta }^{\prime }\gamma }(Q^2)$ with the help of the present experimental data. For such purpose, the quark-flavor mixing scheme is adopted and the pseudoscalar transition form factors are calculated under the light-cone pQCD framework, where 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 $Q^2\to 0$ and $Q^2\to \infty$. By taking the quark-flavor mixing scheme, our results lead to $\varphi =38.0^{\circ }\pm 1.0^{\circ }\pm 2.0^{\circ }$, where the first error coming from experimental uncertainty and the second error coming from the uncertainties of the wavefunction parameters. The possible intrinsic charm component in $\eta$ and ${\eta }^{\prime }$ is discussed and our present analysis also disfavors a large portion of intrinsic charm component in $\eta$ and ${\eta }^{\prime }$, e.g. $|f_{{\eta }^{\prime }}^c|\le 50\mathrm{MeV}$.

Comments: 18 Pages, 3 figures. Several references added. To be published in EPJC