Determination of the $η$ and $η'$ Mixing Angle from the Pseudoscalar Transition Form Factors

Abstract

The possible range of $η-η'$ mixing angle is determined from the transition form factors $F_{ηγ}(Q^2)$ and $F_{η' γ}(Q^2)$ 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 $ϕ= 38.0^{\circ}\pm 1.0^{\circ}\pm 2.0^{\circ}$, 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 $η$ and $η'$ is discussed and our present analysis also disfavors a large portion of intrinsic charm component in $η$ and $η'$, e.g. $|f^c_{η'}|\le 50 {\rm MeV}$.