Probing the $\gamma {\gamma }^{\ast }\to {\eta }^{(\prime )}$ Transition Form Factors with Newly Derived ${\eta }^{(\prime )}$-Meson Light-Cone Distribution Amplitudes

Abstract

In the present work, we analyze the properties of the transition form factors (TFFs) for the $\gamma {\gamma }^{\ast }\to {\eta }^{(\prime )}$ process, employing the ${\eta }^{(\prime )}$-meson light-cone distribution amplitude (LCDA) derived within the light-cone sum rule framework. To this end, we adopt the quark-flavor mixing scheme for the ${\eta }^{(\prime )}$ meson, and compute the TFFs by systematically incorporating transverse-momentum corrections and contributions beyond the leading Fock state. We utilize light-cone harmonic oscillator models to parameterize the longitudinal and transverse behavior of the leading-twist light-cone wavefunction, for which the corresponding LCDA exhibits a unimodal profile. We further examine the potential contributions of intrinsic charm components to the scaled TFFs $Q^2{F}_{\eta \gamma }(Q^2)$ and $Q^2{F}_{{\eta }^{\prime }\gamma }(Q^2)$. Leveraging a range of values for the decay constant $f_{{\eta }_{c_0}}$ and implementing the $\eta$-${\eta }^{\prime }$-${\eta }_c$ and $\eta$-${\eta }^{\prime }$-$G$-${\eta }_c$ mixing mechanisms accordingly, together with the recently updated mixing angles, we investigate the impact of the intrinsic $c\bar{c}$ and gluonic component on these observables. In high-$Q^2$ regime, $Q^2{F}_{{\eta }^{\prime }\gamma }(Q^2)$ exhibits a marked increase in sensitivity to the charm quark component, whereas $Q^2{F}_{\eta \gamma }(Q^2)$ becomes notably stabilized. A detailed discussion of ${\chi }^2/d.o.f$ and $p$-values indicates that the intrinsic charm quark component is important and yields a substantial, non-negligible contribution across the entire $Q^2$ range.

Comments: 13 pages, 5 figures, comments welcome