Systematic twist expansion of $(eta_c,eta_b)togamma^*gamma$ transition form factors in light-front quark model

The light-front quark model analysis of the meson-photon transition form factor $F_{Pgamma} (Q^2)$ amenable both for the spacelike region ($Q^2 >0$) and the timelike region ($Q^2 <0$) provides a systematic twist expansion of $Q^2 F_{Pgamma} (Q^2)$ for the high $|Q^2|$ region. Investigating $F_{Pgamma} (Q^2) (P = eta_c,eta_b)$ for the entire kinematic regions of $Q^2$, we examine the twist-2 and twist-3 distribution amplitudes of $(eta_c,eta_b)$ mesons in the light-front quark model and quantify their contributions to $Q^2 F_{(eta_c,eta_b)gamma}(Q^2)$. Our numerical results for the normalized transition form factor $F_{(eta_c,eta_b)gamma}(Q^2)/F_{(eta_c,eta_b)gamma}(0)$ and the decay width $Gamma_{(eta_c,eta_b)togammagamma}$ are compared with the available data checking the sensitivity of our model to the variation of the constituent quark masses.