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

The light-front quark model analysis of the meson-photon transition form factor $F_{P\gamma} (Q^2)$ amenable both for the spacelike region ($Q^2 >0$) and the timelike region ($Q^2 <0$) provides a systematic twist expansion of $Q^2 F_{P\gamma} (Q^2)$ for the high $|Q^2|$ region. Investigating $F_{P\gamma} (Q^2) (P = \eta_c,\eta_b)$ 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 $\Gamma_{(\eta_c,\eta_b)\to\gamma\gamma}$ are compared with the available data checking the sensitivity of our model to the variation of the constituent quark masses.