Systematic twist expansion of $({\eta }_c,{\eta }_b)\to {\gamma }^{\ast }\gamma$ 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 $\mathrm{\mid }{Q}^2\mathrm{\mid }$ region. Investigating $F_{P\gamma} (Q^2) (P = \eta_c,\eta_b)$fortheentirekinematicregionsof$Q^2$, 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 $F_{({\eta }_c,{\eta }_b)\gamma }(Q^2)\mathrm{/}{F}_{({\eta }_c,{\eta }_b)\gamma }(0)$ and the decay width ${\mathrm{\Gamma }}_{({\eta }_c,{\eta }_b)\to \gamma \gamma }$ are compared with the available data checking the sensitivity of our model to the variation of the constituent quark masses.