Systematic twist expansion of $({\eta }_c,{\eta }_b)\to {\gamma }^{\ast }\gamma$ transition form factors in light-front quark model

Abstract

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.

Comments: 9 pages, 6 figures, Version to appear in Phys.Rev. D. arXiv admin note: text overlap with arXiv:1708.00736