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We investigate the $(\pi^0,\eta,\eta')\to\gamma^*\gamma$ transitions both forthe spacelike region and the timelike region using the light-front quark model(LFQM). In particular, we present the new direct method to explore the timelikeregion without resorting to mere analytic continuation from the spacelikeregion to the timelike region. Our direct calculation in timelike region showsthe complete agreement not only with the analytic continuation result from thespacelike region but also with the result from the dispersion relation betweenthe real and imaginary parts of the form factor. For the low energy regime, wecompare our LFQM results of the transition form factors (TFFs) for the lowtimelike momentum transfer region and the slope parameters at $q^2=0$ with therecent experimental data from the Dalitz decays of $(\pi^0,\eta,\eta')$. Forthe high energy regime, we incorporate the QCD factorization in our LFQM toexamine the asymptotic behavior of TFFs both for the spacelike region and thetimelike region. We compare our results with the available experimental data.

Spacelike and timelike form factors for the $(\pi^0,\eta,\eta')\to\gamma^*\gamma$ transitions in the light-front quark model