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The $P$-wave charmonium electromagnetic Dalitz decays$h_{c}\rightarrow\eta^{(\prime)}\ell^{+}\ell^{-}$ $(\ell=e, \mu)$ with largerecoil momentum are investigated in the framework of perturbative QCD, and thesoft contributions from the small recoil momentum region are described by theoverlap of soft wave functions. The transition form factors$f_{h_{c}\eta^{(\prime)}}(q^{2})$ and the normalized transition form factors$F_{h_{c} \eta^{(\prime)}}(q^{2})$ in full kinematic region are derived for thefirst time. It is noticed that there are no extra IR divergences at theone-loop level and the tree level, and the transition form factors in which therelativistic corrections from the internal momentum of $h_{c}$ are taken intoaccount are insensitive to both the shapes of $\eta^{(\prime)}$ distributionamplitudes and the invariant mass of the lepton pair in the large recoilmomentum region. Furthermore, we find that the contributions from the softmechanism and those from hard mechanism are comparable with each other in thebranching ratios$\mathcal{B}(h_{c}\rightarrow\eta^{(\prime)}\ell^{+}\ell^{-})$. By employingthe obtained $F_{h_{c} \eta^{(\prime)}}(q^{2})$, we give the predictions of thebranching ratios$\mathcal{B}(h_{c}\rightarrow\eta^{(\prime)}\ell^{+}\ell^{-})$, which may comewithin the range of measurement of present or near-future experiments.

QCD analysis of the $P$-wave charmonium electromagnetic Dalitz decays $h_{c}\rightarrow\eta^{(\prime)}\ell^{+}\ell^{-}$