Measurement of $e^{+}{e}^{-}\to \gamma {\chi }_{cJ}$ via initial state radiation at Belle

The process $e^{+}{e}^{-}\to \gamma {\chi }_{cJ}$ ($J$=1, 2) is studied via initial state radiation using 980 fb${}^{-1}$ of data at and around the $\mathrm{{\rm Y}}(nS)$ ($n$=1, 2, 3, 4, 5) resonances collected with the Belle detector at the KEKB asymmetric-energy $e^{+}{e}^{-}$ collider. No significant signal is observed except from $\psi (2S)$ decays. Upper limits on the cross sections between $\sqrt{s}=3.80$ and $5.56\mathrm{G}\mathrm{e}\mathrm{V}$ are determined at the 90% credibility level, which range from few pb to a few tens of pb. We also set upper limits on the decay rate of the vector charmonium [$\psi (4040$), $\psi (4160)$, and $\psi (4415)$] and charmoniumlike [$Y(4260)$, $Y(4360)$, and $Y(4660)$] states to $\gamma {\chi }_{cJ}$.