Measurement of e + e ! γχcJ via initial state radiation at Belle

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