Measurement of $e^+e^- \to γχ_{cJ}$ via initial state radiation at Belle
The process $e^+e^- \to γχ_{cJ}$ ($J$=1, 2) is studied via initial state radiation using 980 fb$^{-1}$ of data at and around the $Υ(nS)$ ($n$=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 $ψ(2S)$ decays. Upper limits on the cross sections between $\sqrt{s}=3.80$ and $5.56~{\rm GeV}$ 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 [$ψ(4040$), $ψ(4160)$, and $ψ(4415)$] and charmoniumlike [$Y(4260)$, $Y(4360)$, and $Y(4660)$] states to $γχ_{cJ}$.
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