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 $\Upsilon(nS)$ ($n$=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 $5.56~{\rm GeV}$ 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 [$\psi(4040$), $\psi(4160)$, and $\psi(4415)$] and charmoniumlike [$Y(4260)$, $Y(4360)$, and $Y(4660)$] states to $\gamma\chi_{cJ}$.
Upper limits on the $e^+e^-\to \gamma\chi_{cJ}$ cross sections.
Upper limits on $\Gamma_{ee} \times \mathcal{B}$ at the 90$\%$ C.L.
Upper limits on branching fractions $\mathcal{B}(R \to \gamma \chi_{cJ})$ at the 90$\%$ C.L.
The CLEO II detector is used to search for the production of χc2 states in two-photon interactions. We use the signature χc2→γJ/ψ→γl+l− with l=e,μ. Using 1.49 fb−1 of data taken with beam energies near 5.29 GeV, the two-photon width of the χc2 is determined to be Γ(χc2→γγ)=1.08±0.30(stat)±0.26(syst) keV, in agreement with predictions from perturbative QCD.
Results below were obtained usign J/psi from-factors in the two photon propogators, and assumes that only transversely polarized photons are significant inthe production of the CHI/C2(1P) state.
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