Further studies on the exclusive productions of $$J/\psi +\chi _{cJ}$$ J/ψ+χcJ ($$J=0,1,2$$ J=0,1,2 ) via $$e^+e^-$$ e+e- annihilation at the B factories

Abstract By including the interference effect between the QCD and the QED diagrams, we carry out a complete analysis on the exclusive productions of $$e^+e^- \rightarrow J/\psi +\chi _{cJ}$$ e+e-→J/ψ+χcJ ($$J=0,1,2$$ J=0,1,2 ) at the B factories with $$\sqrt{s}=10.6$$ s=10.6 GeV at the next-to-leading-order (NLO) level in $$\alpha _s$$ αs , within the nonrelativistic QCD framework. It is found that the $${\mathcal {O}} (\alpha ^3\alpha _s)$$ O(α3αs) -order terms that represent the tree-level interference are comparable with the usual NLO QCD corrections, especially for the $$\chi _{c1}$$ χc1 and $$\chi _{c2}$$ χc2 cases. To explore the effect of the higher-order terms, namely $${\mathcal {O}} (\alpha ^3\alpha _s^2)$$ O(α3αs2) , we perform the QCD corrections to these $${\mathcal {O}} (\alpha ^3\alpha _s)$$ O(α3αs) -order terms for the first time, which are found to be able to significantly influence the $${\mathcal {O}} (\alpha ^3\alpha _s)$$ O(α3αs) -order results. In particular, in the case of $$\chi _{c1}$$ χc1 and $$\chi _{c2}$$ χc2 , the newly calculated $${\mathcal {O}} (\alpha ^3\alpha _s^2)$$ O(α3αs2) -order terms can to a large extent counteract the $${\mathcal {O}} (\alpha ^3\alpha _s)$$ O(α3αs) contributions, evidently indicating the indispensability of the corrections. In addition, we find that, as the collision energy rises, the percentage of the interference effect in the total cross section will increase rapidly, especially for the $$\chi _{c1}$$ χc1 case.