In this paper, we study the $X(3860)$ production associated with $J/\psi$ via $e^{ +}e^{ -}$ annihilation at the next-to-leading-order (NLO) QCD accuracy, within the nonrelativistic QCD (NRQCD) framework. Under the hypothesis of $J^{ PC}_{ X(3860)}=0^{ ++}$, the predicted total cross sections agree well with the Belle's measurements at $\sqrt{ s}=\Upsilon(4S,5S)$, while the theoretical results given by the $2^{ ++}$ hypothesis significantly undershoot the data. This is consistent with the Belle's conclusion that the $0^{ ++}$ hypothesis is favored over the $2^{ ++}$ hypothesis for $X(3860)$. Despite the agreement of the total cross sections, the NRQCD predictions seem to be incompatible with the Belle-measured $J/\psi$ angular distributions. We also perform the NLO calculations of $\sigma_{ e^{ +}e^{ -} \to J/\psi+X(3940)}$ on the assumption of $J^{ PC}_{ X(3940)}=0^{ -+}$, discovering that the NRQCD predictions that coincide with the light-cone results are in good agreement with the experiment.
Categories: hep-ph