$X(3860)$ production in association with $J\mathrm{/}\psi$ via $e^{+}{e}^{-}$ annihilation at Belle

In this paper, we study the $X(3860)$ production associated with $J\mathrm{/}\psi$ via $e^{+}{e}^{-}$ annihilation at the next-to-leading-order (NLO) QCD accuracy, within the nonrelativistic QCD (NRQCD) framework. Under the hypothesis of $J_{X(3860)}^{PC}=0^{++}$, the predicted total cross sections agree well with the Belle’s measurements at $\sqrt{s}=\mathrm{{\rm Y}}(4S,5S)$, 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 $J\mathrm{/}\psi$ angular distributions. We also perform the NLO calculations of ${\sigma }_{e^{+}{e}^{-}\to J\mathrm{/}\psi +X(3940)}$ on the assumption of $J_{X(3940)}^{PC}=0^{-+}$, discovering that the NRQCD predictions that coincide with the light-cone results are in good agreement with the experiment.