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

TL;DR

This study investigates the production of the X(3860) particle with J/psi in electron-positron collisions at Belle, using NLO QCD within NRQCD, and finds the 0++ hypothesis aligns with observed cross sections but not angular distributions.

Contribution

The paper provides NLO QCD predictions for X(3860) production in e+e- annihilation, supporting the 0++ quantum number assignment over 2++, and compares these with experimental data.

Findings

Total cross sections agree with 0++ hypothesis

Angular distributions are incompatible with NRQCD predictions

NRQCD predictions for X(3940) match light-cone results

Abstract

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.