Next-to-leading-order study of $J/\psi$ angular distributions in $e^{+}{e}^{-}\to J/\psi +{\eta }_c,{\chi }_{cJ}$ at $\sqrt{s}\approx 10.6$ GeV

Abstract

In this paper, we present a detailed next-to-leading-order (NLO) study of $J/\psi$ angular distributions in $e^{+}{e}^{-}\to J/\psi +{\eta }_c,{\chi }_{cJ}$ ($J=0,1,2$) within the nonrelativistic QCD factorization (NRQCD). The numerical NLO expressions for total and differential cross sections, i.e., $\frac{d\sigma }{d\cos \theta }=A+B{\cos }^2\theta$, are both derived. With the inclusion of the newly-calculated QCD corrections to $A$ and $B$, the ${\alpha }_{\theta }(=B/A)$ parameters in $J/\psi +{\chi }_{c0}$ and $J/\psi +{\chi }_{c1}$ are moderately enhanced, while the magnitude of ${{\alpha }_{\theta }}_{J/\psi +{\chi }_{c2}}$ is significantly reduced; regarding the production of $J/\psi +{\eta }_c$, the ${\alpha }_{\theta }$ value remains unchanged. By comparing with experiment, we find the predicted ${{\alpha }_{\theta }}_{J/\psi +{\eta }_c}$ is in good agreement with the $\text{B}\text{ELLE}$ measurement; however, ${{\alpha }_{\theta }}_{J/\psi +{\chi }_{c0}}$ is still totally incompatible with the experimental result, and this discrepancy seems to hardly be cured by proper choices of the charm-quark mass, the renormalization scale, and the NRQCD matrix elements.

arXiv comment14 pages, 4 figures, and 7 tables; accepted for publication in JHEP

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