Next-to-leading order QCD corrections for the charmonium production via the channel $e^{+}{e}^{-}\to H(|c\bar{c}⟩)+\gamma$ round the $Z^0$ peak

Abstract

In our previous work [2], it has been found that sizable charmonium events via the channel $e^{+}{e}^{-}\to {\gamma }^{\ast }/Z^0\to H(|c\bar{c}⟩)+\gamma$ can be produced at the suggested super $Z$ factory, where $H(|c\bar{c}⟩)$ represents the dominant color-singlet $S$-wave and $P$-wave charmonium states $J/\psi$, ${\eta }_c$, $h_c$ and ${\chi }_{cJ}$ ($J=0,1,2$), respectively. As an important step forward, in the present paper, we present a next-to-leading order (NLO) QCD analysis within the framework of nonrelativistic QCD. In different to the case of $B$ factory in which the single charmonium production is dominated by the channel via a virtual photon, at the super $Z$ factory, its cross-section is dominated by the channel via a $Z^0$ boson. Estimations up to NLO level are done at both the $B$ factory and the super $Z$ factory experimental conditions. We observe that the NLO distributions have the same shapes as those of LO distributions, but their differences are sizable. This indicates that a NLO calculation is necessary and important to achieve a more accurate estimation. Due to $Z^0$ boson resonance effect, at the super $Z$ factory with a high luminosity up to $10^{36}{\mathrm{cm}}^{-2}{\mathrm{s}}^{-1}$, when summing all the color-singlet states' contribution together, one may observe about $8.0\times 10^4$ charmonium events via the channel $e^{+}{e}^{-}\to Z^0\to H(|c\bar{c}⟩)+\gamma$ in one operation year. Then, such super $Z$ factory could provide another useful platform to study the charmonium properties, even for the higher charmonium states.

Comments: 12 pages, 6 figures. To match the published version, to be published in Phys.Rev.D