Bcmeson production around theZ0peak at a high luminositye+e−collider

Abstract

Considering the possibility to build an ${e}^{+}{e}^{\ensuremath{-}}$ collider at the energies around the ${Z}^{0}$-boson resonance with a planned luminosity as high as $\mathcal{L}\ensuremath{\propto}{10}^{34}\ensuremath{\sim}{10}^{36}\text{ }\text{ }{\mathrm{cm}}^{\ensuremath{-}2}\text{ }{\mathrm{s}}^{\ensuremath{-}1}$ (super $Z$-factory), we make a detailed discussion on the ($c\overline{b}$)-quarkonium production through ${e}^{+}+{e}^{\ensuremath{-}}\ensuremath{\rightarrow}(c\overline{b})[n]+b+\overline{c}$ within the framework of nonrelativistic QCD. Here $n$ stands for the Fock-states $|(c\overline{b}{)}_{\mathbf{1}}[^{1}S_{0}]⟩$, $|(c\overline{b}{)}_{\mathbf{8}}[^{1}S_{0}]g⟩$, $|(c\overline{b}{)}_{\mathbf{1}}[^{3}S_{1}]⟩$, $|(c\overline{b}{)}_{\mathbf{8}}[^{3}S_{1}]g⟩$, $|(c\overline{b}{)}_{\mathbf{1}}[^{1}P_{1}]⟩$ and $|(c\overline{b}{)}_{\mathbf{1}}[^{3}P_{J}]⟩$ (with $J=(1,2,3)$), respectively. To simplify the hard-scattering amplitude as much as possible and to derive analytic expressions for the purpose of future events simulation, we adopt the ``improved trace technology'' to do our calculation, which deals with the hard-scattering amplitude directly at the amplitude level other than the conventional way at the squared-amplitude level. Total cross section uncertainties caused by the quark masses are predicted by taking ${m}_{c}=1.50\ifmmode\pm\else\textpm\fi{}0.30\text{ }\text{ }\mathrm{GeV}$ and ${m}_{b}=4.90\ifmmode\pm\else\textpm\fi{}0.40\text{ }\text{ }\mathrm{GeV}$. If all higher ($c\overline{b}$)-quarkonium states decay to the ground-state ${B}_{c}(|(c\overline{b}{)}_{\mathbf{1}}[^{1}S_{0}]⟩)$ with 100% efficiency, we obtain ${\ensuremath{\sigma}}_{{e}^{+}+{e}^{\ensuremath{-}}\ensuremath{\rightarrow}{B}_{c}+b+\overline{c}}={5.190}_{\ensuremath{-}2.419}^{+6.222}\text{ }\text{ }\mathrm{pb}$, which shows that about ${10}^{5}\ensuremath{\sim}{10}^{7}{B}_{c}$ events per operation year can be accumulated in the super $Z$-factory. If taking the collider energy runs slightly off the ${Z}^{0}$-peak, i.e. $\sqrt{S}=(1.00\ifmmode\pm\else\textpm\fi{}0.05){m}_{Z}$, the total cross section shall be lowered by about one-order from its peak value. Such a super $Z$-factory shall provide another useful platform to study the properties of ${B}_{c}$-meson, or even the properties of its excited $P$-wave states, in addition to its production at the hadronic colliders Tevatron and LHC.