Z 0 boson decays to B^{(*)}_{c} meson and its uncertainties

The planned new e ⁺ e ^? collider with high luminosity shall provide another useful platform to study the properties of the doubly heavy B _c meson in addition to the hadronic colliders as LHC and TEVATRON. In the ‘New Trace Amplitude Approach’, we calculate the production of the spin-singlet B _c and the spin-triplet $B^{*}_{c}$ mesons through the Z ⁰ boson decays, where uncertainties for the production are also discussed. Our results show $\varGamma_{(^{1}S_{0})}=81.4^{+102.1}_{-40.5}$  KeV and $\varGamma_{(^{3}S_{1})}=116.4^{+163.9}_{-62.8}$  KeV, where the errors are caused by varying m _b and m _c within their reasonable regions.