Exclusive production of $B_c$ mesons in $e^{+}{e}^{-}$ colliders

Abstract

Within the framework of the perturbative QCD approach, we calculate the time-like $B_c{B}_c(B_c^{\ast })$ form factors $F(Q^2)$ and $A_2(Q^2)$. We include relativistic corrections and QCD corrections, either of which can give about $20\%$ correction to the leading-order contribution, but there are cancellation effects between them. We calculate the cross sections of the $e^{+}{e}^{-}\to B_c^{-}{B}_c^{+}(B_c^{\ast +})$ processes. The cross sections are enhanced at the $Z$ pole to be ${\sigma }^{PP}(Q=m_Z)\sim 1.3\times 10^{-5}\text{pb}$ and ${\sigma }^{PV}(Q=m_Z)\sim 2.5\times 10^{-5}\text{pb}$, which are still too small to be detected by proposed $e^{+}{e}^{-}$ colliders such as the Circular Electron Positron Collider.