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

TL;DR

This paper calculates the production cross sections of $B_c$ mesons in electron-positron collisions using perturbative QCD, including relativistic and QCD corrections, and finds the cross sections are very small even at the Z boson resonance.

Contribution

It provides the first detailed calculation of $B_c$ meson production cross sections in $e^+e^-$ colliders, incorporating relativistic and QCD corrections and analyzing their effects.

Findings

Cross sections are enhanced at the Z pole but remain too small for detection.

Relativistic and QCD corrections each contribute about 20% correction to the leading order.

Cancellation effects occur between relativistic and QCD corrections.

Abstract

Within the framework of the perturbative QCD approach, we calculate the time-like $B_cB_c(B_c^*)$ 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 $e^+e^-\to B_c^-B_c^+(B_c^{*+})$ processes. The cross sections are enhanced at the $Z$ pole to be $\sigma^{PP}(Q=m_Z) \sim 1.3\times10^{-5}\text{pb}$ and $\sigma^{PV}(Q=m_Z) \sim 2.5\times10^{-5}\text{pb}$, which are still too small to be detected by proposed $e^+e^-$ colliders such as the Circular Electron Positron Collider.