The determination of the $Zb\bar{ b}$ coupling in experiments has been a long-standing challenge, as the limited precision of off $Z$-pole measurements at the LEP has resulted in two degenerate solutions remained to be resolved. In this paper, we propose a novel method to probe the $Zb\bar{ b}$ coupling by measuring the forward-backward asymmetry of the bottom quark, $A^{ b}_\text{ { FB}}$, in the $b\bar{ b}$ system of the $e^+ e^- \to b \bar{ b} \gamma$ and/or $e^+ e^- \to b \bar{ b} g$ processes at the $Z$-pole of future lepton colliders. The additional hard photon or light jet radiation can mimic the energy scanning of the $e^+e^-\to b\bar{ b}$ process, and the $A_{ \rm FB}^b$ distribution from the $\gamma$-$Z$ interference process is linearly sensitive to the $Zb\bar{ b}$ coupling. By combining the expected measurements of $R^0_b$ and $A^{ 0,b}_\text{ { FB}}$ at the $Z$-pole at the CEPC, the $A^{ b}_\text{ { FB}}$ distributions can break the degeneracy observed at the LEP, leading to a unique determination of the $Zb\bar{ b}$ coupling through $Z$-pole running alone.
Categories: hep-ph hep-ex