Probing the $Zb\bar{b}$ coupling at the $Z$-pole of future lepton colliders

Abstract

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, $A_{\text{FB}}^b$, 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 $A_{\mathrm{FB}}^b$ distribution from the $\gamma$-$Z$ interference process is linearly sensitive to the $Zb\bar{b}$ coupling. By combining the expected measurements of $R_b^0$ and $A_{\text{FB}}^{0,b}$ at the $Z$-pole at the CEPC, the $A_{\text{FB}}^b$ 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.

Comments: 4 pages, 6 figures