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The bottom quark forward-backward asymmetry $A_{\rm{FB}}$ is a key observablein electron-positron collisions at the $Z^{0}$ peak. In this paper, we employthe Principle of Maximum Conformality (PMC) to fix the $\alpha_s$-runningbehavior of the next-to-next-to-leading order QCD corrections to $A_{\rm{FB}}$.The resulting PMC scale for this $A_{\rm{FB}}$ is an order of magnitude smallerthan the conventional choice $\mu_r=M_Z$. This scale has the physicallyreasonable behavior and reflects the virtuality of its QCD dynamics, which isindependent to the choice of renormalization scale. Our analyses show that theeffective momentum flow for the bottom quark forward-backward asymmetry shouldbe $\mu_r\ll M_Z$ other than the conventionally suggested $\mu_r=M_Z$.Moreover, the convergence of perturbative QCD series for $A_{\rm{FB}}$ isgreatly improved using the PMC. Our prediction for the bare bottom quarkforward-backward asymmetry is refined to be $A^{0,b}_{\rm FB}=0.1004\pm0.0016$,which diminishes the well known tension between the experimental determinationfor this (pseudo) observable and the respective Standard Model fit to$2.1\sigma$.

Revisiting the Bottom Quark Forward-Backward Asymmetry $A_{\rm {FB}}$ in Electron-Positron Collisions