The bottom quark forward–backward asymmetry \(A_\mathrm{{FB}}\) is a key observable in electron–positron collisions at the \(Z^{0}\) peak. In this paper, we employ the Principle of Maximum Conformality (PMC) to fix the \(\alpha _s\)-running behavior of the next-to-next-to-leading order QCD corrections to \(A_\mathrm{{FB}}\). The resulting PMC scale for this \(A_\mathrm{{FB}}\) is an order of magnitude smaller than the conventional choice \(\mu _r=M_Z\). This scale has the physically reasonable behavior and reflects the virtuality of its QCD dynamics, which is independent to the choice of renormalization scale. Our analyses show that the effective momentum flow for the bottom quark forward–backward asymmetry should be \(\mu _r\ll M_Z\) other than the conventionally suggested \(\mu _r=M_Z\). Moreover, the convergence of perturbative QCD series for \(A_\mathrm{{FB}}\) is greatly improved using the PMC. Our prediction for the bare bottom quark forward–backward asymmetry is refined to be \(A^{0,b}_\mathrm{FB}=0.1004\pm 0.0016\), which diminishes the well known tension between the experimental determination for this (pseudo) observable and the respective Standard Model fit to \(2.1\sigma \).

中文翻译：

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重新讨论电子正电子碰撞中的底部夸克向前-向后不对称$$ A_ \ mathrm {{FB}} $$ AFB

底部夸克向前-向后不对称\（A_ \ mathrm {{FB}} \）是在\（Z ^ {0} \）峰的电子-正电子碰撞中可以观察到的关键。在本文中，我们采用最大保形原理（PMC）将下一个到前一个领先的QCD校正的\（\ alpha _s \）运行行为固定为\（A_ \ mathrm {{FB }} \）。此\（A_ \ mathrm {{FB}} \）的最终PMC标度比常规选择\（\ mu _r = M_Z \）小一个数量级。该量表具有物理上合理的行为，并反映了其QCD动力学的虚拟性，而与重归一化量表的选择无关。我们的分析表明，与传统建议的\（\ mu _r = M_Z \）相比，底部夸克向前和向后不对称的有效动量流应该为\（\ mu _r \ ll M_Z \）。此外，使用PMC极大地改善了\（A_ \ mathrm {{FB}} \）的摄动QCD系列的收敛性。我们对裸底夸克向前-向后不对称的预测被精炼为\（A ^ {0，b} _ \ mathrm {FB} = 0.1004 \ pm 0.0016 \），这减少了为此确定的实验确定之间的张力（伪）可观察到的，并且相应的标准模型适合\（2.1 \西格玛\） 。