The bottom quark forward–backward asymmetry $$A_\mathrm{{FB}}$$AFB is a key observable in electron–positron collisions at the $$Z^{0}$$Z0 peak. In this paper, we employ the Principle of Maximum Conformality (PMC) to fix the $$\alpha _s$$αs-running behavior of the next-to-next-to-leading order QCD corrections to $$A_\mathrm{{FB}}$$AFB. The resulting PMC scale for this $$A_\mathrm{{FB}}$$AFB is an order of magnitude smaller than the conventional choice $$\mu _r=M_Z$$μr=MZ. 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 $$\mu _r\ll M_Z$$μr≪MZ other than the conventionally suggested $$\mu _r=M_Z$$μr=MZ. Moreover, the convergence of perturbative QCD series for $$A_\mathrm{{FB}}$$AFB is greatly improved using the PMC. Our prediction for the bare bottom quark forward–backward asymmetry is refined to be $$A^{0,b}_\mathrm{FB}=0.1004\pm 0.0016$$AFB0,b=0.1004±0.0016, which diminishes the well known tension between the experimental determination for this (pseudo) observable and the respective Standard Model fit to $$2.1\sigma $$2.1σ.

We analyse the top-quark decay at the next-to-next-to-leading order (NNLO) in QCD by using the Principle of Maximum Conformality (PMC) which provides a systematic way to eliminate renormalization scheme and scale ambiguities in perturbative QCD predictions. The PMC renormalization scales of the coupling constant $$\alpha _s$$ α s are determined by absorbing the non-conformal $$\beta $$ β terms that govern the behavior of the running coupling by using the Renormalization Group Equation (RGE). We obtain the PMC scale $$Q_\star =15.5$$ Q ⋆ = 15.5 GeV for the top-quark decay, which is an order of magnitude smaller than the conventional choice $$\mu _r=m_t$$ μ r = m t , reflecting the small virtuality of the QCD dynamics of the top-quark decay process. Moreover, due to the non-conformal $$\beta $$ β terms disappear in the pQCD series, there is no renormalon divergence and the NLO QCD correction term is greatly increased while the NNLO QCD correction term is suppressed compared to the conventional results obtained at $$\mu _r=m_t$$ μ r = m t . By further including the next-to-leading (NLO) electroweak corrections, the finite W boson width and the finite bottom quark mass, we obtain the top-quark total decay width $$\Gamma ^{\textrm{tot}}_t=1.3112^{+0.0190}_{-0.0189}$$ Γ t tot = 1 . 3112 - 0.0189 + 0.0190 GeV, where the error is the squared averages of the top-quark mass $$\Delta m_t=\pm 0.7$$ Δ m t = ± 0.7 GeV, the coupling constant $$\Delta \alpha _s(M_Z)=\pm 0.0009$$ Δ α s ( M Z ) = ± 0.0009 and the estimation of unknown higher-order terms using the PAA method with [N/M]=[1/1]. The PMC improved predictions for the top-quark decay are complementary to the previous PMC calculations for top-quark pair production and helpful for detailed studies of properties of the top-quark.

We analyse the top-quark decay at the next-to-next-to-leading order (NNLO) in QCD by using the Principle of Maximum Conformality (PMC) which provides a systematic way to eliminate renormalization scheme and scale ambiguities in perturbative QCD predictions. The PMC renormalization scales of the coupling constant αs are determined by absorbing the non-conformal β terms that govern the behavior of the running coupling by using the Renormalization Group Equation (RGE). We obtain the PMC scale Q⋆ = 15.7 GeV for the top-quark decay, which is an order of magnitude smaller than the conventional choice µr = mt. Our analyses reveal that the effective momentum flow for the top-quark decay is not the conventionally suggested µr = mt, it should be µr ≪ mt. Moreover, due to the non-conformal β terms disappear in the pQCD series, there is no renormalon divergence and the convergence of the pQCD series for the top-quark decay is greatly improved. By further including the next-to-leading (NLO) electroweak corrections, the finite W boson width and the finite bottom quark mass, we obtain the top-quark total decay width Γ tot t |PMC = 1.3383 +0.0276GeV, where the error is the squared averages of the top-quark mass ∆mt = ±1 GeV, the coupling constant ∆αs(MZ ) = ±0.0009 and the estimation of unknown higher-order terms. The PMC improved predictions for the top-quark decay are complementary to the previous PMC calculations for top-quark pair production and helpful for detailed studies of properties of the top-quark.