Z -boson hadronic decay width up to $${{\mathcal {O}}}(\alpha _s^4)$$ O ( α s 4 ) -order QCD corrections using the single-scale approach of the principle of maximum conformality

In the paper, we study the properties of the Z-boson hadronic decay width by using the $$\mathcal {O}(\alpha _s^4)$$ -order quantum chromodynamics (QCD) corrections with the help of the principle of maximum conformality (PMC). By using the PMC single-scale approach, we obtain an accurate renormalization scale-and-scheme independent perturbative QCD (pQCD) correction for the Z-boson hadronic decay width, which is independent to any choice of renormalization scale. After applying the PMC, a more convergent pQCD series has been obtained; and the contributions from the unknown $$\mathcal {O}(\alpha _s^5)$$ -order terms are highly suppressed, e.g. conservatively, we have $$\Delta \Gamma _{\mathrm{Z}}^{\mathrm{had}}|^{{{\mathcal {O}}}(\alpha _s^5)}_{\mathrm{PMC}}\simeq \pm 0.004$$ MeV. In combination with the known electro-weak (EW) corrections, QED corrections, EW–QCD mixed corrections, and QED–QCD mixed corrections, our final prediction of the hadronic Z decay width is $$\Gamma _{\mathrm{Z}}^{\mathrm{had}}=1744.439^{+1.390}_{-1.433}$$ MeV, which agrees with the PDG global fit of experimental measurements, $$1744.4\pm 2.0$$ MeV.