AbstractIn the paper, we study the properties of the Z-boson hadronic decay width by using the $$\mathcal {O}(\alpha _s^4)$$
O
(
α
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 $$\mathcal {O}(\alpha _s^5)$$
O
(
α
s
5
)
-order terms are highly suppressed, e.g. conservatively, we have $$\Delta \Gamma _{\mathrm{Z}}^{\mathrm{had}}|^{{{\mathcal {O}}}(\alpha _s^5)}_{\mathrm{PMC}}\simeq \pm 0.004$$
Δ
Γ
Z
had
|
PMC
O
(
α
s
5
)
≃
±
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 $$\Gamma _{\mathrm{Z}}^{\mathrm{had}}=1744.439^{+1.390}_{-1.433}$$
Γ
Z
had
=
1744
.
439
-
1.433
+
1.390
MeV, which agrees with the PDG global fit of experimental measurements, $$1744.4\pm 2.0$$
1744.4
±
2.0
MeV.
Setting the renormalization scale in perturbative QCD: Comparisons of the principle of maximum conformality with the sequential extended Brodsky-Lepage-Mackenzie approach