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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 $Delta Gamma_{rm Z}^{rm had}|^{{cal O}(alpha_s^5)}_{rm PMC}simeq pm 0.004$ 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 $Gamma_{rm Z}^{rm had}=1744.439^{+1.390}_{-1.433}$ MeV, which agrees with the PDG global fit of experimental measurements, $1744.4pm 2.0$ MeV.
The Higgs boson decay channel, $Htogammagamma$, is one of the most important channels for probing the properties of the Higgs boson. In the paper, we reanalyze its decay width by using the QCD corrections up to $alpha_s^4$-order level. The principle
In the paper, we analyze the properties of Gross-Llewellyn Smith (GLS) sum rule by using the $mathcal{O}(alpha_s^4)$-order QCD corrections with the help of principle of maximum conformality (PMC). By using the PMC single-scale approach, we obtain an
A key problem in making precise perturbative QCD predictions is the uncertainty in determining the renormalization scale $mu$ of the running coupling $alpha_s(mu^2).$ The purpose of the running coupling in any gauge theory is to sum all terms involvi
In the paper, we study the $Upsilon(1S)$ leptonic decay width $Gamma(Upsilon(1S)to ell^+ell^-)$ by using the principle of maximum conformality (PMC) scale-setting approach. The PMC adopts the renormalization group equation to set the correct momentum
It has been observed that conventional renormalization scheme and scale ambiguities for the pQCD predictions can be eliminated by using the principle of maximum conformality (PMC). However, being the intrinsic nature of any perturbative theory, there