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

Abstract

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 $\Delta {\Gamma }_{\mathrm{Z}}^{\mathrm{had}}{|}_{\mathrm{PMC}}^{\mathcal{O}({\alpha }_s^5)}\simeq \pm 0.004$ 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 ${\Gamma }_{\mathrm{Z}}^{\mathrm{had}}=1744.439_{-1.433}^{+1.390}$ MeV, which agrees with the PDG global fit of experimental measurements, $1744.4\pm 2.0$ MeV.

arXiv comment7 pages, 3 figures

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• The decomposed photon anomalous dimension in QCD and the $\{\beta \}$-expanded representations for the Adler function
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