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}}|^{{{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, 1744.4pm 2.0 MeV.
Highlights
Following the renormalization group invariance, the physical observable should be independent to theoretical conventions, such as the choices of the renormalization scale and scheme, which is ensured by mutual cancellation of the scale and scheme dependence among different orders for an infinite-order perturbative QCD (pQCD) prediction
Under conventional scale-setting approach, the fixed-order scale-setting ambiguity could be softened by including enough higher-order loop terms due to large cancelation among different orders; for the present considered decay width up to O(αs4)-order, the net scale uncertainty is
We have presented an accurate prediction on the Z -boson hadronic decay width by applying the principle of maximum conformality (PMC)
Summary
Following the renormalization group invariance, the physical observable should be independent to theoretical conventions, such as the choices of the renormalization scale and scheme, which is ensured by mutual cancellation of the scale and scheme dependence among different orders for an infinite-order pQCD prediction. The renormalization scale is taken as the “guessed” momentum flow of the process, as well as the one to eliminate the large logs or to minimize the contributions from highorder terms or to achieve the prediction in agreement with the experimental data. Those naive treatment directly causes the mismatching between the strong coupling constant and. The PMC accurate renormalization scale-and-scheme independent conformal series is helpful for achieving precise pQCD predictions and for a reliable prediction on the contributions of unknown higher-orders; some applications can be found in Refs.
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