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In this paper, we make a detailed study on the production of the B c , B c ∗ , B c (2 1 S 0) , and B c ∗ (2 3 S 1) mesons via the three planned running modes (Z, W, and H) at the future Circular Electron–Positron Collider (CEPC). The fragmentation-function and full nonrelativistic QCD approaches are adopted to calculate the production cross sections. Considering the excited states shall decay to the ground B c state (e.g. 1 1 S 0 -state) with almost 100 % probability, our numerical results show that up to next-to-leading order QCD corrections, there are about 1.4 × 10 8 B c events to be accumulated via the Z mode ( s = m Z ) of the CEPC, but only about 1.6 × 10 4 and 1.1 × 10 4 B c events to be accumulated via the W ( s = 160 GeV ) and H ( s = 240 GeV ) modes, respectively. Since the Z mode is the best mode among the three planned modes of the CEPC for studying the production of the B c , B c ∗ , B c (2 1 S 0) , and B c ∗ (2 3 S 1) mesons and the differential distributions of these mesons may be measured precisely at this mode, we further present the differential cross sections d σ / (d z d cos θ) and d σ / d z via the Z mode of the CEPC. [ABSTRACT FROM AUTHOR]

In the paper, we study the properties of the Z-boson hadronic decay width by using the 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 O (α s 5) -order terms are highly suppressed, e.g. conservatively, we have 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 Γ Z had = 1744. 439 - 1.433 + 1.390 MeV, which agrees with the PDG global fit of experimental measurements, 1744.4 ± 2.0 MeV. [ABSTRACT FROM AUTHOR]

The principle of maximum conformality (PMC) has been suggested to eliminate the renormalization scheme and renormalization scale uncertainties, which are unavoidable for the conventional scale setting and are usually important errors for theoretical estimations. In this paper, by applying PMC scale setting, we analyze two important inclusive Standard Model Higgs decay channels, $$H\rightarrow b\bar{b}$$ and $$H\rightarrow gg$$ , up to four-loop and three-loop levels, respectively. After PMC scale setting, it is found that the conventional scale uncertainty for these two channels can be eliminated to a high degree. There is small residual initial scale dependence for the Higgs decay widths due to unknown higher-order $$\{\beta _i\}$$ terms. Up to four-loop level, we obtain $$\Gamma (H\rightarrow b\bar{b}) = 2.389\pm 0.073 \pm 0.041$$ MeV and up to three-loop level, we obtain $$\Gamma (H\rightarrow gg) = 0.373\pm 0.030$$ MeV, where the first error is caused by varying $$M_H=126\pm 4$$ GeV and the second error for $$H\rightarrow b\bar{b}$$ is caused by varying the $$\overline{\mathrm{MS}}$$ -running mass $$m_b(m_b)=4.18\pm 0.03$$ GeV. Taking $$H\rightarrow b\bar{b}$$ as an example, we present a comparison of three BLM-based scale-setting approaches, e.g. the PMC-I approach based on the PMC-BLM correspondence, the $$R_\delta $$ -scheme and the seBLM approach, all of which are designed to provide effective ways to identify non-conformal $$\{\beta _i\}$$ -series at each perturbative order. At four-loop level, all those approaches lead to good pQCD convergence, they have almost the same pQCD series, and their predictions are almost independent on the initial renormalization scale. In this sense, those approaches are equivalent to each other. [ABSTRACT FROM AUTHOR]

In this paper, we present a new analysis on the P-wave charmonium annihilation into two photons up to next-to-next-to-leading order (NNLO) QCD corrections by using the principle of maximum conformality (PMC). The conventional perturbative QCD prediction shows strong scale dependence and deviates largely from the BESIII measurements. After applying the PMC, we obtain a more precise scale-invariant pQCD prediction, which also agrees with the BESIII measurements within errors, i.e. R = Γ γ γ (χ c 2) / Γ γ γ (χ c 0) = 0.246 ± 0.013 , where the error is for Δ α s (M τ) = ± 0.016 . By further considering the color-octet contributions, even the central value can be in agreement with the data. This shows the importance of a correct scale-setting approach. We also give a prediction for the ratio involving χ b 0 , b 2 → γ γ , which could be tested in future Belle II experiment. [ABSTRACT FROM AUTHOR]