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In the paper, we calculate the fragmentation functions for g → Bc and g → B c ∗ . The ultraviolet divergences in the calculation are removed through the renormalization of the operator definition of the fragmentation functions under the modified minimal subtrac- tion scheme. We then obtain the fragmentation functions D g → B c (z, μF) and D g → B c ∗ (z, μF), which are presented as figures and fitting functions. The obtained fragmentation functions are complementary to the previous work on the next-to-leading order fragmentation functions for b ¯ → Bc( B c ∗ ) and c → Bc( B c ∗ ). [ABSTRACT FROM AUTHOR]

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 calculate the fragmentation functions for c → ηc and b → ηb up to next-to-leading-order (NLO) QCD accuracy. The ultraviolet divergences in the real corrections are removed through operator renormalization under the modified min- imal subtraction scheme. We then obtain the fragmentation functions D c → η c (z, μF) and D b → η b (z, μF) up to NLO QCD accuracy, which are presented as figures and fitting functions. The numerical results show that the NLO corrections are significant. The sensitives of the fragmentation functions to the renormalization scale and the factorization scale are analyzed explicitly. [ABSTRACT FROM AUTHOR]

The photoproduction of P-wave doubly charmed baryon (Ξcc) is investigated in the context of future high-energy and high-luminosity e+e− colliders. The direct photoproduction via the sub-process γ + γ → Ξ cc + c ¯ + c ¯ and the resolved channel γ + g → Ξ cc + c ¯ + c ¯ are considered. Within the framework of non-relativistic QCD, the calculation encompasses four P-wave (cc)-diquark configurations: cc 3 ¯ [1P1], (cc)6[3P0], (cc)6[3P1] and (cc)6[3P2]. The two S-wave states, cc 3 ¯ [3S1] and (cc)6[1S0], are also included for comparison. The cross sections, as well as the differential distributions involving transverse momentum, rapidity, and angular variables, have been computed. Numerical results reveal that the resolved photoproduction process plays a significant role and can provide dominant contributions. The photoproduction rate of the P-wave Ξcc is approximately one order of magnitude lower than that of the S-wave. [ABSTRACT FROM AUTHOR]

Based on the non-relativistic quantum chromodynamics factorization framework, we study the inclusive J/ψ photoproduction at the future high energy e+e− collider, International Linear Collider(ILC), where the initial photons come from the back-scattering of laser and electron (positron). The intermediate states, c c ¯ (3 S 1 1 ,1 S 0 8 ,3 S 1 8 , 3 P 0 , 1 , 2 8 ), and resolved photoproduction processes are considered. Numerical results show that the cross section of J/ψ photoproduction at the ILC could be very large, and the single resolved pro- cess via c c ¯ (3 S 0 8 ) intermediate state dominates primarily the production. We also present various kinematic distributions for J/ψ photoproduction. Combining the high luminosity of the collision, J/ψ photoproduction at the ILC shall provide a good platform to test the NRQCD factorization. [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]

The principle of maximum conformality (PMC) provides a convenient way for setting the optimal renormalization scales for high-energy processes, which can eliminate the conventional renormalization scale error via an order-by-order manner. At present, we make a detailed PMC analysis on the Higgs decay H → γγ up to three-loop QCD corrections. As an important point of deriving reliable PMC estimation, it is noted that only those {βi}-terms that rightly determine the running behavior of coupling constant via the renormalization group equation should be absorbed into the coupling constant, and those {βi}-terms that pertain to the quark mass renormalization and etc should be kept as a separate. To avoid confusion of separating and absorbing different types of {βi}-terms into the coupling constant, we first transform the decay width in terms of top-quark mass into that of on-shell mass and then apply the PMC scale setting. After applying PMC scale setting, the final estimation is conformal and is scheme-independent and scale-independent. Up to three-loop QCD corrections, we obtain a PMC scale GeV ∼2MH, which is optimal and highly independent of any choice of initial scale. Thus, we obtain a more accurate scale-independent prediction by taking the Higgs mass as the same as that of ATLAS and CMS measurements, i.e., and keV, where the error is caused by the measured Higgs mass, i.e. the Higgs mass MH is taken as GeV for ATLAS and 125.7 ± 0.3 ± 0.3 GeV for CMS, respectively. [ABSTRACT FROM AUTHOR]

In the paper, we analyze the properties of Gross-Llewellyn Smith (GLS) sum rule by using the O (α s 4) -order QCD corrections with the help of principle of maximum conformality (PMC). By using the PMC single-scale approach, we obtain an accurate renormalization scale-and-scheme independent fixed-order pQCD contribution for GLS sum rule, e.g. S GLS (Q 0 2 = 3 GeV 2) | PMC = 2.559 − 0.024 + 0.023 , where the error is squared average of those from Δ α s (M Z) , the predicted O (α s 5) -order terms predicted by using the Padé approximation approach. After applying the PMC, a more convergent pQCD series has been obtained, and the contributions from the unknown higher-order terms are highly suppressed. In combination with the nonperturbative high-twist contribution, our final prediction of GLS sum rule agrees well with the experimental data given by the CCFR collaboration. [ABSTRACT FROM AUTHOR]