Xu-Dong Huang

Based on the operator product expansion, the perturbative and nonperturbative contributions to the polarized Bjorken sum rule (BSR) can be separated conveniently, and the nonperturbative one can be fitted via a proper comparison with the experimental data. In the paper, we first give a detailed study on the pQCD corrections to the leading-twist part of BSR. Basing on the accurate pQCD prediction of BSR, we then give a novel fit of the non-perturbative high-twist contributions by comparing with JLab data. Previous pQCD corrections to the leading-twist part derived under conventional scale-setting approach still show strong renormalization scale dependence. The principle of maximum conformality (PMC) provides a systematic and strict way to eliminate conventional renormalization scale-setting ambiguity by determining the accurate $$\alpha _s$$α s -running behavior of the process with the help of renormalization group equation. Our calculation confirms the PMC prediction satisfies the standard renormalization group invariance, e.g. its fixed-order prediction does scheme-and-scale independent. In low $$Q^2$$Q 2 -region, the effective momentum of the process is small and in order to derive a reliable prediction, we adopt four low-energy $$\alpha _s$$α s models to do the analysis, i.e. the model based on the analytic perturbative theory (APT), the Webber model (WEB), the massive pQCD model (MPT) and the model under continuum QCD theory (CON). Our predictions show that even though the high-twist terms are generally power suppressed in high $$Q^2$$Q 2 -region, they shall have sizable contributions in low and intermediate $$Q^2$$Q 2 domain. Based on the more accurate scheme-and-scale independent pQCD prediction, our newly fitted results for the high-twist corrections at $$Q^2=1\;\mathrm{GeV}^2$$Q 2 = 1 GeV 2 are, $$f_2^{p-n}|_{\mathrm{APT}}=-0.120\pm 0.013$$f 2 p - n | APT = - 0.120 ± 0.013 , $$f_2^{p-n}|_\mathrm{WEB}=-0.081\pm 0.013$$f 2 p - n | WEB = - 0.081 ± 0.013 , $$f_2^{p-n}|_{\mathrm{MPT}}=-0.128\pm 0.013$$f 2 p - n | MPT = - 0.128 ± 0.013 and $$f_2^{p-n}|_{\mathrm{CON}}=-0.139\pm 0.013$$f 2 p - n | CON = - 0.139 ± 0.013 ; $$\mu _6|_\mathrm{APT}=0.003\pm 0.000$$μ 6 | APT = 0.003 ± 0.000 , $$\mu _6|_{\mathrm{WEB}}=0.001\pm 0.000$$μ 6 | WEB = 0.001 ± 0.000 , $$\mu _6|_\mathrm{MPT}=0.003\pm 0.000$$μ 6 | MPT = 0.003 ± 0.000 and $$\mu _6|_{\mathrm{CON}}=0.002\pm 0.000$$μ 6 | CON = 0.002 ± 0.000 , respectively, where the errors are squared averages of those from the statistical and systematic errors from the measured data.

In the present paper, we first give a detailed study on the pQCD corrections to the leading-twist part of BSR. Previous pQCD corrections to the leading-twist part derived under conventional scale-setting approach up to ${\cal O}(\alpha_s^4)$-level still show strong renormalization scale dependence. The principle of maximum conformality (PMC) provides a systematic way to eliminate conventional renormalization scale-setting ambiguity by determining the accurate $\alpha_s$-running behavior of the process with the help of renormalization group equation. Our calculation confirms the PMC prediction satisfies the standard renormalization group invariance, e.g. its fixed-order prediction does scheme-and-scale independent. In low $Q^2$-region, the effective momentum of the process is small and to have a reliable prediction, we adopt four low-energy $\alpha_s$ models to do the analysis. Our predictions show that even though the high-twist terms are generally power suppressed in high $Q^2$-region, they shall have sizable contributions in low and intermediate $Q^2$ domain. By using the more accurate scheme-and-scale independent pQCD prediction, we present a novel fit of the non-perturbative high-twist contributions by comparing with the JLab data.

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. $$R={\Gamma _{\gamma \gamma }(\chi _{c2})} /{\Gamma _{\gamma \gamma }(\chi _{c0})}=0.246\pm 0.013$$R = Γ γ γ ( χ c 2 ) / Γ γ γ ( χ c 0 ) = 0.246 ± 0.013 , where the error is for $$\Delta \alpha _s(M_\tau )=\pm 0.016$$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 $$\chi _{b0, b2} \rightarrow \gamma \gamma $$χ b 0 , b 2 → γ γ , which could be tested in future Belle II experiment.

In the paper, we present QCD predictions for γ + η_c production at an electron-positron collider up to next-to-next-to-leading order (NNLO) accuracy without renormalization scale ambiguities. The NNLO total cross-section for e⁺ + e⁻ → γ + η_c using the conventional scale-setting approach has large renormalization scale ambiguities, usually estimated by choosing the renormalization scale to be the e⁺e⁻ center-of-mass collision energy $$ \sqrt{s} $$s . The Principle of Maximum Conformality (PMC) provides a systematic way to eliminate such renormalization scale ambiguities by summing the nonconformal β contributions into the QCD coupling α_s(Q²). The renormalization group equation then sets the value of α_s for the process. The PMC renormalization scale reflects the virtuality of the underlying process, and the resulting predictions satisfy all of the requirements of renormalization group invariance, including renormalization scheme invariance. After applying the PMC, we obtain a renormalization scale-and-scheme independent prediction, σ|_NNLO,PMC ≃ 41.18 fb for $$ \sqrt{s} $$s =10.6 GeV. The resulting pQCD series matches the series for conformal theory and thus has no divergent renormalon contributions. The large K factor which contributes to this process reinforces the importance of uncalculated NNNLO and higher-order terms. Using the PMC scale-and-scheme independent conformal series and the Padé approximation approach, we predict σ|_{NNNLO,PMC+Pade} ≃ 18.99 fb, which is consistent with the recent BELLE measurement $$ {\sigma}^{\mathrm{obs}}={16.58}_{-9.93}^{+10.51} $$σ obs = 16.58 − 9.93 + 10.51 fb at $$ \sqrt{s} $$s ≃ 10.6 GeV. This procedure also provides a first estimate of the NNNLO contribution.

The next-to-next-to-leading order (NNLO) pQCD correction to the inclusive decays of the heavy quarkonium $\eta_Q$ ($Q$ being $c$ or $b$) has been done in the literature within the framework of nonrelativistic QCD. One may observe that the NNLO decay width still has large conventional renormalization scale dependence due to its weaker pQCD convergence, e.g. about $(^{+4\%}_{-34\%})$ for $\eta_c$ and $(^{+0.0}_{-9\%})$ for $\eta_b$, by varying the scale within the range of $[m_Q, 4m_Q]$. The principle of maximum conformality (PMC) provides a systematic way to fix the $\alpha_s$-running behavior of the process, which satisfies the requirements of renormalization group invariance and eliminates the conventional renormalization scheme and scale ambiguities. Using the PMC single-scale method, we show that the resultant PMC conformal series is renormalization scale independent, and the precision of the $\eta_Q$ inclusive decay width can be greatly improved. Taking the relativistic correction $\mathcal{O}(\alpha_{s}v^2)$ into consideration, the ratios of the $\eta_{Q}$ decays to light hadrons or $\gamma\gamma$ are: $R^{\rm NNLO}_{\eta_c}|_{\rm{PMC}}=(3.93^{+0.26}_{-0.24})\times10^3$ and $R^{\rm NNLO}_{\eta_b}|_{\rm{PMC}}=(22.85^{+0.90}_{-0.87})\times10^3$, respectively. Here the errors are for $\Delta\alpha_s(M_Z) = \pm0.0011$. As a step forward, by applying the Pad$\acute{e}$ approximation approach (PAA) over the PMC conformal series, we obtain approximate NNNLO predictions for those two ratios, e.g. $R^{\rm NNNLO}_{\eta_c}|_{\rm{PAA+PMC}} =(5.66^{+0.65}_{-0.55})\times10^3$ and $R^{\rm NNNLO}_{\eta_b}|_{\rm{PAA+PMC}}=(26.02^{+1.24}_{-1.17})\times10^3$. The $R^{\rm NNNLO}_{\eta_c}|_{\rm{PAA+PMC}}$ ratio agrees with the latest PDG value $R_{\eta_c}^{\rm{exp}}=(5.3_{-1.4}^{+2.4})\times10^3$, indicating the necessity of a strict calculation of NNNLO terms.

The next-to-next-to-leading order (NNLO) pQCD correction to the inclusive decays of the heavy quarkonium $$\eta _Q$$ηQ (Q being c or b) has been done in the literature within the framework of nonrelativistic QCD. One may observe that the NNLO decay width still has large conventional renormalization scale dependence due to its weaker pQCD convergence, e.g. about $$\left( ^{+4\%}_{-34\%}\right) $$-34%+4% for $$\eta _c$$ηc and $$\left( ^{+0.0}_{-9\%}\right) $$-9%+0.0 for $$\eta _b$$ηb , by varying the scale within the range of $$[m_Q, 4m_Q]$$[mQ,4mQ] . The principle of maximum conformality (PMC) provides a systematic way to fix the $$\alpha _s$$αs -running behavior of the process, which satisfies the requirements of renormalization group invariance and eliminates the conventional renormalization scheme and scale ambiguities. Using the PMC single-scale method, we show that the resultant PMC conformal series is renormalization scale independent, and the precision of the $$\eta _Q$$ηQ inclusive decay width can be greatly improved. Taking the relativistic correction $${\mathcal {O}}(\alpha _{s}v^2)$$O(αsv2) into consideration, the ratios of the $$\eta _{Q}$$ηQ decays to light hadrons or $$\gamma \gamma $$γγ are: $$R^\mathrm{NNLO}_{\eta _c}|_{\mathrm{PMC}}=(3.93^{+0.26}_{-0.24})\times 10^3$$RηcNNLO|PMC=(3.93-0.24+0.26)×103 and $$R^\mathrm{NNLO}_{\eta _b}|_{\mathrm{PMC}}=(22.85^{+0.90}_{-0.87})\times 10^3$$RηbNNLO|PMC=(22.85-0.87+0.90)×103 , respectively. Here the errors are for $$\Delta \alpha _s(M_Z) = \pm 0.0011$$Δαs(MZ)=±0.0011 . As a step forward, by applying the Pad $$\acute{e}$$e´ approximation approach (PAA) over the PMC conformal series, we obtain approximate NNNLO predictions for those two ratios, e.g. $$R^{\mathrm{NNNLO}}_{\eta _c}|_{\mathrm{PAA+PMC}} =(5.66^{+0.65}_{-0.55})\times 10^3$$RηcNNNLO|PAA+PMC=(5.66-0.55+0.65)×103 and $$R^{\mathrm{NNNLO}}_{\eta _b}|_{\mathrm{PAA+PMC}}=(26.02^{+1.24}_{-1.17})\times 10^3$$RηbNNNLO|PAA+PMC=(26.02-1.17+1.24)×103 . The $$R^{\mathrm{NNNLO}}_{\eta _c}|_{\mathrm{PAA+PMC}}$$RηcNNNLO|PAA+PMC ratio agrees with the latest PDG value $$R_{\eta _c}^\mathrm{{exp}}=(5.3_{-1.4}^{+2.4})\times 10^3$$Rηcexp=(5.3-1.4+2.4)×103 , indicating the necessity of a strict calculation of NNNLO terms.

The Higgs boson decay channel, $H\to\gamma\gamma$, 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 of maximum conformality has been adopted to achieve a precise pQCD prediction without conventional renormalization scheme-and-scale ambiguities. By taking the Higgs mass as the one given by the ATLAS and CMS collaborations, i.e. $M_{H}=125.09\pm0.21\pm0.11$ GeV, we obtain $\Gamma(H\to \gamma\gamma)|_{\rm LHC}=9.364^{+0.076}_{-0.075}$ KeV.