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We present the results for the complete next-to-leading order electroweak corrections to $pp \to HH$ at the Large Hadron Collider, focusing on the dominant gluon-gluon fusion process. While the corrections at the total cross-section level are approximately $-4\%$, those near the energy of $HH$ production threshold exceed $+15\%$, and corrections at the high-energy region are around $-10\%$, leading to a shape distortion for the differential distributions. Our findings substantially diminish the theoretical uncertainties associated with this pivotal process, providing valuable input for understanding the shape of the Higgs boson potential upon comparison with experimental measurements., Comment: 7 pages, 4 figures, version published in PRL

In this paper, we study the next-to-next-to-leading-order (NNLO) QCD corrections for the process $e^+e^- \to J/\psi+J/\psi$ at the $B$ factories. By including the NNLO corrections, the cross section turns negative due to the poor convergence of perturbative expansion. Consequently, to obtain a reasonable estimation for the cross section, the square of the amplitude up to NNLO is used. In addition, the contributions from the bottom quark and the light-by-light part, which are usually neglected, are also included. The final cross section is obtained as $1.76^{+2.42}_{-1.66} ~{\rm fb}$ at a center-of-mass energy of $\sqrt{s}=10.58$ GeV. Our result for total cross section and differential cross section could be compared with precise experimental measurement in future at the $B$ factories., Comment: 15 pages, 3 figures, matches published version

In the paper, we present QCD predictions for $\eta_{c} + \gamma$ production at an electron-position collider up to next-to-next-to-leading order (NNLO) accuracy without renormalization scale ambiguities. The NNLO total cross-section for $e^{+}+e^{-}\to\gamma+\eta_{c}$ 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 $\sqrt{s}$. The Principle of Maximum Conformality (PMC) provides a systematic way to eliminate such renormalization scale ambiguities by summing the nonconformal $\beta$ contributions into the QCD coupling $\alpha_s(Q^2)$. The renormalization group equation then sets the value of $\alpha_s$ 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 scale-and-scheme independent prediction, $\sigma|_{\rm NNLO, PMC}\simeq 41.18$ fb for $\sqrt{s}$=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 $\rm Pad\acute{e}$ approximation approach, we predict $\sigma|_{\rm NNNLO, PMC+Pade} \simeq 21.36$ fb, which is consistent with the recent BELLE measurement $\sigma^{\rm obs}$=$16.58^{+10.51}_{-9.93}$ fb at $\sqrt{s} \simeq 10.6$ GeV. This procedure also provides a first estimate of the NNNLO contribution., Comment: 8 pages, 5 figures. Discussions improved and references updated. Revised version to be published in JHEP

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., Comment: 10 pages, 4 figures