Wen-Long Sang

The $X(6900)$ resonance, recently discovered in the double-$J/\psi$ channel at the LHCb experiment, has spurred intensive interest in unraveling the nature of the fully charmed tetraquark state. The aim of this paper is to present a model-independent framework to study the inclusive production of this novel species of exotic hadrons, the resonances composed of four heavy quark (commonly referred to as $T_{4c}$), at large $p_T$ in hadron colliders. Appealing to asymptotic freedom and the fact $m_c\gg {\mathrm{\Lambda }}_{\mathrm{QCD}}$, we propose that the universal gluon-to-$T_{4c}$ fragmentation function, can be decomposed into the product of the perturbatively calculable short-distance coefficients and the long-distance nonrelativistic QCD (NRQCD) matrix elements. We compute the short-distance coefficient at lowest order in ${\alpha }_s$ and velocity expansion. Adopting the phenomenological four-body wave functions at the origin to roughly estimate those not-yet-known NRQCD matrix elements, and applying the standard QCD factorization theorem, we predict the differential production rates for the $T_{4c}$ ($0^{++}$ and $2^{++}$) at large $p_T$ in $pp$ collision, which eagerly awaits the confrontation with the future LHC experiments.

Within the nonrelativistic QCD (NRQCD) factorization framework, we compute the long-awaited ${\mathcal O}(\alpha_s^2)$ correction for the exclusive double charmonium production process at $B$ factories, {\it i.e.}, $e^+e^-\to J/\psi+\eta_c$ at $\sqrt{s}=10.58$ GeV. For the first time, we confirm that NRQCD factorization does hold at next-to-next-to-leading-order (NNLO) for exclusive double charmonium production. It is found that including the NNLO QCD correction considerably reduces the renormalization scale dependence, and also implies the reasonable perturbative convergence behavior for this process. Our state-of-the-art prediction is consistent with the BaBar measurement within errors.

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.

We study the ${\eta }_c$ photoproduction in $ep$ collisions in this paper. The short-distance coefficients for $c\overline{c}({}^1{S}_0^{[1]})$, $c\overline{c}({}^1{S}_0^{[8]})$, $c\overline{c}({}^3{S}_1^{[8]})$, and $c\overline{c}({}^1{P}_1^{[8]})$ photoproductions via both direct and resolved photons are evaluated at leading order in ${\alpha }_s$ expansion, where the color-singlet contribution is achieved for the first time. The dependence of the cross sections on the renormalization and factorization scales, and the charm quark mass is studied in this paper. As an interesting result, the color-singlet cross section is dominated by the resolved photoproduction, which is almost two orders of magnitude larger than the contributions from the direct photons. The resolved photoproduction also enhances the color-octet cross sections considerably. By including the contributions from direct and resolved photons, we find the color-singlet channel dominates the integrated cross section. Making use of different sets of long-distance matrix elements, we observe some apparently distinguishable predictions, which can be utilized to scrutinize the validity of these matrix elements. Moreover, we carefully analyze different kinematic distributions of the cross sections and find that, in high $p_t$ regions, the color-singlet contribution is considerably suppressed comparing with the color-octet parts for most sets of long-distance matrix elements. This feature renders the ${\eta }_c$ photoproduction process another laboratory to test the color-octet mechanism in nonrelativistic QCD.

We study the $\eta_c$ photoproduction in $ep$ collisions in this paper. The short-distance coefficients for $c\bar{c}(^1S_0^{[1]})$, $c\bar{c}(^1S_0^{[8]})$, $c\bar{c}(^3S_1^{[8]})$, and $c\bar{c}(^1P_1^{[8]})$ photoproductions are evaluated at leading order in $\alpha_s$ expansion, where the color-singlet contribution is achieved for the first time. We have carefully analyzed different kinematic distributions of the cross sections and found that the color-singlet contribution is considerably suppressed comparing with the color-octet parts. This feature renders the $\eta_c$ photoproduction process an ideal laboratory to test the color-octet mechanism in nonrelativistic QCD. By taking different sets of long-distance matrix elements, we have observed some apparently distinguishable predictions, which can be utilized to scrutinize the validity of these matrix elements.

The associated production of Higgs boson with a muon pair, $e^+e^-\to \mu^+\mu^- H$, is one of the golden channels to pin down the properties of the Higgs boson in the prospective Higgs factories exemplified by \textsf{CEPC}. The projected accuracy of the corresponding cross section measurement is about per cent level at CEPC. In this work, we investigate both ${\mathcal O}(\alpha)$ weak correction and the ${\mathcal O}(\alpha\alpha_s)$ mixed electroweak-QCD corrections for this channel, appropriately taking into account the effect of finite $Z^0$ width. The $\mu^+\mu^-$ invariant mass spectrum is also predicted. The mixed electroweak-QCD correction turns out to reach 1.5\% of the Born-order result, and thereby must be included in future confrontation with the data. We also observe that, after including higher-order corrections, the simplified prediction for the integrated cross section employing the narrow-width-approximation may deviate from our full result by a few per cents.

The next-to-next-to-leading-order (NNLO) pQCD prediction for the $\gamma {\gamma }^{*}\to {\eta }_c$ form factor was evaluated in 2015 using nonrelativistic QCD (NRQCD). A strong discrepancy between the NRQCD prediction and the BABAR measurements was observed. Until now there has been no solution for this puzzle. In this paper, we present a NNLO analysis by applying the Principle of Maximum Conformality (PMC) to set the renormalization scale. By carefully dealing with the light-by-light diagrams at the NNLO level, the resulting high precision PMC prediction agrees with the BABAR measurements within errors, and the conventional renormalization scale uncertainty is eliminated. The PMC is consistent with all of the requirements of the renormalization group, including scheme-independence. The application of the PMC thus provides a rigorous solution for the $\gamma {\gamma }^{*}\to {\eta }_c$ form factor puzzle, emphasizing the importance of correct renormalization scale-setting. The results also support the applicability of NRQCD to hard exclusive processes involving charmonium.

The next-to-next-to-leading order (NNLO) pQCD prediction for the $\gamma\gamma^* \to \eta_c$ form factor was evaluated in 2015 using nonrelativistic QCD (NRQCD). A strong discrepancy between the NRQCD prediction and the BaBar measurements was observed. Until now there has been no solution for this puzzle. In this paper, we present a NNLO analysis by applying the Principle of Maximum Conformality (PMC) to set the renormalization scale. By carefully dealing with the light-by-light diagrams at the NNLO level, the resulting high precision PMC prediction agrees with the BaBar measurements within errors, and the conventional renormalization scale uncertainty is eliminated. The PMC is consistent with all of the requirements of the renormalization group, including scheme-independence. The application of the PMC thus provides a rigorous solution for the $\gamma\gamma^* \to \eta_c$ form factor puzzle, emphasizing the importance of correct renormalization scale-setting. The results also support the applicability of NRQCD to hard exclusive processes involving charmonium.