Optimized O(α_{s}

The failure of observing the e^{+}e^{-}→J/ψJ/ψ events at B factories to date is often attributed to the significant negative order-α_{s} correction. In this work we compute the O(α_{s}^{2}) correction to this process for the first time. The magnitude of the next-to-next-to-leading order (NNLO) perturbative correction is substantially negative so that the standard nonrelativistic QCD prediction would suffer from an unphysical, negative cross section. This dilemma may be traced in the fact that the bulk contribution of the fixed-order radiative corrections stems from the perturbative corrections to the J/ψ decay constant. We thus implement an improved nonrelativistic QCD factorization framework, by decomposing the amplitude into the photon-fragmentation piece and the nonfragmentation piece. With the measured J/ψ decay constant as input, which amounts to resumming a specific class of radiative and relativistic corrections to all orders, the fragmentation-induced production rate can be predicted accurately and serves a benchmark prediction. The nonfragmentation type of the amplitude is then computed through NNLO in α_{s} and at lowest order in velocity. Both the O(α_{s}) and O(α_{s}^{2}) corrections in the interference term become positive and exhibit a decent convergence behavior. Our finest prediction is σ(e^{+}e^{-}→J/ψJ/ψ)=2.13_{-0.06}^{+0.30} fb at sqrt[s]=10.58 GeV. With the projected integrated luminosity of 50 ab^{-1}, the prospect to observe this exclusive process at Belle 2 experiment appears to be bright.

Higher-Order QCD Corrections to ϒ Decay into Double Charmonia.

In this Letter, we study the exclusive decay of ϒ into J/ψ in association with η_{c} (χ_{c0,1,2}). The decay widths for different helicity configurations are evaluated up to QCD next-to-leading order within the nonrelativistic QCD framework. We find that the QCD corrections notably mitigate the renormalization scale dependence of the decay widths for all the processes. The branching fraction of ϒ→J/ψ+χ_{c1} is obtained as 3.73_{-2.06-1.19}^{+5.10+0.10}×10^{-6}, which agrees well with the Belle measurement, i.e., Br(ϒ→J/ψ+χ_{c1})=(3.90±1.21±0.23)×10^{-6}. For the other processes, our results of the branching fractions are compatible with the upper limits given by the Belle experiments, except for ϒ(2S)→J/ψ+χ_{c1}, where some tension exists between theory and experiment. Having the polarized decay widths, we study the J/ψ polarization, which turns out to be independent of any nonperturbative parameters. Further, according to our calculation, it is promising to measure all the processes at Super B factory thanks to the high luminosity.

Next-to-Next-to-Leading-Order QCD Corrections to the Hadronic Width of Pseudoscalar Quarkonium.

We compute the next-to-next-to-leading-order QCD corrections to the hadronic decay rates of the pseudoscalar quarkonia, at the lowest order in velocity expansion. The validity of nonrelativistic QCD (NRQCD) factorization for inclusive quarkonium decay process, for the first time, is verified to relative order α_{s}^{2}. As a by-product, the renormalization group equation of the leading NRQCD four-fermion operator O_{1}(^{1}S_{0}) is also deduced to this perturbative order. By incorporating this new piece of correction together with available relativistic corrections, we find that there exists severe tension between the state-of-the-art NRQCD predictions and the measured η_{c} hadronic width and, in particular, the branching fraction of η_{c}→γγ. NRQCD appears to be capable of accounting for η_{b} hadronic decay to a satisfactory degree, and our most refined prediction is Br(η_{b}→γγ)=(4.8±0.7)×10^{-5}.

Can Nonrelativistic QCD Explain the γγ

Unlike the bewildering situation in the γγ^{*}→π form factor, a widespread view is that perturbative QCD can decently account for the recent BABAR measurement of the γγ^{*}→η_{c} transition form factor. The next-to-next-to-leading-order perturbative correction to the γγ^{*}→η_{c,b} form factor, is investigated in the nonrelativistic QCD (NRQCD) factorization framework for the first time. As a byproduct, we obtain, by far, the most precise order-α_{s}^{2} NRQCD matching coefficient for the η_{c,b}→γγ process. After including the substantial negative order-α_{s}^{2} correction, the good agreement between NRQCD prediction and the measured γγ^{*}→η_{c} form factor is completely ruined over a wide range of momentum transfer squared. This eminent discrepancy casts some doubts on the applicability of the NRQCD approach to hard exclusive reactions involving charmonium.

Impact of η(c) hadroproduction data on charmonium production and polarization within the nonrelativistic QCD framework.

With the recent LHCb data on η_{c} production and based on heavy quark spin symmetry, we obtain the long-distance matrix elements for both η_{c} and J/ψ productions, among which, the color-singlet one for η_{c} is obtained directly by the fit of experiment for the first time. Using our long-distance matrix elements, we can provide good description of the η_{c} and J/ψ hadroproduction measurements. Our predictions on J/ψ polarization are in good agreement with the LHCb data, explain most of the CMS data, and pass through the two sets of CDF measurements in the medium p_{t} region. Considering all the possible uncertainties carefully, we obtained quite narrow bands of the J/ψ polarization curves.