One of the most challenging open problems in heavy quarkonium physics is the double charm production in e + e − annihilation at B factories. The measured cross section of e + e − → J/ψ + ηc is much larger than leading order (LO) theoretical predictions. With the nonrelativistic QCD factorization formalism, we calculate the next-to-leading order (NLO) QCD correction to this process. Taking all one-loop self-energy, triangle, box, and pentagon diagrams into account, and factoring the Coulomb-singular term into the cc bound state wave function, we get an ultraviolet and infrared finite correction to the cross section of e + e − → J/ψ + ηc at √ s = 10.6 GeV. We find that the NLO QCD correction can substantially enhance the cross section with a K factor (the ratio of NLO to LO ) of about 1.8-2.1; hence it greatly reduces the large discrepancy between theory and experiment.With mc = 1.4GeV and µ = 2mc, the NLO cross section is estimated to be 18.9 fb, which reaches to the lower bound of experiment.

With nonrelativistic QCD factorization, we present a full next-to-leading order computation of the polarization observable for J/ψ production at hadron colliders including all important Fock states, i.e., 3S(1)([1,8]), 1S(0)([8]), and 3P(J)([8]). We find the 3P(J)([8]) channel contributes a positive longitudinal component and a negative transverse component, so the J/ψ polarization puzzle may be understood as the transverse components canceling between the 3S(1)([8]) and 3P(J)([8]) channels, which results in mainly the unpolarized (even slightly longitudinally polarized) J/ψ. This may give a possible solution to the long-standing J/ψ polarization puzzle. Predictions for J/ψ polarization at the LHC are also presented.

In heavy quarkonium production, the measured ratio R_{cc[over ]}=sigma[J/psi+cc[over ]+X]/sigma[J/psi+X] at B factories is much larger than existing theoretical predictions. To clarify this discrepancy, in nonrelativistic QCD we find the next-to-leading-order (NLO) QCD correction to e;{+}e;{-}-->J/psi+gg can enhance the cross section by about 20%. Together with the calculated NLO result for e;{+}e;{-}-->J/psi+cc[over ], we show that the NLO corrections can significantly improve the fit to the ratio R_{cc[over ]}. The effects of leading logarithm resummation near the end point on the J/psi momentum distribution and total cross section are also considered. Comparison of the calculated cross section for e;{+}e;{-}-->J/psi+gg with the observed cross section for e;{+}e;{-}-->J/psi+non-(cc[over ]) is expected to provide unique information on the issue of color-octet contributions.

The inclusive J/psi production in e;{+}e;{-}-->J/psicc at B factories is one of the most challenging open problems in heavy quarkonium physics. The observed cross section of this double-charm production process is larger than existing leading order (LO) QCD predictions by a factor of 5. In the nonrelativistic QCD (NRQCD) factorization formalism, we calculate the next-to-leading order (NLO) QCD virtual and real corrections to this process, and find that these corrections can substantially enhance the cross section with a K factor of about 1.8. We further take into account the feeddown contributions from higher charmonium states [mainly the psi(2S) as well as chi_{cJ}] and the two-photon contributions, and find that the discrepancy between theory and experiment can be largely removed.

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