We present a complete evaluation for the prompt η_{c} production at the LHC at next-to-leading order in α_{s} in nonrelativistic QCD. By assuming heavy-quark spin symmetry, the recently observed η_{c} production data by LHCb results in a very strong constraint on the upper bound of the color-octet long-distance matrix element ⟨O^{J/ψ}(^{1}S_{0}^{[8]})⟩ of J/ψ. We find this upper bound is consistent with our previous study of the J/ψ yield and polarization and can give good descriptions for the measurements, but the upper bound is inconsistent with some other theoretical estimates. This may provide important information for understanding the nonrelativistic QCD factorization formalism.

We reexamine the rescattering mechanism for the X(3872), as a candidate for the 2P charmonium state c1 2P, decaying to J= ! through exchanging D mesons between intermediate states D D and D D . We evaluate the dispersive part, as well as the absorptive one, of the rescattering amplitude and find that the contribution from the dispersive part is dominant even when X(3872) lies above the threshold of the neutral channel th n m D 0 m D 0 . We predict R =! ' 1 for the m X region scanned by experiments. Meanwhile, we also estimate the rate of X ! D 0 D 0 0 . Our results favor a charmonium interpretation of X(3872) when it lies slightly below the threshold of D 0 D 0 . Furthermore, we evaluated the width of X ! J= with the help of a phenomenological effective coupling constant g X , and find the total width of X(3872) to be in the range of 1-2 MeV.

Using the same quenched limit as input, we compare the charmonium spectra predicted by two different models, i.e., the coupled-channel model and the screened potential model in the mass region below 4 GeV, in which the contributions from decay channels involving P-wave (as well as even higher excited) D mesons can be neglected. We find that the two models have similar global features in describing the charmonium spectrum since they approximately embody the same effect of the vacuum polarization of dynamical light quark pairs. Adopting these models will be helpful to clarify the nature of the newly discovered charmonium or charmoniumlike states; and the coupled-channel model is more adept in investigating the influences of open-charm thresholds on the charmonium spectrum. In particular, we show the S-wave decay coupling effect on lowering the c1 ð2PÞ mass toward the D " D Ã threshold, in support of the assignment of the Xð3872Þ as a c1 ð2PÞ-dominated charmonium state.

Υ(nS) and χ b (nP ) (n=1,2,3) production at the LHC is studied at next-to-leading order in αs in nonrelativistic QCD. Feeddown contributions from higher χ b and Υ states are all considered for lower Υ cross sections and polarizations. The long distance matrix elements (LDMEs) are extracted from the yield data, and then used to make predictions for the Υ(nS) polarizations, which are found to be consistent with the measured polarization data within errors. In particular, the Υ(3S) polarization puzzle can be understood by a large feeddown contribution from χ b (3P ) states. Our results may provide a good description for both cross sections and polarizations of prompt Υ(nS) and χ b (nP ) production at the LHC.

We give predictions of J/ψ and ψ(2S) yields and polarizations in prompt production at hadron colliders based on non-relativistic QCD factorization formula. We calculate short-distance coefficients of all important color-octet intermediate channels as well as color-singlet channels up to O(α 4 S ), i.e. next-to-leading order in α S . For prompt J/ψ production, we also take into account feeddown contributions from χ cJ (J=0,1,2) and ψ(2S) decays. Color-singlet long-distance matrix elements (LDMEs) are estimated by using potential model, and color-octet LDMEs are extracted by fitting the Tevatron yield data only. The predictions are satisfactory for both yields and polarizations of prompt J/ψ and prompt ψ(2S) production at the Tevatron and the LHC. In particular, we find our predictions for polarizations of prompt J/ψ production have only a little difference from our previous predictions for polarizations of direct J/ψ production.