Impact of $J/psi$ pair production at the LHC and predictions in nonrelativistic QCD

For $J/psi$ pair production at hadron colliders, we present the full next-to-leading order (NLO) calculations with the color-singlet channel in nonrelativistic QCD. We find that the NLO result can reasonably well describe the LHCb measured cross section, but exhibits very different behaviors from the CMS data in the transverse momentum distribution and mass distribution of $J/psi$ pair. Moreover, by adding contributions of gluon fragmentation and quark fragmentation, which occur at even higher order in $alpha_s$, it is still unable to reduce the big differences. In particular, the observed flat distribution in the large invariant mass region is hard to explain. New processes or mechanisms are needed to understand the CMS data for $J/psi$ pair production.

X(3872) and its production at hadron colliders

We evaluate the production cross sections of $X(3872)$ at the LHC and Tevatron at NLO in $alpha_s$ in NRQCD by assuming that the short-distance production proceeds dominantly through its $chi_{c1}$ component in our $chi_{c1}mbox{-}D^0bar{D}^{*0}$ mixing model for $X(3872)$. The outcomes of the fits to the CMS $p_T$ distribution can well account for the recent ATLAS data in a much larger range of transverse momenta ($10~mbox{GeV}<p_T<70~mbox{GeV}$), and the CDF total cross section data, and are also consistent with the value of $k=Z_{cbar c}cdot Br(Xto J/psipi^+pi^-)$ constrained by the $B$-meson decay data. %It can also well describe the behavior of the CDF $psi(2S)$ data, which show a strong %resemblance to that of the X(3872). For LHCb the predicted X(3872) total cross section is larger than the data by a factor of 2, which is due to the problem of the fixed-order NRQCD calculation that may not be applicable for the region with small $p_T$ ($p_Tsim 5 ~mbox{GeV}$) and large forward rapidity $(2.5<y<4.5)$. In comparison, the prediction of molecule production mechanism for $X(3872)$ is inconsistent with both $p_T$ distributions and total cross sections of CMS and ATLAS, and the total cross section of CDF.

Spin correlations in polarizations of P-wave charmonia $chi_{cJ}$ and impact on $J/psi$ polarization

Based on a general form of the effective vertex functions for the decays of P-wave charmonia $chicj$, angular distribution formulas for the subsequent decays $chicjrightarrow jpsi gamma$ and $jpsi to mu^+mu^-$ are derived. The formulas are the same as those obtained in a different approach in the literature. Our formulas are expressed in a more general form, including parity violation effects and the full angular dependence of $jpsi$ and muon in the cascade decay $chicjtojpsigammatomu^+mu^-gamma$. The $chicj$ polarization observables are expressed in terms of rational functions of the spin density matrix elements of $chicj$ production. Generalized rotation-invariant relations for arbitrary integer-spin particles are also derived and their expressions in terms of observable angular distribution parameters are given in the $chi_{c1}$ and $chi_{c2}$. To complement our previous direct-$jpsi$ polarization result, we also discuss the impact on the observable prompt-$jpsi$ polarization. As an illustrative application of our angular distribution formulas, we present the angular distributions in terms of the tree-level spin density matrix elements of $chi_{c1}$ and $chi_{c2}$ production in several different frames at the Large Hadron Collider. Moreover, a reweighting method is also proposed to determine the entire set of the production spin density matrix elements of the $chi_{c2}$, some of which disappear or are suppressed for vanishing higher-order multipole effects making the complete extraction difficult experimentally.

QCD and Relativistic $O(alpha_{s}v^2)$ Corrections to Hadronic Decays of Spin-Singlet Heavy Quarkonia $h_c, h_b$ and $eta_b$

We calculate the annihilation decay widths of spin-singlet heavy quarkonia $h_c, h_b$ and $eta_b$} into light hadrons with both QCD and relativistic corrections at order $O(alpha_{s}v^{2})$ in nonrelativistic QCD. With appropriate estimates for the long-distance matrix elements by using the potential model and operator evolution method, we find that our predictions of these decay widths are consistent with recent experimental measurements. We also find that the $O(alpha_{s}v^{2})$ corrections are small for $bbar{b}$ states but substantial for $cbar{c}$ states. In particular, the negative contribution of $O(alpha_{s}v^{2})$ correction to the $h_{c}$ decay can lower the decay width, as compared with previous predictions without the $O(alpha_{s}v^{2})$ correction, and thus result in a good agreement with the recent BESIII measurement.