X(3872) and its production at hadron colliders

Abstract

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 ${\chi }_{c1}^{\prime }$ component in our ${\chi }_{c1}^{\prime }\text{mbox}-D^0{\bar{D}}^{\ast 0}$ 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 ($10\text{mbox}GeV<p_T<70\text{mbox}GeV$), and the CDF total cross section data, and are also consistent with the value of $k=Z_{c\bar{c}}\cdot Br(X\to J/\psi {\pi }^{+}{\pi }^{-})$ 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 $p_T$ ($p_T\sim 5\text{mbox}GeV$) 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.

Comments: Version published in PRD. More explanations added for the LHCb data. More references added for recent experimental and theoretical results: the ATLAS measurement on the X(3872) pT distribution in 10-70 GeV; the LHCb measurement on the X(3872) radiative decays; the lattice calculation on X(3872); the small $x$ resummation method, etc. No changes for the calculated result and the conclusion