Production of the Exotic $1^{--}$ Hadrons $φ(2170)$, X(4260) and $Y_b(10890)$ at the LHC and Tevatron via the Drell-Yan Mechanism

Abstract: We calculate the Drell-Yan production cross sections and differential distributions in the transverse momentum and rapidity of the $J<sup>{PC}=1<sup>{--}$ exotic hadrons $\phi(2170)$, X(4260) and $Y_b(10890)$ at the hadron colliders LHC and the Tevatron. These hadrons are tetraquark (four-quark) candidates, with a hidden $s\bar{s}$, $c\bar{c}$ and $b\bar{b}$ quark pair, respectively. In deriving the distributions and cross sections, we include the order $\alpha_s$ QCD corrections, resum the large logarithms in the small transverse momentum region in the impact-parameter formalism, and use the state of the art parton distribution functions. Taking into account the data on the production and decays of these vector hadrons from the $e<sup>+e<sup>-$ experiments, we present the production rates for the processes $$pp(\bar{p}) \to \phi(2170)(\to \phi(1020) \pi^{+\pi^-} \to K^{+K^-} \pi<sup>+\pi<sup>-)+...$$, $$pp(\bar{p}) \to X(4260)(\to J/\psi \pi^{+\pi^-} \to \mu<sup>+\mu<sup>-\pi<sup>+\pi<sup>-)+...$$, and $$pp(\bar{p}) \to Y_b(10890)(\to (\Upsilon(1S), \Upsilon(2S), \Upsilon(3S)) \pi^{+\pi^-} \to \mu<sup>+\mu<sup>-\pi<sup>+\pi<sup>-)+...$$. Their measurements at the hadron colliders will provide new experimental avenues to explore the underlying dynamics of these hadrons.