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

We calculate the Drell-Yan production cross sections and differential distributions in the transverse momentum and rapidity of the $J^{PC}=1^{--}$ exotic hadrons $ϕ(2170)$, 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 $α_s$ 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 $e^+e^-$ experiments, we present the production rates for the processes $pp(\bar{p}) \to ϕ(2170)(\to ϕ(1020) π^+π^- \to K^+K^- π^+π^-)+...$, $pp(\bar{p}) \to X(4260)(\to J/ψπ^+π^- \to μ^+μ^-π^+π^-)+...$, and $pp(\bar{p}) \to Y_b(10890)(\to (Υ(1S), Υ(2S), Υ(3S)) π^+π^- \to μ^+μ^-π^+π^-)+...$. Their measurements at the hadron colliders will provide new experimental avenues to explore the underlying dynamics of these hadrons.