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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 $\chi_{c1}'\mbox{-}D^0\bar{D}^{*0}$ mixing model for $X(3872)$.
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