We study prompt hadroproduction of the charged bottomonium-like states$Z_b^\pm (10610)$ and $Z_b^\pm (10650)$, and the charged charmonium-like states$Z_c^\pm (3900)$ and $Z_c^\pm (4020)$, at the Tevatron and the LHC, providedthat these states are $S$-wave hadronic molecules. Using two Monte Carlo eventgenerators, Herwig and Pythia, to simulate the production of heavy meson pairs,we derive an order-of-magnitude estimate of the production rates for these fourparticles. Our estimates yield a cross section at the nb level for the$Z_b(10610)$ and $Z_b(10650)$. The results for the $Z_c(3900)$ and $Z_c(4020)$are larger by a factor of 20-30. These cross sections are large enough to beobserved, and measurements at hadron colliders in the future will supplementthe study using electron-positron collisions, and therefore allow to explorethe mysterious nature of these exotic states.
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