Flavorful leptoquarks at hadron colliders

$B$-physics data and flavor symmetries suggest that leptoquarks can have masses as low as few ${\cal{O}}(\mbox{TeV})$, predominantly decay to third generation quarks, and highlight $pp \to b \mu \mu$ signatures from single production and $pp \to b b \mu \mu$ from pair production. Abandoning flavor symmetries could allow for inverted quark hierarchies, and cause sizable $pp \to j \mu \mu$ and $jj \mu \mu$ cross sections, induced by second generation couplings. Final states with leptons other than muons including lepton flavor violation (LFV) ones can also arise. The corresponding couplings can also be probed by precision studies of the $B \to (X_s, K^*,\phi) ee$ distribution and LFV searches in $B$-decays. We demonstrate sensitivity in single leptoquark production for the LHC and extrapolate to the high luminosity HL-LHC. Exploration of the bulk of the phase space requires a hadron collider beyond the reach of the LHC, with $b$-identification capabilities.