Prospects for supersymmetric charged Higgs boson discovery at the Fermilab Tevatron and the CERN Large Hadron Collider

We investigate the prospects for heavy charged Higgs boson production through the mechanisms $p\overline{p}(\mathrm{pp})\ensuremath{\rightarrow}{H}^{\ifmmode\pm\else\textpm\fi{}}tb+X$ at the upgraded Fermilab Tevatron and at the upcoming LHC at CERN, respectively. We focus on the minimal supersymmetric standard model case and include the leading quantum corrections at high $\mathrm{tan}\ensuremath{\beta}.$ A detailed study is performed for all important production modes and basic background processes for the $t\overline{t}b\overline{b}$ signature. At the upgraded Tevatron a charged Higgs signal is potentially viable in the $220--250 \mathrm{GeV}$ range or excluded at 95% C.L. up to $300 \mathrm{GeV}.$ At the LHC, a ${H}^{\ifmmode\pm\else\textpm\fi{}}$ of mass up to $800 \mathrm{GeV}$ can be discovered at $5\ensuremath{\sigma}$ or else be excluded up to a mass of $\ensuremath{\sim}1.5 \mathrm{TeV}.$ The presence of SUSY quantum effects may highly influence the discovery potential in both machines and can typically shift these limits by $200 \mathrm{GeV}$ at the LHC.