Exclusive Higgs boson production with bottom quarks at hadron colliders

We present the next-to-leading order QCD corrected rate for the production of a scalar Higgs boson with a pair of high [Formula Presented] bottom and antibottom quarks at the Fermilab Tevatron and at the CERN Large Hadron Collider. Results are given for both the standard model and the minimal supersymmetric standard model. The exclusive [Formula Presented] production rate is small in the standard model, but it can be greatly enhanced in the minimal supersymmetric standard model for large [Formula Presented] making [Formula Presented] an important discovery mode. We find that the next-to-leading order QCD results are much less sensitive to the renormalization and factorization scales than the lowest order results, but have a significant dependence on the choice of the renormalization scheme for the bottom quark Yukawa coupling.