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We present analytic results for the partonic cross sections for theproduction of a Higgs boson via the fusion of two bottom quarks at N$^3$LO inQCD perturbation theory in the five-flavour scheme. We combine thisperturbative result with NLO accurate predictions in the four-flavour schemethat include the full bottom quark mass dependence by appropriately removingany double-counting stemming from contributions included in both predictions.We thereby obtain state-of-the-art predictions for the inclusive productionprobability of a Higgs boson via bottom quark fusion at hadron colliders.

Higgs production in bottom quark fusion: Matching the 4- and 5-flavour schemes to third order in the strong coupling