Higgs boson production in bottom quark fusion at next-to-next-to-leading order

The total cross section for Higgs boson production in bottom-quark annihilation is evaluated at next-to-next-to-leading order in QCD. This is the first time that all terms at order ${\alpha }_s^2$ are taken into account. We find a greatly reduced scale dependence with respect to lower order results, for both the factorization and the renormalization scales. The behavior of the result is consistent with earlier determinations of the appropriate factorization scale for this process of ${\mu }_F\approx M_H/4,$ and supports the validity of the bottom parton density approach for computing the total inclusive rate. We present precise predictions for the cross section at the Fermilab Tevatron and the CERN Large Hadron Collider.