Higgs-boson production via bottom-quark fusion

Higgs bosons with enhanced coupling to bottom quarks are copiously produced at hadron colliders via $b\overline{b}\ensuremath{\rightarrow}h,$ where the initial b quarks reside in the proton sea. We reexamine the calculation of the next-to-leading-order cross section for this process and argue that the appropriate factorization scale for the b distribution functions is approximately ${m}_{h}/4,$ rather than ${m}_{h},$ as had been previously assumed. This greatly improves the convergence of the perturbation series, and yields a result with mild factorization-scale dependence. We also show that the leading-order calculation of $g\stackrel{\ensuremath{\rightarrow}}{g}b\overline{b}h,$ integrated over the momenta of the final-state particles, is very sensitive to the factorization and renormalization scales. For scales of order ${m}_{h}/4$ the $g\stackrel{\ensuremath{\rightarrow}}{g}b\overline{b}h$ cross section is comparable to that of $b\overline{b}\ensuremath{\rightarrow}h,$ in contrast with the order-of-magnitude discrepancy between these two calculations for the scale ${m}_{h}.$ The result we obtain improves the prospects for Higgs-boson discovery at hadron colliders for large values of $\mathrm{tan}\ensuremath{\beta}.$