We present the inclusive cross section at next-to-next-to-next-to-leading order (${\mathrm{N}}^3\mathrm{LO}$) in perturbative QCD for the production of a Higgs boson via bottom-quark fusion. We employ the five-flavor scheme, treating the bottom quark as a massless parton while retaining a nonvanishing Yukawa coupling to the Higgs boson. We find that the dependence of the hadronic cross section on the renormalization and factorization scales is substantially reduced. For judicious choices of the scales the perturbative expansion of the cross section shows a convergent behavior. We present results for the ${\mathrm{N}}^3\mathrm{LO}$ cross section at various collider energies. In comparison to the cross section obtained from the Santander matching of the four- and five-flavor schemes, we predict a slightly higher cross section, though the two predictions are consistent within theoretical uncertainties.

• Received 8 May 2019
• Revised 8 July 2020
• Accepted 10 July 2020

DOI:https://doi.org/10.1103/PhysRevLett.125.051804

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Published by the American Physical Society