Higgs production in bottom-quark fusion to third order in the strong coupling

TL;DR

This work delivers the first complete $N^3LO$ QCD prediction for Higgs production through bottom-quark fusion in the five-flavor scheme, treating the bottom as massless with a Yukawa coupling to the Higgs. The authors employ advanced techniques (diagram generation, master integrals via differential equations, and three-loop splitting functions) and perform extensive cross-checks, including UV/IR cancellation and factorisation universality. They demonstrate markedly reduced renormalisation and factorisation scale uncertainties and good perturbative convergence, with a central choice of $\mu_f\approx m_H/4$. A comparison with Santander-matching shows agreement within uncertainties, reinforcing the reliability of the $5$FS $N^3LO$ prediction for this process and its role in probing the bottom Yukawa coupling.

Abstract

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

Figures (2)

• Figure 1: Variation of the hadronic cross section with the hadronic centre-of-mass energy. The upper figure shows nominal values, in the lower figure all predictions are normalised to the central value of the N$^3$LO prediction. LO, NLO, NNLO and N$^3$LO corrections are shown in green, yellow, blue and red respectively. The bands correspond to scale variation uncertainties as described in the text.
• Figure 2: Comparison of $\sigma_{1,2}^{\textrm{S-M}}$ (blue) and the cross section computed in the 5FS at N$^3$LO (red) and NNLO (green). The bands represent a linear sum of PDF, scale-variation and bottom quark mass uncertainties. For the 5 flavour scheme also an uncertainty for the miss-match of the PDF order and the order of the partonic cross section is included.