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

TL;DR

The paper delivers a state-of-the-art precision prediction for Higgs production via bottom-quark fusion by combining a complete N^3LO calculation in the five-flavour scheme with NLO accuracy in the four-flavour scheme using the FONLL matching. It provides analytic N^3LO partonic coefficient functions, discusses their SV/regular structure and evaluates them with extensive numerical expansions and public ancillary data. A thorough phenomenological study assesses scale, PDF, α_s, and bottom mass uncertainties, and demonstrates that the FONLL-C matched prediction increases the 5FS N^3LO result by about 2% while greatly reducing residual scale dependence. The work delivers the most precise inclusive bbH cross section to date and demonstrates the critical role of consistent high-order matching for precision Higgs physics at the LHC and future colliders.

Abstract

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

Figures (6)

• Figure 1: Regular part of the partonic coefficient function at N$^3$LO for all contributing initial state combinations. Notice, that the $b\bar{b}$, $bg$ and $qg$ initial state were rescaled uniformly to be visible in the plot.
• Figure 2: Variation of the $b\bar{b}\rightarrow H+X$ cross section with the factorisation scale $\mu_F$ (left) and renormalisation scale $\mu_R$ (right). The bands in the left (resp. right) panel indicate the range of the variation of the prediction when modifying the factorisation scale $\mu_F$ (resp. $\mu_R$) by the two factors $\frac{1}{2}$ and $2$. Predictions in green, yellow, blue and red correspond to LO, NLO, NNLO and N$^3$LO respectively.
• Figure 3: The hadronic cross section as a function of the collider energy. Green, orange, blue and red bands correspond to predictions through LO, NLO, NNLO and N$^3$LO respectively. The left figure shows predictions with $\mu_F^{\text{cent.}}=(m_H+2 m_b)/4$ and the right figure with $\mu_F^{\text{cent.}}=m_H$. The bottom panel of both pictures shows the cross section predictions normalised to the N$^3$LO prediction with $\mu_F^{\text{cent.}}=(m_H+2 m_b)/4$.
• Figure 4: Dependence of the cross section on the choice of PDF as a function of the energy normalised to the central value computed according to eq. \ref{['eq:PDFMean']}. On the left the red band shows the uncertainty computed with the PDF4LHC15 Monte-Carlo prescription and the lines correspond to predictions obtained with other PDF sets. On the right the dark and light red bands correspond to $\delta(\alpha_S)$ and $\delta(\alpha_S+\textrm{PDF})$ respectively. The green line on the right is the ratio of the prediction obtained with the central PDF set of PDF4LHC15 to the central value obtained according to eq. \ref{['eq:PDFMean']}.
• Figure 5: Impact of missing N$^3$LO PDFs and bottom quark mass schemes on the $b\bar{b} H$ cross section.