Matched predictions for the $b\bar{b}H$ cross section at the 13 TeV LHC

TL;DR

This work delivers a state-of-the-art matched prediction for $b\bar{b}H$ production at 13 TeV by coherently combining fixed-order 4FS calculations with all-order 5FS resummation, while explicitly separating perturbative and parametric uncertainties, including the $Y_bY_t$ interference. The methodology redefines how heavy-quark initiated processes are treated by distinguishing the bottom-quark matching scale $\mu_b$ from the bottom mass $m_b$, and provides a detailed uncertainty budget. The authors report a central SM cross section of $\sigma(b\bar{b}H) \approx 0.52$ pb at $m_H=125$ GeV with quantified perturbative and parametric uncertainties, and demonstrate the framework across $m_H$ in $[50,750]$ GeV. The approach is general and applicable to other heavy-quark initiated LHC processes, with public code to reproduce the predictions.

Abstract

We present up-to-date matched predictions for the $b\bar{b}H$ inclusive cross section at the LHC at $\sqrt{s}=13$ TeV. Using a previously developed method, our predictions consistently combine the complete NLO contributions that are present in the 4-flavor scheme calculation, including finite b-quark mass effects as well as top-loop induced $Y_b Y_t$ interference contributions, with the resummation of collinear logarithms of $m_b/m_H$ as present in the 5-flavor scheme calculation up to NNLO. We provide a detailed estimate of the perturbative uncertainties of the matched result by examining its dependence on the factorization and renormalization scales, the scale of the Yukawa coupling, and also the low b-quark matching scale in the PDFs. We motivate the use of a central renormalization scale of $m_H$/2, which is halfway between the values typically chosen in the 4-flavor and 5-flavor scheme calculations. We evaluate the parametric uncertainties due to the PDFs and the b-quark mass, and in particular discuss how to systematically disentangle the parametric $m_b$ dependence and the unphysical b-quark matching scale dependence. Our best prediction for the $b\bar{b} H$ production cross section in the Standard Model at 13 TeV and for $m_H$ = 125 GeV is $σ(b\bar b H) = 0.52 \,{\rm pb}\, [1 \pm 9.6\% {\rm (perturbative)}\,{}^{+2.9\%}_{-3.6\%} {\rm (parametric)}]$. We also provide predictions for a range of Higgs masses $m_H\in [50, 750]$ GeV. Our method to compute the matched prediction and to evaluate its uncertainty can be readily applied to other heavy-quark-initiated processes at the LHC.

Figures (7)

• Figure 1: Pictorial representation with sample diagrams appearing in the computation of the $b\bar{b}H$ cross section, grouped according to the different perturbative countings adopted in the 4FS (green boxes), 5FS (blue areas) and our matched resummed result (red boxes).
• Figure 2: Sample 1-loop diagrams contributing to the $Y_bY_t$ interference contribution at fixed order.
• Figure 3: Dependence of the cross sections on $\mu_R$ and $\mu_Y$ at LO$+$LL (dotted), NLO[$Y_b^2$]$+$NLL (dashed), and NLO[$Y_b^2$]$+$NNLL$_\mathrm{partial}$ (solid) for $m_H=125$ GeV and 13 TeV. The blue curves show the total scale dependence when setting $\mu_R=\mu_Y=\mu$, the green curves show the dependence on $\mu_R=\mu$ for fixed $\mu_Y=m_H/2$, and the red curves show the dependence on $\mu_Y=\mu$ for fixed $\mu_R=m_H/2$. In call cases $\mu_F$ is held fixed at its central value.
• Figure 4: Matched $b\bar{b}H$ cross section as a function of $m_H$, comparing different orders at LO+LL (green band), NLO[$Y_b^2\!+\!Y_bY_t$]+NLL (orange band), and NLO[$Y_b^2\!+\!Y_bY_t$]+NNLL$_\mathrm{partial}$ (blue band). The cross section is rescaled by $(m_H/125\,\mathrm{GeV})^3$. The lower panel shows the ratio of the central predictions NLO[$Y_b^2\!+\!Y_bY_t$]+NLL over NLO[$Y_b^2$]+NLL. The uncertainty bands are obtained by adding the $\{ \mu_F,\mu_R \}$ and $\mu_b$ uncertainties in quadrature.
• Figure 5: Comparison of the cross sections for $m_H=125$ GeV at the 13 TeV LHC at NLO[$Y_b^2$], NLO[$Y_b^2\!+\!Y_bY_t$] without resummation and at NLO[$Y_b^2$]+NLL, NLO[$Y_b^2\!+\!Y_bY_t$]+NLL, and NLO[$Y_b^2\!+\!Y_bY_t$]+NNLL$_\mathrm{partial}$. A full breakdown of the uncertainties at NLO[$Y_b^2\!+\!Y_bY_t$]+NLL is also shown.