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

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 $\sigma(b\bar b H) = 0.52 \,{\rm pb}\, [1 \pm 9.6\% {\rm (perturbative)}\,{}^{+2.9\%}_{-3.6\%} {\rm (parametric)}]$. 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.