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

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.

RIP $$ Hb\overline{b} $$: how other Higgs production modes conspire to kill a rare signal at the LHC

“…[50][51][52][53] and very recently in ref. [54], which matches the 5FS prediction at N 3 LO QCD accuracy and the 4FS prediction at NLO QCD.…”

“…In conclusion, the combination of 4FS and 5FS predictions as done in refs. [50][51][52][53][54] is definitely important for improving the precision of the description of the contribution from the "genuine" Hbb topology, but not compulsory for providing a sensible prediction and the 4FS can be safely used for the purpose of our work.…”

“…We do not evaluate uncertainties related to the value of m b ; they are discussed, e.g., in refs. [53,54] and are of the order of a few percents. For the factorisation scale µ F and the renormalisation scale µ R , which enters the definition of α s (µ R ) and y b = √ 2m MS b (µ R )/v in the NLO QCD calculation, we use a central value…”

N-jettiness beam functions at N3LO

“…So far, only inclusive Drell-Yan and Higgs production have been calculated at next-tonext-to-next-to-leading order (N 3 LO) in QCD [10][11][12][13][14][15][16][17], while significant progress is being made to reach the same precision for differential distributions [18,19]. A key challenge for such calculations is the cancellation of infrared divergences between real and virtual corrections, and hence a necessary prerequisite is a profound understanding of the infrared singular structure at three loops.…”

Tree-level splitting amplitudes for a gluon into four collinear partons

“…While over the last years a lot of progress was made in NNLO computations, so far, only very few hadron collider processes are known at N 3 LO. Inclusive N 3 LO cross sections are known for Higgs in gluon fusion [5][6][7], bottom-quark fusion [8,9] and vector boson fusion in the DIS approach [10,11], as well as double Higgs production [12,13] and Drell-Yan JHEP10(2020)093 production (via the intermediate of an off-shell photon) [14]. At the differential level, only the Higgs rapidity and transverse momentum distributions in vector boson fusion in the DIS approximation [10,15,16] are known.…”