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

The hadroproduction of a Higgs boson in association with a bottom-quark pair ($ Hb\overline{b} $) is commonly considered as the key process for directly probing the Yukawa interaction between the Higgs boson and the bottom quark (y$_{b}$). However, in the Standard-Model (SM) this process is also known to suffer from very large irreducible backgrounds from other Higgs production channels, notably gluon-fusion (ggF). In this paper we calculate for the first time the so-called QCD and electroweak complete-NLO predictions for $ Hb\overline{b} $ production, using the four-flavour scheme. Our calculation shows that not only the ggF but also the ZH and even the vector-boson-fusion channels are sizeable irreducible backgrounds. Moreover, we demonstrate that, at the LHC, the rates of these backgrounds are very large with respect to the “genuine” and y$_{b}$-dependent $ Hb\overline{b} $ production mode. In particular, no suppression occurs at the differential level and therefore backgrounds survive typical analysis cuts. This fact further jeopardises the chances of measuring at the LHC the y$_{b}$-dependent component of $ Hb\overline{b} $ production in the SM. Especially, unless y$_{b}$ is significantly enlarged by new physics, even for beyond-the SM scenarios the direct determination of y$_{b}$ via this process seems to be hopeless at the LHC.