QCD corrections to Higgs boson production and $H \to b \bar{b}$ decay in weak boson fusion

We study QCD corrections to the process where a Higgs boson is produced in weak boson fusion and then decays into a pair of massive $b$ quarks. We find that typical experimental criteria used to identify $b$ jets in this process affect QCD corrections to the decay, making it necessary to account for them in the proper description of this process. Indeed, if corrections to the production and decay are combined, the fiducial cross section of the weak boson fusion process $p p \to H(\to b \bar{b}) j j$ is reduced by about $40\%$ relative to leading-order predictions, compared to just about $8\%$ if only corrections to the production process are considered. We investigate the origin of these large corrections through next-to-next-to-leading-order and conclude that they appear because a number of independent moderately-large effects conspire to significantly reduce the fiducial cross section for this process.