Associated production of a Higgs boson decaying into bottom quarks and a weak vector boson decaying leptonically at NNLO in QCD

We present the calculation of next-to-next-to-leading order (NNLO) corrections in perturbative QCD for the production of a Higgs boson decaying into a pair of bottom quarks in association with a leptonically decaying weak vector boson: $ \mathrm{pp}\to V\mathrm{H}+X\to \mathrm{\ell}\overline{\mathrm{\ell}}\mathrm{b}\overline{\mathrm{b}}+X. $ We consider the corrections to both the production and decay sub-processes, retaining a fully differential description of the final state including off-shell propagators of the Higgs and vector boson. The calculation is carried out using the antenna subtraction formalism and is implemented in the NNLOjet framework. Clustering and identification of b-jets is performed with the flavour-k$_{t}$ algorithm and results for fiducial cross sections and distributions are presented for the LHC at $ \sqrt{s} $ = 13 TeV. We assess the residual theory uncertainty by varying the production and decay scales independently and provide scale uncertainty bands in our results, yielding percent-level accurate predictions for observables in this Higgs production mode computed at NNLO. Confronting a na¨ıve perturbative expansion of the cross section against the customary re-scaling procedure to a fixed branching ratio reveals that starting from NNLO, the latter could be inadequate in estimating missing higher-order effects through scale variations.