$VH+\text{jet}$ production in hadron-hadron collisions up to order $\alpha_s^3$ in perturbative QCD

TL;DR

This paper provides precise NNLO QCD predictions for Higgs production with a gauge boson and a jet in proton-proton collisions, improving theoretical accuracy and uncertainty estimates across various observables.

Contribution

It presents the first complete NNLO QCD corrections to Higgs plus vector boson plus jet production, including heavy quark loop effects, enhancing prediction stability.

Findings

NNLO corrections significantly reduce theoretical uncertainties.

Inclusion of NNLO stabilizes predictions for both inclusive and exclusive jet categories.

Heavy quark loop contributions impact high transverse momentum regions.

Abstract

We present precise predictions for the hadronic production of an on-shell Higgs boson in association with a leptonically decaying gauge boson and a jet up to order $\alpha_s^3$. We include the complete set of NNLO QCD corrections to both charged- and neutral-current Drell-Yan type contributions, as well as the previously known leading heavy quark loop induced contributions which involve a direct Higgs-quark coupling. As an application, we study a range of differential observables in proton-proton collisions at $\sqrt{s} = 13~\text{TeV}$ for both the charged- and neutral-current production modes. For each Higgs production process, we assess the improvement in the theoretical uncertainty for both the exclusive ($n_{\text{jet}} = 1$) and inclusive ($n_{\text{jet}} \geq 1$) jet categories. We find that the inclusion of the NNLO corrections to the Drell-Yan type contributions is essential in stabilising the predictions and in reducing the theoretical uncertainty for both inclusive and exclusive jet production for all three modes. This is particularly true in the kinematical regimes associated with low to medium values of the transverse momentum of the produced vector boson and where the differential cross sections are the largest. For the neutral-current process, we find that the heavy quark loop induced contributions have their largest phenomenological impact (an increase in the size of the NNLO corrections, a distortion of the distribution shape and an enlargement of the left over remaining uncertainties) in kinematical regions associated to large values of $p_{T,Z}$ (typically above $150~\text{GeV}$) where the cross sections are smaller.