Phenomenology of the $Z$ boson plus jet process at NNLO

We present a detailed phenomenological study of $Z$-boson production in association with a jet through next-to-next-to-leading order (NNLO) in perturbative QCD. Fiducial cross sections and differential distributions for both 8 TeV and 13 TeV LHC collisions are presented. We study the impact of different parton distribution functions (PDFs) on predictions for the $Z+\mathrm{jet}$ process. Upon inclusion of the NNLO corrections, the residual scale uncertainty is reduced such that both the total rate and the transverse momentum distributions can be used to discriminate between various PDF sets.

Figure 1

Plots of the $Z$-boson transverse momentum distribution for both 8 TeV and 13 TeV collisions. In each plot, the upper inset shows the LO, NLO, and NNLO distributions, while the lower inset shows $K_{\mathrm{NLO}}$ and $K_{\mathrm{NNLO}}$. The bands indicate the scale variation.

Figure 2

Plots of the transverse momentum distribution of the leading jet for both 8 TeV and 13 TeV collisions. In each plot, the upper inset shows the LO, NLO, and NNLO distributions, while the lower inset shows $K_{\mathrm{NLO}}$ and $K_{\mathrm{NNLO}}$. The bands indicate the scale variation.

Figure 3

Plots of the $H_T$ distribution for both 8 TeV and 13 TeV collisions. In each plot the upper inset shows the LO, NLO and NNLO distributions, while the lower inset shows $K_{\mathrm{NLO}}$ and $K_{\mathrm{NNLO}}$. The bands indicate the scale variation.

Figure 4

Plots of the pseudorapidity distribution of the leading jet for both 8 TeV and 13 TeV collisions. In each plot the upper inset shows the LO, NLO and NNLO distributions, while the lower inset shows $K_{\mathrm{NLO}}$ and $K_{\mathrm{NNLO}}$. The bands indicate the scale variation.

Figure 5

Plots of the $Z$-boson rapidity distribution for both 8 TeV and 13 TeV collisions. In each plot the upper inset shows the LO, NLO and NNLO distributions, while the lower inset shows $K_{\mathrm{NLO}}$ and $K_{\mathrm{NNLO}}$. The bands indicate the scale variation.

Figure 6

Plots of the transverse momentum distribution of the leading lepton for both 8 TeV and 13 TeV collisions. In each plot the upper inset shows the LO, NLO and NNLO distributions, while the lower inset shows $K_{\mathrm{NLO}}$ and $K_{\mathrm{NNLO}}$. The bands indicate the scale variation.

Figure 7

Plots of the transverse momentum distribution of the softer lepton for both 8 TeV and 13 TeV collisions. In each plot the upper inset shows the LO, NLO and NNLO distributions, while the lower inset shows $K_{\mathrm{NLO}}$ and $K_{\mathrm{NNLO}}$. The bands indicate the scale variation.

Figure 8

The prediction of several PDF sets for the $Z$-boson transverse momentum distribution, shown as a ratio to the CT14 result. The distribution for each PDF choice has been normalized by the fiducial cross section for that set. The bands indicate the scale variation of the CT14 result, and the combined $\mathrm{PDF}+\text{scale}$ uncertainty.

Figure 9

The prediction of several PDF sets for the leading-jet transverse momentum distribution, shown as a ratio to the CT14 result. The distribution for each PDF choice has been normalized by the fiducial cross section for that set. The bands indicate the scale variation of the CT14 result and the combined $\mathrm{PDF}+\text{scale}$ uncertainty.

Figure 10

The prediction of several PDF sets for the $H_T$ distribution, shown as a ratio to the CT14 result. The distribution for each PDF choice has been normalized by the fiducial cross section for that set. The bands indicate the scale variation of the CT14 result, and the combined $\mathrm{PDF}+\text{scale}$ uncertainty.