NNLO QCD corrections for Z boson plus jet production

TL;DR

The paper delivers a complete NNLO QCD calculation for Z boson production in association with a jet, including leptonic Z decay and all partonic channels. It employs antenna subtraction to manage infrared divergences and a highly parallelized phase-space integration (VEGAS) to evaluate the challenging double-real contribution, ensuring stable, fully differential predictions. A key finding is the substantial NNLO correction in the gg-initiated channel and the overall improvement in precision across cross sections and lepton distributions, aided by a robust method for combining many parallel runs. The results support precise QCD tests and more accurate PDF and αs extractions from LHC data, including spin correlations in Z decays.

Abstract

We discuss the next-to-next-to-leading order (NNLO) QCD corrections to Z boson production in association with a jet including all partonic channels at all color levels and including the leptonic decay of the Z boson. We focus on the optimization of the numerical evaluation of the double-real contribution and demonstrate that our procedure for spreading the Monte Carlo integration over $\mathcal{O}(1000)$ cores and recombining the results afterwards lead to stable results with sensible error estimates. We apply representative cuts on the jet and charged lepton transverse momenta and pseudorapidities at LHC energies and present the transverse momentum and rapidity distributions of the charged leptons.

Figures (6)

• Figure 1: Representative Feynman diagrams for (a) two-loop $Z$ boson-plus-three-parton amplitudes (b) one-loop $Z$ boson-plus-four-parton amplitudes and (c) tree-level $Z$ boson-plus-five-parton amplitudes. nameref-fig:FD fith LAB: fig:FD
• Figure 2: The total cross section $\sigma(N/k, k\cdot M)$ at NNLO as a function of $k$, the number of runs combined to form a pseudorun. The cross section is then the weighted average of the pseudoruns. The errors on the individual data points are statistical. nameref-fig:wgt fith LAB: fig:wgt
• Figure 3: The integral of the $y^Z$ distribution, $\sigma(N/k, k\cdot M)$ at NNLO as a function of $k$. The errors on the individual data points are statistical. The green band denotes the total cross section evaluated at $k = 100$ with its statistical uncertainty. nameref-fig:wgtdist fith LAB: fig:wgtdist
• Figure 4: The ratio of the NNLO against the NLO prediction for individual bins of the rapidity distribution of the $Z$ boson for different values of $k$. The grey bands are the unweighted result. The errors on the individual data points are statistical. nameref-fig:yzcomp fith LAB: fig:yzcomp
• Figure 5: The ratio of the NNLO against the NLO prediction for individual bins of the $p_T$ distribution of the $Z$ boson for different values of $k$. The grey bands are the unweighted result. The errors on the individual data points are statistical. nameref-fig:ptzcomp fith LAB: fig:ptzcomp