Z-boson production in association with a jet at next-to-next-to-leading order in perturbative QCD

Abstract: We present the first complete calculation of Z-boson production in association with a jet in hadronic collisions through next-to-next-to-leading order in perturbative QCD. Our computation uses the recently-proposed N-jettiness subtraction scheme to regulate the infrared divergences that appear in the real-emission contributions. We present phenomenological results for 13 TeV proton-proton collisions with fully realistic fiducial cuts on the final-state particles. The remaining theoretical uncertainties after the inclusion of our calculations are at the percent-level, making the Z+jet channel ready for precision studies at the LHC Run II.

• The paper presents a comprehensive NNLO calculation for Z-boson plus jet production using the N-jettiness subtraction scheme to precisely handle infrared divergences.
• It employs factorization into hard, beam, soft, and jet functions to achieve percent-level uncertainty reductions and improved alignment with experimental data.
• The study boosts computational efficiency with parallelized MCFM enhancements, offering insights for refining parton distribution functions and new physics searches.

$Z$-Boson Production with Jet at NNLO: A Precision Study

The production of a $Z$-boson in association with a jet is pivotal in understanding various processes at the Large Hadron Collider (LHC), including the background for studies of new physics phenomena like supersymmetry and dark matter. This paper by Boughezal et al. presents a comprehensive calculation of this process at next-to-next-to-leading order (NNLO) in perturbative Quantum Chromodynamics (QCD), utilizing the $N$-jettiness subtraction scheme, which mitigates infrared divergences in real-emission contributions.

Conceptual and Methodological Contributions

The theoretical foundation hinges on the $N$-jettiness variable, a tool designed to probe events with a specific number of jets. The $N$-jettiness subtraction scheme leverages this variable to handle the singularity cancellations and phase space integrations required for NNLO calculations. Specifically, the NNLO cross section is partitioned into regions below and above a cutoff on the $N$-jettiness variable ($\tau$), each treated with different techniques. When $\tau$ is small, factorization theorems allow the process to be dissected into hard, beam, soft, and jet functions, each calculated to the required order. Above the cutoff, a next-to-leading order (NLO) calculation is necessary, as the configuration involves additional resolved partons.

The methodology is validated through checks such as the consistency of scale dependence across varying $\tau$ and comparisons with known results for related processes, ensuring a high level of numerical accuracy—a crucial attribute given the precision demanded in matching theory with data at the LHC.

Numerical Results and Implications

The numerical results are notably robust, reducing the theoretical uncertainties to the percent level—an impressive feat that brings theoretical predictions into closer alignment with the precision of experimental measurements. For instance, the total cross-section at NNLO is found to differ by merely 1% from the NLO result. Despite relatively small modifications over much of the studied phase space, the NNLO corrections are pronounced in regions of high transverse momentum, where they reach an increase of 10%. This can have significant implications, particularly because experimental uncertainties in these regions are very small.

The impact of these results is profound, particularly for precision Higgs measurements and new physics searches where $Z$+jet processes act predominantly as backgrounds. Furthermore, the calculated NNLO corrections could refine the information on parton distribution functions, especially the gluon distribution, enriching our understanding of hadronic structure.

Computational Advances

An exciting feature of this study is its computational efficiency, achieved through enhancements to the MCFM software to exploit parallel computing architectures. This development is as much about increased computational power as it is about making large, complex calculations tractable and scalable. This attribute will likely enable rapid iterations of similar calculations for other processes, aligning theoretical predictions with the experimental frontier.

Future Perspectives

The successful application of $N$-jettiness subtraction to $Z$-boson production with a jet paves the way for adopting this method in other complex hadronic processes at NNLO. Anticipated future improvements might involve extending these techniques to multi-jet processes or incorporating electroweak corrections to further tighten the match between theory and reality. Moreover, as LHC experiments deliver more data with increased luminosity, the demand for precise theoretical predictions will continue to grow. This research represents a necessary step toward meeting that challenge.

In conclusion, the work of Boughezal et al. significantly advances our ability to perform precision calculations in QCD, setting a benchmark for theoretical predictions in high-energy physics that is commensurate with the precision of LHC experiments. The techniques developed and validated here are likely to play an increasingly critical role in future analyses at the energy frontier.