[Paper Review] Inclusive Production Cross Sections at N3LO

Julien Baglio, Claude Duhr+2 more|arXiv (Cornell University)|Sep 13, 2022

Particle physics theoretical and experimental studies4 citations

TL;DR

This paper presents the first next-to-next-to-next-to-leading order (N³LO) QCD calculations for inclusive Higgs boson production in association with a massive gauge boson (VH) at hadron colliders, introducing the public n3loxs software tool for precise N³LO cross-section computations. It delivers comprehensive phenomenological predictions for W±H and ZH production, including scale and PDF uncertainties, and reveals significant 1σ deviations among global PDF sets at N³LO accuracy.

ABSTRACT

We present for the first time the inclusive cross section for associated Higgs boson production with a massive gauge boson at next-to-next-to-next-to-leading order in QCD. Furthermore, we introduce n3loxs, a public, numerical program for the evaluation of inclusive cross sections at the third order in the strong coupling constant. Our tool allows to derive predictions for charged- and neutral-current Drell-Yan production, gluon- and bottom-quark-fusion Higgs boson production and Higgs boson associated production with a heavy gauge boson. We discuss perturbative and parton distribution function (PDF) uncertainties of the aforementioned processes. We perform a comparison of global PDF sets for a variety of process including associated Higgs boson production and observe $1σ$ deviations among predictions for several processes.

Motivation & Objective

• To compute inclusive cross sections for Higgs boson production in association with W± and Z bosons at N³LO in QCD, a critical step toward precision Standard Model phenomenology.
• To develop and release n3loxs, a public numerical program for evaluating N³LO inclusive cross sections across multiple processes including Drell-Yan, gluon- and bottom-quark fusion Higgs production, and VH production.
• To assess perturbative scale uncertainties and parton distribution function (PDF) uncertainties at N³LO, providing a benchmark for future LHC and HL-LHC analyses.
• To compare predictions across global PDF sets, identifying 1σ deviations in cross-section predictions that highlight the sensitivity of high-precision QCD calculations to PDF choice.

Proposed method

• The authors compute N³LO QCD corrections for inclusive VH production using advanced fixed-order perturbative QCD techniques, including virtual, real, and rational contributions.
• The n3loxs software framework is implemented to numerically evaluate N³LO cross sections, supporting various processes such as Drell-Yan, Higgs production via gluon fusion and bottom-quark fusion, and VH production.
• Scale uncertainties are estimated using a 7-point scale variation around a dynamical central scale choice (μ₀ = MH + MW or MH + MZ), following standard QCD practice.
• PDF uncertainties are evaluated using the PDF4LHC15_nnlo_mc set, with additional PDF+αS and PDF-TH uncertainty estimates to assess PDF and strong coupling dependence.
• The code supports both total and binned cross sections, enabling differential predictions in invariant mass windows around Z and W boson peaks.
• Phenomenological results are presented at multiple center-of-mass energies (7–100 TeV), including detailed tables of cross sections and uncertainties.

Experimental results

Research questions

• RQ1 What are the N³LO QCD corrections to inclusive associated Higgs boson production with a massive gauge boson (W±H and ZH) at hadron colliders?
• RQ2 How do scale and PDF uncertainties evolve at N³LO, and do they exhibit the expected convergence compared to lower orders?
• RQ3 To what extent do different global PDF sets yield divergent predictions for VH production at N³LO, and what are the implications for precision phenomenology?
• RQ4 How does the n3loxs code enable accurate and efficient computation of N³LO cross sections across a broad class of processes?
• RQ5 What is the impact of the strong coupling constant αS on the overall uncertainty budget in N³LO predictions?

Key findings

• The inclusive cross sections for W±H and ZH production at N³LO are presented for the first time, with values ranging from 0.218 pb at √s = 7 TeV to 8.93 pb at 100 TeV for ZH production.
• Scale uncertainties at N³LO are reduced compared to lower orders, with variations of ±0.22–0.58% for W⁻H and ±0.15–0.48% for ZH, indicating improved perturbative convergence.
• PDF uncertainties at N³LO range from ±1.56% to ±2.59%, with the largest uncertainties observed at high energies and for W⁺H production.
• 1σ deviations among global PDF sets are observed in cross-section predictions, particularly for W⁺H and ZH processes, highlighting the sensitivity of N³LO results to PDF choice.
• The n3loxs code successfully computes binned cross sections in invariant mass windows, enabling differential predictions with bin sizes as small as 0.5 GeV around the Z and W peaks.
• The study confirms that PDF and αS uncertainties remain significant at N³LO, with PDF+αS and PDF-TH uncertainties often exceeding scale uncertainties, especially at high energies.