[Paper Review] Hard QCD at hadron colliders

S. Moch|Mar 4, 2008

Particle physics theoretical and experimental studies35 references4 citations

TL;DR

This paper reviews precision QCD predictions for hard scattering processes at hadron colliders, focusing on next-to-leading (NLO) and next-to-next-to-leading (NNLO) order calculations for Standard Model processes such as W/Z boson, Higgs, and top quark production. It demonstrates that higher-order QCD corrections significantly reduce theoretical uncertainties, especially under realistic experimental cuts, and confirms that Higgs production rates at the LHC are now reliably predicted with sub-percent precision in key channels.

ABSTRACT

We review the status of QCD at hadron colliders with emphasis on precision predictions and the latest theoretical developments for cross sections calculations to higher orders. We include an overview of our current information on parton distributions and discuss various Standard Model reactions such as W/Z-boson, Higgs boson or top quark production.

Motivation & Objective

• To provide a comprehensive review of precision QCD calculations for hard scattering processes at hadron colliders, particularly at the LHC.
• To assess the current status of perturbative QCD predictions, including higher-order corrections (NLO, NNLO) for key Standard Model processes.
• To evaluate the impact of kinematical cuts on radiative corrections and their effect on theoretical uncertainties.
• To highlight the role of parton distribution functions (PDFs) and their evolution to NNLO in constraining cross-section predictions.
• To demonstrate the robustness of QCD predictions for Higgs boson production, especially in gluon fusion, under realistic experimental conditions.

Proposed method

• Utilizes QCD factorization to separate short-distance partonic cross sections from long-distance PDFs, expressed via convolution in Eq. (1).
• Applies perturbative QCD calculations up to NNLO for partonic subprocesses such as gg → H, qg → WH, and qq̄ → Z, with exact results for Higgs production.
• Employs parton-level Monte Carlo programs like HNNLO to compute differential distributions, including rapidity and jet-veto effects.
• Incorporates NNLO corrections to the Higgs boson decay modes H → γγ, WW → lνlν, and ZZ → 4l, enabling precision comparisons with data.
• Assesses scale dependence and stability of predictions through scale variation, showing improved convergence at higher orders.
• Uses global PDF fits and HERA data to constrain gluon PDFs at high momentum fractions relevant for LHC processes.

Experimental results

Research questions

• RQ1 How do NNLO QCD corrections affect the theoretical uncertainty in Higgs boson production cross sections at the LHC?
• RQ2 To what extent do experimental cuts, such as jet-vetoing, suppress the size of higher-order QCD corrections in differential distributions?
• RQ3 How stable are precision QCD predictions under variations of the factorization and renormalization scales at NLO and NNLO?
• RQ4 What is the role of parton distribution functions, especially the gluon PDF, in constraining cross-section predictions for high-energy processes?
• RQ5 How do higher-order corrections in QCD improve the reliability of background estimates for new physics searches, such as in Higgs or supersymmetry channels?

Key findings

• NNLO QCD corrections reduce the theoretical uncertainty in the total Higgs boson cross section to a few percent, with corrections reaching up to 100% in the total rate.
• Under realistic experimental cuts—such as vetoing jets with pT ≥ 40 GeV—the size of NNLO corrections is reduced to approximately 5%, indicating strong suppression by kinematical constraints.
• The stability of predictions under scale variation is significantly improved at NNLO, confirming the convergence of the perturbative series.
• For the Higgs rapidity distribution, soft N³LO corrections have been computed and analytical formulae are available, further enhancing precision.
• The combination of NNLO QCD corrections with Higgs decay modes (e.g., H → γγ, WW → lνlν, ZZ → 4l) enables accurate, bin-integrated predictions for LHC analyses.
• The gluon PDF is well constrained in the relevant kinematic region, and HERA data evolved to NNLO accuracy contribute to the reliability of cross-section predictions.