Hard Interactions of Quarks and Gluons: a Primer for LHC Physics

TL;DR

This primer distills the perturbative QCD framework for hard scattering at hadron colliders, detailing factorization, higher-order corrections, and the role of PDFs. It surveys Drell–Yan, heavy-quark, and Higgs production, as well as W/Z pT and jet-formation, while explaining jet algorithms, matching of matrix elements with parton showers, and all-orders resummation. By comparing to Tevatron data and laying out LHC benchmarks, the paper clarifies uncertainties, scale choices, and the practical paths toward robust predictions. It also presents a pragmatic view of current and future NNLO/NLO techniques, PDF interfaces (LHAPDF), and the strategic wishlist for advancing multi-jet predictions at the LHC. Overall, it serves as a comprehensive guide to predict and interpret SM processes and backgrounds with controlled perturbative accuracy in the LHC era.

Abstract

In this review article, we develop the perturbative framework for the calculation of hard scattering processes. We undertake to provide both a reasonably rigorous development of the formalism of hard scattering of quarks and gluons as well as an intuitive understanding of the physics behind the scattering. We emphasize the importance of logarithmic corrections as well as power counting of the strong coupling constant in order to understand the behavior of hard scattering processes. We include "rules of thumb" as well as "official recommendations", and where possible seek to dispel some myths. Experiences that have been gained at the Fermilab Tevatron are recounted and, where appropriate, extrapolated to the LHC.

Figures (107)

• Figure 1: Diagrammatic structure of a generic hard scattering process.
• Figure 2: Standard Model cross sections at the Tevatron and LHC colliders.
• Figure 3: Graphical representation of the relationship between parton $(x,Q^2)$ variables and the kinematic variables corresponding to a final state of mass $M$ produced with rapidity $y$ at the LHC collider with $\sqrt{s} = 14$ TeV.
• Figure 4: Predictions for the $W$ and $Z$ total cross sections at the Tevatron and LHC, using MRST2004 Martin:2004ir and CTEQ6.1 pdfs Stump:2003yu, compared with recent data from CDF and D0. The MRST predictions are shown at LO, NLO and NNLO. The CTEQ6.1 NLO predictions and the accompanying pdf error bands are also shown.
• Figure 5: Representative Feynman diagrams for the production of a pair of heavy quarks at hadron colliders, via $gg$ (left) and $q{\bar{q}}$ (right) initial states.