Progress in One-Loop QCD Computations

TL;DR

The paper surveys advances in computing one-loop QCD amplitudes relevant to NLO predictions, emphasizing compact, gauge-invariant building blocks over brute-force Feynman diagrams. It integrates spinor helicity, color decomposition, and supersymmetry identities with string-inspired organization and unitarity methods (Cutkosky rules and cut constructibility) to derive complete amplitudes, including novel SUSY decompositions and all-MHV results. It also demonstrates how factorization constrains amplitudes in collinear and multi-particle limits and illustrates these techniques with explicit examples for gluon amplitudes, including both supersymmetric and non-supersymmetric cases. The work highlights significant progress toward all-plate one-loop calculations, with implications for efficient NLO computations and a pathway toward higher-loop extensions. The methodologies unify multiple strands of perturbative QCD, enabling compact analytic results and practical numerical implementations for collider phenomenology.

Abstract

We review progress in calculating one-loop scattering amplitudes required for next-to-leading-order corrections to QCD processes. The underlying technical developments include the spinor helicity formalism, color decompositions, supersymmetry, string theory, factorization and unitarity. We provide explicit examples illustrating these techniques.

Figures (14)

• Figure 1: The inclusive cross section for single-jet production in $p \bar{p}$ collisions at $\sqrt{s} = 1.8$ TeV and jet transverse energy $E_T=100$ GeV (using MRS D${}_0'$ structure functions MRS), showing the sensitivity of the LO result to the choice of renormalization scale, $\mu_R$, and the reduced sensitivity at NLO. The CDF data shown is extracted from ref. CDFinclusiveJet; the band shows statistical errors only.
• Figure 2: In (a) the parton subprocesses required for the LO contribution to two-jet production at hadron colliders are shown schematically. In (b) the corresponding real and virtual NLO contributions are shown.
• Figure 3: The five-gluon pentagon diagram.
• Figure 4: Color-ordered Feynman rules in Lorentz-Feynman gauge. Curly lines represent gluons and lines with arrows fermions.
• Figure 5: The four-point Feynman diagrams. Color-ordered Feynman rules do not include diagram (c) for $A_4(1,2,3,4)$.