On the Structure of Infrared Singularities of Gauge-Theory Amplitudes

Abstract: A closed formula is obtained for the infrared singularities of dimensionally regularized, massless gauge-theory scattering amplitudes with an arbitrary number of legs and loops. It follows from an all-order conjecture for the anomalous-dimension matrix of n-jet operators in soft-collinear effective theory. We show that the form of this anomalous dimension is severely constrained by soft-collinear factorization, non-abelian exponentiation, and the behavior of amplitudes in collinear limits. Using a diagrammatic analysis, we demonstrate that these constraints imply that to three-loop order the anomalous dimension involves only two-parton correlations, with the possible exception of a single color structure multiplying a function of conformal cross ratios depending on the momenta of four external partons, which would have to vanish in all two-particle collinear limits. We argue that such a function does not appear at three-loop order, and that the same is true in higher orders. Our formula predicts Casimir scaling of the cusp anomalous dimension to all orders in perturbation theory, and we explicitly check that the constraints exclude the appearance of higher Casimir invariants at four loops. Using known results for the quark and gluon form factors, we derive the three-loop coefficients of the 1/epsilon^n pole terms (with n=1,...,6) for an arbitrary n-parton scattering amplitude in massless QCD. This generalizes Catani's two-loop formula proposed in 1998.

• The paper derives a closed-form expression for IR divergences in gauge-theory amplitudes using soft-collinear effective theory.
• It employs soft-collinear factorization and non-abelian exponentiation to confine the anomalous-dimension matrix to two-parton correlations up to three-loop order.
• Explicit three-loop calculations with QCD form factors validate the framework and hint at improved resummation for high-energy collider analyses.

An Analysis of Infrared Singularities in Gauge-Theory Amplitudes

The paper "On the Structure of Infrared Singularities of Gauge-Theory Amplitudes" by Thomas Becher and Matthias Neubert presents a comprehensive investigation into the infrared (IR) singularities of massless gauge-theory amplitudes using advanced techniques derived from soft-collinear effective theory (SCET). The authors derive a closed-form expression for the IR divergences that arise in scattering amplitudes, encapsulating them within an anomalous-dimension matrix applicable across an arbitrary number of legs and loops.

The crux of their analysis lies in leveraging the soft-collinear factorization properties of SCET, alongside the principles of non-abelian exponentiation and the behavior of gauge-theory amplitudes in collinear limits. This theoretical framework enables the authors to rigorously constrain the form of the anomalous-dimension matrix to predominantly include two-parton correlations. These two-parton correlations are analyzed up to the three-loop order, suggesting simplicity even when considering potential complexities introduced by multiloop interactions.

The paper substantiates its theoretical propositions with explicit calculations, notably using known results from quark and gluon form factors in Quantum Chromodynamics (QCD). They derive the coefficients of the $1/\epsilon^n$ pole terms (for $n=1,...,6$) at three-loop order, generalizing Catani's earlier work on two-loop formulas.

A remarkable aspect of the derivation is the prediction of Casimir scaling for the cusp anomalous dimension, asserting its validity across all perturbative orders. This aspect is particularly significant within the context of gauge theories, where comparisons indicate a consistent relationship between quarks and gluons' cusp anomalous dimensions.

Furthermore, the paper rigorously tests these theoretical constructs by evaluating the derived anomalous-dimension matrix against known constraints, including soft-collinear factorization and collinear limit behaviors. At three-loop order, the authors identify possible deviations attributable to specific color structures that must vanish within two-particle collinear limits, hence reinforcing their primary conjecture's robustness.

It's crucial to note that the authors abstain from making sensational claims about the impact of their findings but instead offer an optimistic forecast on how these insights could be pivotal in collider physics, particularly in the context of calculating jet-production processes and resumming large logarithms efficiently.

This analysis has implications that transcend current knowledge, promising advancements in understanding the deep structures of gauge-theory amplitudes. Moreover, by establishing connections with the resummation techniques applicable in SCET, the work opens avenues for higher precision in theoretical predictions relevant to high-energy physics experiments. As the community progresses with further testing and validation of these conjectures, especially through numerical and analytical calculations like those possible in ${\cal N}=4$ super-Yang-Mills theory, the framework laid out by Becher and Neubert could indeed redefine the understanding of IR singularities in perturbative QCD and beyond.