Journal
JOURNAL OF HIGH ENERGY PHYSICS
Volume -, Issue 9, Pages -Publisher
SPRINGER
DOI: 10.1007/JHEP09(2012)138
Keywords
Scattering Amplitudes; Resummation; R,enormalization Group; QCD
Categories
Funding
- European Research Council (ERC) [EFT4LHC]
- German Research Foundation (DFG) [NE 398/3-1]
- German Federal Ministry for Education and Research (BMBF) [05H09UME, 05H12UME]
- Rhineland-Palatinate Research Center Elementary Forces and Mathematical Foundations
- DFG Graduate Training Center [GRK 1581]
- Alexander von Humboldt Foundation
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The infrared divergences of massless n-parton scat tering amplitudes can be derived from the anomalous dimension of n-jet operators in soft-collinear effective theory. Up to three-loop order, the latter has been shown to have a very simple structure: it contains pairwise color-dipole interactions among the external partons, governed by the cusp anomalous dimension and a logarithm of the kinematic invariants s(ij), plus a possible three-loop correlation involving four particles, which is described by a yet unknown function of conformal cross ratios of kinematic invariants. This function is constrained by two-particle collinear limits and by the known behavior of amplitudes in the high-energy limit. We construct a class of relatively simple functions satisfying these constraints. We also extend the analysis to four-loop order, finding that three additional four-particle correlations and a single five-particle correlation appear, which again are governed by functions of conformal cross ratios. Our results suggest that the dipole conjecture, which states that only two-particle color-dipole correlations appear in the anomalous dimension, may need to be generalized. We present a weaker form of the conjecture, stating that to all orders in perturbation theory corrections to the dipole formula are governed by functions of conformal cross ratios, and are O(1/N-c(2)) suppressed relative to the dipole term. If true, this conjecture implies that the cusp anomalous dimension obeys Casimir scaling to all orders in perturbation theory.
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