Erratum: On the structure of infrared singularities of gauge-theory amplitudes

By T. Becher, M. Neubert. Journal of High Energy Physics, 2009

431 citations recorded by the source corpus.

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 suggest 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/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.

Subfields: Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/481883e5b2704ce04e5817893d6c031c1e69a825

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Citations in the corpus

When does the gluon reggeize? (2013, background): “[23, 24, 89] is that in the massless case the soft-anomalous dimension should take form of a sum over “dipole” terms”
Introduction to Soft-Collinear Effective Theory (2014, methodology): “The UV singularities in the Wilson coefficients can be subtracted by means of a multiplicative renormalization factor Z, which is a matrix in color space [70,71].”
Predictions for diphoton production at the LHC through NNLO in QCD (2016, methodology): “The aim of this section is to re-write the above expressions in the SCET renormalized form, which is obtained via the following re-definitions [78, 79]”
Next-to-eikonal corrections to soft gluon radiation: a diagrammatic approach (2010, neutral): “Recent significant developments in the understanding of the all-order structure of infrared divergences in non-abelian gauge theories [5, 6, 7, 8] were also derived with the help of the special properties of the eikonal approximation.”
Calculation of the transverse parton distribution functions at next-to-next-to-leading order (2014, background): “Higher order coefficients of Γi, γi and β can be found in [11, 40, 41], respectively.”
Factorization at the LHC: From PDFs to Initial State Jets (Ph.D. thesis) (2009, background): “tion Hqq can be obtained [41, 118] from the IR divergences of the on-shell massless quark form factor which is known to three loops [148]. Similarly, the anomalous dimension for Hgg can be extracted [40] from the gluon form factor, which has also been calculated to three loops [149]. qq H0 = 12C F; ”
Factorization properties of soft graviton amplitudes (2011, background): “Such factorization properties are important both for resummation applications, and also for understanding the structure of infrared singularities to all orders [33, 34, 35, 36, 37, 38, 39, 40, 41].”