Factorization constraints for soft anomalous dimensions in QCD scattering amplitudes

By E. Gardi, L. Magnea. 2009

402 citations recorded by the source corpus.

We study the factorization of soft and collinear singularities in dimensionally- regularized fixed-angle scattering amplitudes in massless gauge theories. Our factorization is based on replacing the hard massless partons by light-like Wilson lines, and defining gauge-invariant jet and soft functions in dimensional regularization. In this scheme the factorized amplitude admits a powerful symmetry: it is invariant under rescaling of indi- vidual Wilson-line velocities. This symmetry is broken by cusp singularities in both the soft and the eikonal jet functions. We show that the cancellation of these cusp anomalies in any multi-leg amplitude imposes all-order constraints on the kinematic dependence of the corresponding soft anomalous dimension, relating it to the cusp anomalous dimension. For amplitudes with two or three hard partons the solution is unique: the constraints fully determine the kinematic dependence of the soft function. For amplitudes with four or more hard partons we present a minimal solution where the soft anomalous dimension is a sum over colour dipoles, multiplied by the cusp anomalous dimension. In this case additional contributions to the soft anomalous dimension at three loops or beyond are not excluded, but they are constrained to be functions of conformal cross ratios of kinematic variables.

Subfields: Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/1fd7032c1dde8db6ce496309f606480550bdd4a7

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In Nuclear and High Energy Physics

Citations in the corpus

Erratum: On the structure of infrared singularities of gauge-theory amplitudes (2009, background): “In very recent work, Gardi and Magnea have pushed this approach further and derived a set of constraint relations for the soft-anomalous dimension matrix, which hold to all orders in perturbation theory [29].”
When does the gluon reggeize? (2013, neutral): “[22–24] and references therein).”
Calculation of the quark and gluon form factors to three loops in QCD (2010, background): “Independently, Becher and Neubert [39] and Gardi and Magnea [ 44 ] have proposed a remarkable all-loops conjecture that describes the pole structure of massless on-shell multi-loop multi-leg QCD amplitudes (generalizing earlier results at two [45] and three loops [46]) in terms of the cusp anomalous”
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].”
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.”
Introduction to Soft-Collinear Effective Theory (2014, neutral): “With four or more partons, it is possible to use exclusively soft logarithms to build conformal cross ratios, which do not depend on the small collinear squared momenta p(2)i but only on the Mandelstam invariants sij [73].”