Factorization constraints for soft anomalous dimensions in QCD scattering amplitudes - High Energy Physics - PhenomenologyReport as inadecuate




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Abstract: We study the factorization of soft and collinear singularities indimensionally-regularized fixed-angle scattering amplitudes in massless gaugetheories. Our factorization is based on replacing the hard massless partons bylight-like Wilson lines, and defining gauge-invariant jet and soft functions indimensional regularization. In this scheme the factorized amplitude admits apowerful symmetry: it is invariant under rescaling of individual Wilson-linevelocities. This symmetry is broken by cusp singularities in both the soft andthe eikonal jet functions. We show that the cancellation of these cuspanomalies in any multi-leg amplitude imposes all-order constraints on thekinematic dependence of the corresponding soft anomalous dimension, relating itto the cusp anomalous dimension. For amplitudes with two or three hard partonsthe solution is unique: the constraints fully determine the kinematicdependence of the soft function. For amplitudes with four or more hard partonswe present a minimal solution where the soft anomalous dimension is a sum overcolour dipoles, multiplied by the cusp anomalous dimension. In this caseadditional contributions to the soft anomalous dimension at three loops orbeyond are not excluded, but they are constrained to be functions of conformalcross ratios of kinematic variables.



Author: Einan Gardi, Lorenzo Magnea

Source: https://arxiv.org/







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