Infrared singularities of QCD amplitudes with massive partons

Abstract

A formula for the two-loop infrared singularities of dimensionally regularized QCD scattering amplitudes with an arbitrary number of massive and massless legs is derived. The singularities are obtained from the solution of a renormalization-group equation, and factorization constraints on the relevant anomalous-dimension matrix are analyzed. The simplicity of the structure of the matrix relevant for massless partons does not carry over to the case with massive legs, where starting at two-loop order new color and momentum structures arise, which are not of the color-dipole form. The resulting two-loop three-parton correlations can be expressed in terms of two functions, for which some general properties are derived. This explains observations recently made by Mitov et al. in terms of symmetry arguments.

7 pages, 1 figure; v2: minor changes, reference added; v3: note added, correcting some statements regarding F1 and f2 in light of the recent calculations in [45,46], references updated

References in corpus (10)

• Gluon scattering amplitudes at strong coupling
• Factorization constraints for soft anomalous dimensions in QCD scattering amplitudes
• Comments on operators with large spin
• The Two-loop Soft Anomalous Dimension Matrix and Resummation at Next-to-next-to Leading Pole
• The Two-loop Anomalous Dimension Matrix for Soft Gluon Exchange
• Tops from Light Quarks: Full Mass Dependence at Two-Loops in QCD
• Two-loop QED corrections to Bhabha scattering
• Heavy-quark production in massless quark scattering at two loops in QCD
• The Massive Soft Anomalous Dimension Matrix at Two Loops
• Anomalous Dimensions from a Spinning D5-Brane

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