Two-loop divergences of massive scattering amplitudes in non-abelian gauge theories

Abstract

The infrared divergences of QCD scattering amplitudes can be derived from an anomalous dimension Γ, which is a matrix in color space and depends on the momenta and masses of the external partons. It has recently been shown that in cases where there are at least two massive partons involved in the scattering process, starting at two-loop order Γreceives contributions involving color and momentum correlations between three (and more) partons. The three-parton correlations can be described by two universal functions F_1 and f_2. In this paper these functions are calculated at two-loop order in closed analytic form and their properties are studied in detail. Both functions are found to be suppressed like O(m^4/s^2) in the limit of small parton masses, in accordance with mass factorization theorems proposed in the literature. On the other hand, both functions are O(1) and even diverge logarithmically near the threshold for pair production of two heavy particles. As an application, we calculate the infrared poles in the q qbar --> t tbar and g g --> t tbar scattering amplitudes at two-loop order.

27 pages, 2 figures, includes 3 Mathematica files; v2: bug in one of the Mathematica files fixed, minor changes in the first four lines of Table 1

References in corpus (14)

• Factorization constraints for soft anomalous dimensions in QCD scattering amplitudes
• The Two-loop Soft Anomalous Dimension Matrix and Resummation at Next-to-next-to Leading Pole
• Feynman Integral Evaluation by a Sector decomposiTion Approach (FIESTA)
• Infrared singularities of QCD amplitudes with massive partons
• The Two-loop Anomalous Dimension Matrix for Soft Gluon Exchange
• Tops from Light Quarks: Full Mass Dependence at Two-Loops in QCD
• Two-loop soft anomalous dimensions and NNLL resummation for heavy quark production
• Two-loop QED corrections to Bhabha scattering
• Two-Loop Fermionic Corrections to Heavy-Quark Pair Production: the Quark-Antiquark Channel
• Heavy-quark production in massless quark scattering at two loops in QCD
• The Massive Soft Anomalous Dimension Matrix at Two Loops
• Two-Loop Planar Corrections to Heavy-Quark Pair Production in the Quark-Antiquark Channel
• Electroweak Corrections using Effective Field Theory: Applications to the LHC
• Matter Dependence of the Three-Loop Soft Anomalous Dimension Matrix

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