Infrared singularities of scattering amplitudes and N3LL resummation for n-jet processes
Thomas Becher, Matthias Neubert
Abstract
A bstract We revisit the multi-loop structure of the anomalous-dimension matrix governing the infrared divergences of massless n -particle scattering amplitudes in non-abelian gauge theories. In particular, we derive its most general form at four-loop order, significantly simplifying corresponding expressions given previously. By carefully reevaluating the constraints imposed by two-particle collinear limits, we find that at four-loop order color structures involving $$ {d}_R^{abcd} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>d</mml:mi> <mml:mi>R</mml:mi> <mml:mtext>abcd</mml:mtext> </mml:msubsup> </mml:math> , the symmetrized trace of four group generators, appear along with cusp logarithms ln[ μ 2 / ( −s ij )]. As a consequence, naive Casimir scaling of the cusp anomalous dimensions associated with the quark and gluon form factors is violated, while a generalized form of Casimir scaling still holds. Our results provide an important ingredient for resummations of large logarithms in n -jet cross sections with next-to-next-to-next-to leading logarithmic (N 3 LL) accuracy.