Structure of non-global logarithms with Cambridge/Aachen clustering

We determine the structure of both Abelian and non-Abelian non-global logarithms up to four loops for e^+e^- <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:msup> <mml:mi>e</mml:mi> <mml:mo>+</mml:mo> </mml:msup> <mml:msup> <mml:mi>e</mml:mi> <mml:mo>−</mml:mo> </mml:msup> </mml:mrow> </mml:math> processes in perturbative QCD, where final-state jets are defined using the Cambridge-Aachen (C/A) clustering algorithm. The calculations are performed within the soft (eikonal) approximation using strong-energy ordering of the final-state partons for the case of the dijet invariant mass. The resulting expressions include full colour and complete jet-radius dependence. Compared to the anti- k_t <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:msub> <mml:mi>k</mml:mi> <mml:mi>t</mml:mi> </mml:msub> </mml:math> and k_t <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:msub> <mml:mi>k</mml:mi> <mml:mi>t</mml:mi> </mml:msub> </mml:math> clustering algorithms, the C/A distribution minimises the impact of these non-global logarithms, making it the preferred choice among the three algorithms.