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Abstract
We present compact integral representations for the calculation of two-loop anomalous dimensions for a generic class of soft functions that are defined in terms of two light-like Wilson lines. Our results are relevant for the resummation of Sudakov logarithms for e+e− event-shape variables and inclusive hadron-collider observables at next-to-next-to-leading logarithmic accuracy within Soft-Collinear Effective Theory (SCET). Our formalism applies to both SCET-1 and SCET-2 soft functions and we clarify the relation between the respective soft anomalous dimension and the collinear anomaly exponent. We confirm existing two-loop results for about a dozen dijet soft functions and obtain new predictions for the angularity event shape and the soft-drop jet-grooming algorithm.
Highlights
We present compact integral representations for the calculation of two-loop anomalous dimensions for a generic class of soft functions that are defined in terms of two light-like Wilson lines
Our formalism applies to both Soft-Collinear Effective Theory (SCET)-1 and SCET-2 soft functions and we clarify the relation between the respective soft anomalous dimension and the collinear anomaly exponent
We have developed a novel formalism for the calculation of two-loop soft anomalous dimensions that is relevant for processes with two hard, massless and colour-charged partons
Summary
Scattering cross sections at large momentum transfer Q are often sensitive to large logarithmic corrections that spoil the convergence of the perturbative expansion in the strong coupling αs(Q) 1. By computing corrections of the form αs(Q)L ∼ 1 to all orders, where L 1 represents the large logarithm, the theoretical predictions can be systematically improved with respect to a fixed-order expansion This reorganisation of the perturbative series – commonly called resummation – can be achieved on the basis of factorisation theorems which disentangle the relevant scales of the scattering process to all orders in perturbation theory. The soft functions that enter the factorisation theorem (1) are given by vacuum matrix elements of a configuration of Wilson lines that reflect the structure of the scattering process at the Born level For SCET-2 observables, on the other hand, the jet and soft scales are of the same order and additional techniques like the collinear anomaly [10] or the rapidity RG [11] are needed to resum the logarithmic corrections.
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