Abstract
In this article we show how the resummation of infrared and collinear logarithms within Soft-Collinear Effective Theory (SCET) can be formulated in a way that makes it suitable for a Monte-Carlo implementation. This is done by applying the techniques developed for automated resummation using the branching formalism, which have resulted in the general resummation approach CAESAR/ARES. This work builds a connection between the two resummation approaches, and paves the way to automated resummation in SCET. As a case study we consider the resummation of the thrust distribution in electron-positron collisions at next-to-leading logarithm (NLL). The generalization of the results presented here to more complicated observables as well as to higher logarithmic orders will be considered in a future publication.
Highlights
In this paper we will study the 2-jet cross section at lepton colliders, that we denote as
In this article we show how the resummation of infrared and collinear logarithms within Soft-Collinear Effective Theory (SCET) can be formulated in a way that makes it suitable for a Monte-Carlo implementation
In this work we have shown how to formulate a numerical approach to resummation in SCET using the example of next-to-leading logarithm (NLL) resummation of the thrust distribution
Summary
The general strategy of the CAESAR/ARES approach is to write the cross section for a rIRC safe observable v into the cross section of a simpler observable vs which has the same logarithmic structure as v at lowest order, and a transfer function that accounts for the difference between the two observables v and vs. The latter is formulated in such a way that it can be evaluated efficiently using Monte Carlo methods. This can be achieved, for instance, by using the soft-collinear approximation of the full observable V = Vsc instead of its full form V This besides simplifying further the computation of Σmax, guarantees that this ingredient can be directly used for the resummation of all observables that share the same soft-collinear limit for a single emission, which defines a much broader class than the first definition given above. For the two ratios required in the transfer function eq (2.5), the argument of the numerator and denominator scale with the observable v This implies that to compute the ratio to a given logarithmic accuracy, one needs the numerator and denominator at one logarithmic order lower [10, 13]. We perform the calculation at NLL for the thrust event shape
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