Abstract
The resummation of logarithmically-enhanced terms to all perturbative orders is a prerequisite for many studies of QCD final-states. Until now such resummations have always been performed by hand, for a single observable at a time. In this Letter we present a general ‘master’ resummation formula (and applicability conditions), suitable for a large class of observables. This makes it possible for next-to-leading logarithmic resummations to be carried out automatically given only a computer routine for the observable. To illustrate the method we present the first next-to-leading logarithmic resummed prediction for an event shape in hadronic dijet production.
Highlights
QCD is unique among the theories of the standard model in that both strong and weak coupling regimes are relevant to modern collider experiments
Final states are a privileged laboratory for QCD studies: perturbative investigations have for example led to many measurements of the strong coupling, αs [1], and to tests of the underlying SU(3) group structure of the theory [2]; and final-states are proving to be a rich source of information on the poorly understood relation between perturbative, partonic predictions and the non-perturbative, hadronic degrees of freedom observed in practice [3, 4]
In this letter we have provided the elements needed for a novel, automated approach to general next-to-leading logarithmic (NLL) resummation, for the case of continuously global, exponentiable (n+1)-jet final-state observables in the n-jet limit
Summary
QCD is unique among the theories of the standard model in that both strong and weak coupling regimes are relevant to modern collider experiments. Fixed-order perturbative calculations, which involve a small number of additional partons, are suitable for describing large departures from the Born-event energy flow pattern, in which the extra partons are energetic and at large angles. Such configurations are rare, their likelihood being suppressed by powers of the perturbative coupling. The next-to-leading logarithmic (NLL) terms, αsn lnn 1/v, factorise and can be calculated to all orders [5] To obtain this NLL accuracy one needs a detailed understanding of the observable’s analytical properties and of the corresponding phase-space integrals. The final answer for some specific observable will be expressed in terms of straightforwardly (and automatically) identifiable characteristics of the observable
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