Abstract
Event shapes are classical tools for the determination of the strong coupling and for the study of hadronization effects in electron-positron annihilation. In the context of analytical studies, hadronization corrections take the form of power-suppressed contributions to the cross section, which can be extracted from the perturbative ambiguity of Borel-resummed distributions. We propose a simplified version of the well-established method of Dressed Gluon Exponentiation (DGE), which we call Eikonal DGE (EDGE), which determines all dominant power corrections to event shapes by means of strikingly elementary calculations. We believe our method can be generalized to hadronic event shapes and jet shapes of relevance for LHC physics.
Highlights
Where μf is a perturbative factorization scale, to be traded for the strong interaction scale Λ
We propose a simplified version of the well-established method of Dressed Gluon Exponentiation (DGE), which we call Eikonal DGE (EDGE), which determines all dominant power corrections to event shapes by means of strikingly elementary calculations
In this article we undertake the calculation of the Borel function that was defined in eq (2.5) for three very well known event shape variables: (a) the thrust [41,42,43,44], (b) the C-parameter [45,46,47,48] and, (c) the angularities [49,50,51], and we propose a simplified version of the well-established method of Dressed Gluon Exponentiation (DGE), which we call Eikonal DGE (EDGE), which determines all dominant power corrections to event shapes by means of strikingly elementary calculations
Summary
The cornerstone of eq (2.1) is the characteristic function F (e, ξ), which is the one-loop event shape distribution with a non-vanishing gluon virtuality k2 [25, 39],. The Borel function B(e, u) has a simple structure in the u plane, without renormalon singularities. Renormalon poles are generated when the single dressed gluon distribution is exponentiated via a Laplace transform [31]. Matrix element leads to the exponentiation of the logarithmically enhanced terms in the Laplace space and the resummed cross section is given by [32, 33],. Bνe (u), where the Borel function in the Laplace space, Bνe(u), is defined as (2.8). This exponentiation effectively resums both large Sudakov logarithms and power corrections in the two-jet region
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