|Title: ||A Dispersive approach to Sudakov resummation.|
|Authors: ||Gardi, Einan|
|Issue Date: ||Sep-2007|
|Publisher: ||High Energy Physics, Cavendish Laboratory, University of Cambridge|
|Series/Report no.: ||Cavendish-HEP-07-06|
|Abstract: ||We present a general all–order formulation of Sudakov resummation in QCD in terms
of dispersion integrals. We show that the Sudakov exponent can be written as a dispersion
integral over spectral density functions, weighted by characteristic functions that
encode information on power corrections. The characteristic functions are defined and
computed analytically in the large–β0 limit. The spectral density functions encapsulate
the non-Abelian nature of the interaction. They are defined by the time–like discontinuity
of specific effective charges (couplings) that are directly related to the familiar Sudakov
anomalous dimensions and can be computed order–by–order in perturbation theory. The
dispersive approach provides a realization of Dressed Gluon Exponentiation, where Sudakov
resummation is enhanced by an internal resummation of running–coupling corrections.
We establish all–order relations between the scheme–invariant Borel formulation
and the dispersive one, and address the difference in the treatment of power corrections.
We find that in the context of Sudakov resummation the infrared–finite–coupling hypothesis
is of special interest because the relevant coupling can be uniquely identified to any
order, and may have an infrared fixed point already at the perturbative level. We prove
that this infrared limit is universal: it is determined by the cusp anomalous dimension.
To illustrate the formalism we discuss a few examples including B-meson decay spectra,
deep inelastic structure functions and Drell–Yan or Higgs production.|
|Appears in Collections:||Scholarly works - High Energy Physics|
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