  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-beta_0 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.
