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Abstract: We present a general all-order formulation of Sudakov resummation in QCD interms of dispersion integrals. We show that the Sudakov exponent can be writtenas a dispersion integral over spectral density functions, weighted bycharacteristic functions that encode information on power corrections. Thecharacteristic functions are defined and computed analytically in thelarge-beta 0 limit. The spectral density functions encapsulate the non-Abeliannature of the interaction. They are defined by the time-like discontinuity ofspecific effective charges couplings that are directly related to thefamiliar Sudakov anomalous dimensions and can be computed order-by-order inperturbation theory. The dispersive approach provides a realization of DressedGluon Exponentiation, where Sudakov resummation is enhanced by an internalresummation of running-coupling corrections. We establish all-order relationsbetween the scheme-invariant Borel formulation and the dispersive one, andaddress the difference in the treatment of power corrections. We find that inthe context of Sudakov resummation the infrared-finite-coupling hypothesis isof special interest because the relevant coupling can be uniquely identified toany order, and may have an infrared fixed point already at the perturbativelevel. We prove that this infrared limit is universal: it is determined by thecusp anomalous dimension. To illustrate the formalism we discuss a few examplesincluding B-meson decay spectra, deep inelastic structure functions andDrell-Yan or Higgs production.



Autor: Einan Gardi, Georges Grunberg

Fuente: https://arxiv.org/



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