Dispersive approach in Sudakov resummation

The dispersive approach to power corrections is given a precise implementation, valid beyond single gluon exchange, in the framework of Sudakov resummation for deep inelastic scattering and the Drell-Yan process. It is shown that the assumption of infrared finite Sudakov effective couplings implies the universality of the corresponding infrared fixed points. This property is closely tied to the universality of the virtual contributions to space-like and time-like processes, encapsulated in the second logarithmic derivative of the quark form factor.Comment: 3 pages, talk given at Quark Confinement and the Hadron Spectrum 7, Ponta Delgada, Azores, Portugal, 2-7 Sep 2006, LaTeX, uses aip-6s.clo, aipproc.cls and aipxfm.sty (included

Conformal window and Landau singularities

A physical characterization of Landau singularities is emphasized, which should trace the lower boundary N_f^* of the conformal window in QCD and supersymmetric QCD. A natural way to disentangle ``perturbative'' from ``non-perturbative'' contributions below N_f^* is suggested. Assuming an infrared fixed point is present in the perturbative part of the QCD coupling even in some range below N_f^* leads to the condition gamma(N_f^*)=1, where gamma is the critical exponent. This result is incompatible with the existence of an analogue of Seiberg free dual magnetic phase in QCD. Using the Banks-Zaks expansion, one gets 4<N_f^*<6. The low value of N_f^* gives some justification to the infrared finite coupling approach to power corrections, and suggests a way to compute their normalization from perturbative input. If the perturbative series are still asymptotic in the negative coupling region, the presence of a negative ultraviolet fixed point is required both in QCD and in supersymmetric QCD to preserve causality within the conformal window. Some evidence for such a fixed point in QCD is provided through a modified Banks-Zaks expansion. Conformal window amplitudes, which contain power contributions, are shown to remain generically finite in the N_f=-\infty one-loop limit in simple models with infrared finite perturbative coupling.Comment: 35 pages, 1 figure, JHEP style. A new section added to point out the results give some justification to the infrared finite coupling approach to power corrections, and suggest a way to compute their normalization from perturbative inpu

Large-x structure of physical evolution kernels in Deep Inelastic Scattering

The modified evolution equation for parton distributions of Dokshitzer, Marchesini and Salam is extended to non-singlet Deep Inelastic Scattering coefficient functions and the physical evolution kernels which govern their scaling violation. Considering the x->1 limit, it is found that the leading next-to-eikonal logarithmic contributions to the physical kernels at any loop order can be expressed in term of the one-loop cusp anomalous dimension, a result which can presumably be extended to all orders in (1-x), and has eluded so far threshold resummation. Similar results are shown to hold for fragmentation functions in semi-inclusive e+ e- annihilation. Gribov-Lipatov relation is found to be satisfied by the leading logarithmic part of the modified physical evolution kernels.Comment: 12 pages; version 2: eq.(4.6) and comment below corrected (main results unchanged), section on fragmentation functions added; version 3: new results added: all-order relation in section 3.5, O(1-x) terms adressed in section 5; version 4: incorrect suggestion on Gribov-Lipatov reciprocity removed; version 5: slight extension of the version to be published in Physics Letters B, contains a discussion of O((1-x)^2) terms and added reference

Evidence for infrared finite coupling in Sudakov resummation

New arguments are presented in favor of the infrared finite coupling approach to power corrections in the context of Sudakov resummation. The more regular infrared behavior of some peculiar combinations of Sudakov anomalous dimensions, free of Landau singularities at large Nf, is pointed out. A general conflict between the infrared finite coupling and infrared renormalon approaches to power corrections is explained, and a possible resolution is proposed, which makes use of the arbitrariness of the choice of constant terms in the Sudakov exponent. A simple ansatz for a `universal' non-perturbative Sudakov effective coupling at large Nf emerges naturally from these considerations. An alternative evidence for an infrared finite {\em perturbative} effective coupling in the Drell-Yan process at large Nf (albeit at odds with the infrared renormalon argument) is found within the framework of Sudakov resummation for eikonal cross sections of Laenen, Sterman and Vogelsang.Comment: 5 pages; version 2: one sentence and one equation added (to appear in the Proceedings of the FRIF Workshop on First Principles Non-Perturbative QCD of Hadron Jets (Paris, 12-14 January 2006); version 3: additional material, comments and references (to appear in Physical Review D (Rapid Communication)

Infrared finite coupling in Sudakov resummation: the precise set-up

I show that Sudakov resummation takes a transparent form if one deals with the second logarithmic derivative of the short distance coefficient functions for deep inelastic scattering and the Drell-Yan process. A uniquely defined Sudakov exponent emerges, and the constant terms not included in the exponent are conjectured to be given by the second logarithmic derivative of the massless quark form factor. The precise framework for the implementation of the dispersive approach to power corrections is set-up, yielding results in agreement with infrared renormalon expectations, but which are not tied to the single (dressed) gluon exchange approximation. Indications for a Banks-Zaks type of perturbative fixed point in the Sudakov effective coupling at low N_f are pointed out. Existence of a fixed point in the Sudakov coupling is argued to imply its universality.Comment: 5 pages, improved version of hep-ph/0606033, new result on universality of power corrections; version 2: added material, comments and references (to appear in Physical Review D (Rapid Communication)); version 3: a few misprints corrected, one reference added (journal version