Perturbative and non-perturbative aspects of moments of the thrust distribution in e+e- annihilation

Resummation and power-corrections play a crucial role in the phenomenology of event-shape variables like the thrust T. Previous investigations showed that the perturbative contribution to the average thrust is dominated by gluons of small invariant mass, of the order of 10% of Q, where Q is the center-of-mass energy. The effect of soft gluons is also important, leading to a non-perturbative 1/Q correction. These conclusions are based on renormalon analysis in the single dressed gluon (SDG) approximation. Here we analyze higher moments of the thrust distribution using a similar technique. We find that the characteristic gluon invariant mass contributing to increases with m. Yet, for m=2 this scale is quite low, around 27% of Q, and therefore renormalon resummation is still very important. On the other hand, the power-correction to from a single soft gluon emission is found to be highly suppressed: it scales as 1/Q^3. In practice, and higher moments depend also on soft gluon emission from configurations of three hard partons, which may lead to alpha_s(Q^2)/Q power-corrections. This issue is yet to be investigated.Comment: 27 pages including 3 postscript figures; final version - to appear in JHEP; note the extended discussion in the conclusion sectio

Inclusive distributions near kinematic thresholds.

The main challenge in computing inclusive cross sections and decay spectra in QCD is posed by kinematic thresholds. The threshold region is characterized by stringent phase–space constraints that are reflected in large perturbative corrections due to soft and collinear radiation as well as large non-perturbative effects. Major progress in addressing this problem was made in recent years by Dressed Gluon Exponentiation (DGE), a formalism that combines Sudakov and renormalon resummation in moment space. DGE has proven effective in extending the range of applicability of perturbation theory well into the threshold region and in identifying the relevant non-perturbative corrections. Here we review the method from a general perspective using examples from deep inelastic structure functions, event– shape distributions, heavy–quark fragmentation and inclusive decay spectra. A special discussion is devoted to the applications of DGE to radiative and semileptonic B decays that have proven valuable for the interpretation of data from the B factories

Inclusive B decays from resummed perturbation theory.

I review the recent progress in computing inclusive B decay widths and spectra and its implications on the interpretation of measurements from the B factories. I discuss the inclusive charmless semileptonic decay, ¯B ! Xul¯ , which provides the most robust determination of the CKM parameter |Vub|, and the rare radiative decay, ¯B ! Xs , which constrains flavor violation beyond the Standard Model. I demonstrate that precise predictions for the experimentally–relevant branching fractions can be derived from resummed perturbation theory and explain the way in which the resummation further provides guidance in parametrizing non-perturbative Fermi–motion effects. Finally I address the comparison between theory and data and discuss future prospects

Infrared singularities in multi-leg scattering amplitudes

I discuss the state-of-the-art knowledge of long-distance singularities in multi-leg gauge-theory scattering amplitudes and report on an on-going calculation of the three-loop soft anomalous dimension through the renormalization of correlators of semi-infinite Wilson lines. I also discuss the non-Abelian exponentiation theorem that has been recently generalised to multiple Wilson lines and demonstrate its application in computing the soft anomalous dimension. Finally, I present recent results for multiple-gluon-exchange webs and discuss their analytic structure.Comment: 16 page, 5 figure

Soft and Collinear Radiation and Factorization in Perturbation Theory and Beyond

Power corrections to differential cross sections near a kinematic threshold are analysed by Dressed Gluon Exponentiation. Exploiting the factorization property of soft and collinear radiation, the dominant radiative corrections in the threshold region are resummed, yielding a renormalization-scale-invariant expression for the Sudakov exponent. The interplay between Sudakov logs and renormalons is clarified, and the necessity to resum the latter whenever power corrections are non-negligible is emphasized. The presence of power-suppressed ambiguities in the exponentiation kernel suggests that power corrections exponentiate as well. This leads to a non-perturbative factorization formula with non-trivial predictions on the structure of power corrections, which can be contrasted with the OPE. Two examples are discussed. The first is event-shape distributions in the two-jet region, where a wealth of precise data provides a strong motivation for the improved perturbative technique and an ideal situation to study hadronization. The second example is deep inelastic structure functions. In contrast to event shapes, structure functions have an OPE. However, since the OPE breaks down at large x, it does not provide a practical framework for the parametrization of power corrections. Performing a detailed analysis of twist 4 it is shown precisely how the twist-2 renormalon ambiguity eventually cancels out. This analysis provides a physical picture which substantiates the non-perturbative factorization conjecture.Comment: 11 pages, 6 postscript figures; talk presented at the XXXVII Rencontres de Moriond `QCD and high energy hadronic interactions', Les Arcs, France, and at the Workshop `Continuous Advances in QCD 2002/Arkadyfest', Minnesot

Inclusive B-decay spectra and IR renormalons.

I illustrate the role of infrared renormalons in computing inclusive B-decay spectra. I explain the relation between the leading ambiguity in the definition of Sudakov form factor exp(N /M) and that of the pole mass, and show how these ambiguities cancel out between the perturbative and non-perturbative components of the b-quark distribution in the meson

Resummation and power corrections by Dressed Gluon Exponentiation

Event-shape distributions in $e^+e^-$ annihilation offer a unique lab oratory for understanding perturbative and non-perturbative aspects of QCD. Dressed Gluon Exponentiation is a resummation method designed to evaluate differ ential cross sections close to a kinematic threshold and provide the basis for parametrization of power corrections. The method and its application in the case of the thrust and the heavy jet mass distributions in the two-jet region are briefly presented.Comment: 5 pages, 3 figures in ps, talk given at XXXI International Symposium on Multiparticle Dynamics, Sept 1-7, 2001, Datong China. URL http://ismd31.ccnu.edu.cn

Infrared singularities in QCD amplitudes

We review recent progress in determining the infrared singularity structure of on-shell scattering amplitudes in massless gauge theories. We present a simple ansatz where soft singularities of any scattering amplitude of massless partons, to any loop order, are written as a sum over colour dipoles, governed by the cusp anomalous dimension. We explain how this formula was obtained, as the simplest solution to a newly-derived set of equations constraining the singularity structure to all orders. We emphasize the physical ideas underlying this derivation: the factorization of soft and collinear modes, the special properties of soft gluon interactions, and the notion of the cusp anomaly. Finally, we briefly discuss potential multi-loop contributions going beyond the sum-over-dipoles formula, which cannot be excluded at present.Comment: 20 pages, 3 figures. To be published in the proceedings of 23rd Les Rencontres de Physique de la Vallee d'Aoste, La Thuile, Aosta Valley, Italy, 1 - 7 March 200