On near forward high energy scattering in QCD

We consider elastic quark-quark scattering at high energy and fixed transferred momentum. Performing factorization of soft gluon exchanges into Wilson lines vacuum expectation values and studying their properties, we find that the asymptotics of the scattering amplitude is controlled by the renormalization properties of the so called cross singularities of Wilson loops. Using this fact, we evaluate the scattering amplitude and show that its asymptotics is determined by the properties of the $2\times 2$ matrix of anomalous dimensions which appears after one renormalizes the cross singularities of Wilson loops. A generalization to the case of quark-antiquark and gluon-gluon elastic scattering is discussed.Comment: LaTeX style, 13 pages, 4 figures (included

Infrared Factorization, Wilson Lines and the Heavy Quark Limit

It is shown that, in QCD, the same universal function \Gamma_{cusp}(\vartheta, \alpha_\s) determines the infrared behaviour of the on-shell quark form factor, the velocity-dependent anomalous dimension in the heavy quark effective field theory (HQET) and the renormalization properties of the vacuum averaged Wilson lines with a cusp. It is demonstrated that a combined use of the methods developed in the relevant different branches of quantum field theory essentially facilitates the all-order study of the asymptotic and analytic properties of this function.Comment: 10 page

Energy flow in QCD and event shape functions

Hadronization corrections to the thrust and related event shape distributions in the two-jet kinematical region of e+e- annihilation are summarized by nonperturbative shape functions. The moments of shape functions are given by universal matrix elements in QCD, which describe the energy flow in QCD final states. We show how the nonperturbative structure of these matrix elements may be inferred from resummed perturbation theory and Lorentz invariance. This analysis suggests the same functional forms for the shape functions as were found in phenomenological studies, and sheds light on the physical significance of the parameters that characterize these functions.Comment: 15 pages, LaTeX, 2 figure

Power corrections to event shapes and factorization

We study power corrections to the differential thrust, heavy mass and related event shape distributions in $e^+e^-$-annihilation, whose values, $e$, are proportional to jet masses in the two-jet limit, $e\to 0$. The factorization properties of these differential distributions imply that they may be written as convolutions of nonperturbative "shape" functions, describing the emission of soft quanta by the jets, and resummed perturbative cross sections. The infrared shape functions are different for different event shapes, and depend on a factorization scale, but are independent of the center-of-mass energy $Q$. They organize all power corrections of the form $1/(eQ)^n$, for arbitrary $n$, and carry information on a class of universal matrix elements of the energy-momentum tensor in QCD, directly related to the energy-energy correlations.Comment: 15 pages, LaTeX style, 1 figure embedded with epsf.st

Designing Gapped Soft Functions for Jet Production

Distributions in jet production often depend on a soft function, S, which describes hadronic radiation between the jets. Near kinematic thresholds S encodes nonperturbative information, while far from thresholds S can be computed with an operator product expansion (OPE). We design soft functions for jets that serve this dual purpose, reducing to the perturbative result in the OPE region and to a consistent model in the nonperturbative region. We use the MSbar scheme, and in both regions S displays the appropriate renormalization group scale dependence. We point out that viable soft function models should have a gap associated with the minimum hadronic energy deposit. This gap is connected to the leading O(Lambda_QCD) renormalon ambiguity in jet event shapes. By defining the gap in a suitable scheme we demonstrate that the leading renormalon can be eliminated. This improves the convergence of perturbative results, and also the stability by which non-perturbative parameters encode the underlying soft physics.Comment: 17 pages, 5 figure

On power corrections to the event shape distributions in QCD

We study power corrections to the differential thrust, heavy jet mass and C-parameter distributions in the two-jet kinematical region in e^+e^- annihilation. We argue that away from the end-point region, e>> \Lambda_{QCD}/Q, the leading 1/Q-power corrections are parameterized by a single nonperturbative scale while for e \Lambda_{QCD}/Q one encounters a novel regime in which power corrections of the form 1/(Qe)^n have to be taken into account for arbitrary n. These nonperturbative corrections can be resummed and factor out into a universal nonperturbative distribution, the shape function, and the differential event shape distributions are given by convolution of the shape function with perturbative cross-sections. Choosing a simple ansatz for the shape function we demonstrate a good agreement of the obtained QCD predictions for the distributions and their lowest moments with the existing data over a wide energy interval.Comment: 18 pages, LaTeX style, 4 figure

Dressed gluon exponentiation

Perturbative and non-perturbative aspects of differential cross-sections close to a kinematic threshold are studied applying ``dressed gluon exponentiation'' (DGE). The factorization property of soft and collinear gluon radiation is demonstrated using the light-cone axial gauge: it is shown that the singular part of the squared matrix element for the emission of an off-shell gluon off a nearly on-shell quark is universal. We derive a generalized splitting function that describes the emission probability and show how Sudakov logs emerge from the phase-space boundary where the gluon transverse momentum vanishes. Both soft and collinear logs associated with a single dressed gluon are computed through a single integral over the running-coupling to any logarithmic accuracy. The result then serves as the kernel for exponentiation. The divergence of the perturbative series in the exponent indicates specific non-perturbative corrections. We identify two classes of observables according to whether the radiation is from an initial-state quark, as in the Drell-Yan process, or a final-state quark, forming a jet with a constrained invariant mass, as in fragmentation functions, event-shape variables and deep inelastic structure functions.Comment: 28 page