946 research outputs found
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 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 -annihilation, whose values, , are
proportional to jet masses in the two-jet limit, . 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 .
They organize all power corrections of the form , for arbitrary ,
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
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