15 research outputs found
Light--like Wilson loops and gauge invariance of Yang--Mills theory in 1+1 dimensions
A light-like Wilson loop is computed in perturbation theory up to for pure Yang--Mills theory in 1+1 dimensions, using Feynman and
light--cone gauges to check its gauge invariance. After dimensional
regularization in intermediate steps, a finite gauge invariant result is
obtained, which however does not exhibit abelian exponentiation. Our result is
at variance with the common belief that pure Yang--Mills theory is free in 1+1
dimensions, apart perhaps from topological effects.Comment: 10 pages, plain TeX, DFPD 94/TH/
Exponentiation of the Drell-Yan cross section near partonic threshold in the DIS and MSbar schemes
It has been observed that in the DIS scheme the refactorization of the
Drell-Yan cross section leading to exponentiation of threshold logarithms can
also be used to organize a class of constant terms, most of which arise from
the ratio of the timelike Sudakov form factor to its spacelike counterpart. We
extend this exponentiation to include all constant terms, and demonstrate how a
similar organization may be achieved in the MSbar scheme. We study the
relevance of these exponentiations in a two-loop analysis.Comment: 20 pages, JHEP style, no figure
Resummed heavy quark production cross sections to next-to-leading logarithm
We study how next-to-leading logarithms modify predictions from leading
logarithmic soft-gluon resummation in the heavy quark production cross section
near threshold. Numerical results are presented for top quark production at the
Fermilab Tevatron and bottom quark production at fixed-target energies.Comment: 35 pages LaTeX, 10 figures, some corrections to the text, discussion
of scale and scheme dependence added, tables added, figures updated, accepted
for publication in Phys. Rev.
Instanton Contribution to the Quark Form Factor
The nonperturbative effects in the quark form factor are considered in the
Wilson loop formalism. The properties of the Wilson loops with cusp
singularities are studied taking into account the perturbative and
nonperturbative contributions, where the latter are considered within the
framework of the instanton liquid model. For the integration path corresponding
to this form factor -- the angle with infinite sides -- the explicit expression
for the vacuum expectation value of the Wilson operator is found to leading
order. The calculations are performed in the weak-field limit for the instanton
vacuum contribution and compared with the one- and two-loop order results for
the perturbative part. It is shown that the instantons produce the powerlike
corrections to the perturbative result, which are comparable in magnitude with
the perturbative part at the scale of order of the inverse average instanton
size. It is demonstrated that the instanton contributions to the quark form
factor are exponentiated to high orders in the small instanton density
parameter.Comment: Version coincident with the journal publication. LaTeX, 15 pages, 1
figur
The Extraction of from Inclusive B Decays and the Resummation of End Point Logs
In this paper we discuss the theoretical difficulties in extracting
using the data from inclusive B decays. Specifically, we address the issue of
the end point singularities. We perform the resummation of both the leading and
next to leading end point logs and include the leading corrections to the hard
scattering amplitude. We find that the resummation is a effect in
the end point region where the resummation is valid. Furthermore, the resummed
sub-leading logs dominate the resummed double logs. The consequences of this
result for a model independent extraction of the mixing angle are
explored.Comment: Published Version. Minor changes in discussion. 31 pages, 4 figure
Instanton Corrections to Quark Form Factor at Large Momentum Transfer
Within the Wilson integral formalism, we discuss the structure of
nonperturbative corrections to the quark form factor at large momentum transfer
analyzing the infrared renormalon and instanton effects. We show that the
nonperturbative effects determine the initial value for the perturbative
evolution of the quark form factor and attribute their general structure to the
renormalon ambiguities of the perturbative series. It is demonstrated that the
instanton contributions result in the finite renormalization of the
next-to-leading perturbative result and numerically are characterized by a
small factor reflecting the diluteness of the QCD vacuum within the instanton
liquid model.Comment: Version coincident with the journal publication, 9 pages; REVTe
Drell-Yan production at small q_T, transverse parton distributions and the collinear anomaly
Using methods from effective field theory, an exact all-order expression for
the Drell-Yan cross section at small transverse momentum is derived directly in
q_T space, in which all large logarithms are resummed. The anomalous dimensions
and matching coefficients necessary for resummation at NNLL order are given
explicitly. The precise relation between our result and the
Collins-Soper-Sterman formula is discussed, and as a by-product the previously
unknown three-loop coefficient A^(3) is obtained. The naive factorization of
the cross section at small transverse momentum is broken by a collinear
anomaly, which prevents a process-independent definition of x_T-dependent
parton distribution functions. A factorization theorem is derived for the
product of two such functions, in which the dependence on the hard momentum
transfer is separated out. The remainder factors into a product of two
functions of longitudinal momentum variables and x_T^2, whose
renormalization-group evolution is derived and solved in closed form. The
matching of these functions at small x_T onto standard parton distributions is
calculated at O(alpha_s), while their anomalous dimensions are known to three
loops.Comment: 32 pages, 2 figures; version to appear in Eur. Phys. J.
The B-Meson Distribution Amplitude in QCD
The B-meson distribution amplitude is calculated using QCD sum rules. In
particular we obtain an estimate for the integral relevant to exclusive
B-decays \lambda_B = 460 \pm 110 MeV at the scale 1 GeV. A simple QCD-motivated
parametrization of the distribution amplitude is suggested.Comment: 17 pages, 8 figures, Latex styl
Scaling Rule for Nonperturbative Radiation in a Class of Event Shapes
We discuss nonperturbative radiation for a recently introduced class of
infrared safe event shape weights, which describe the narrow-jet limit.
Starting from next-to-leading logarithmic (NLL) resummation, we derive an
approximate scaling rule that relates the nonperturbative shape functions for
these weights to the shape function for the thrust. We argue that the scaling
reflects the boost invariance implicit in NLL resummation, and discuss its
limitations. In the absence of data analysis for the new event shapes, we
compare these predictions to the output of the event generator PYTHIA.Comment: 23 pages, 3 figures, uses JHEP3.cls (included); v2 - version to
appear in JHE
Recoil and Threshold Corrections in Short-distance Cross Sections
We identify and resum corrections associated with the kinematic recoil of the
hard scattering against soft-gluon emission in single-particle inclusive cross
sections. The method avoids double counting and conserves the flow of partonic
energy. It reproduces threshold resummation for high-p_T single-particle cross
sections, when recoil is neglected, and Q_T-resummation at low Q_T, when
higher-order threshold logarithms are suppressed. We exhibit explicit resummed
cross sections, accurate to next-to-leading logarithm, for electroweak
annihilation and prompt photon inclusive cross sections.Comment: minor modifications of the text, some references added. 51 pages,
LaTeX, 6 figures as eps file