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 ${\cal O} (g^4)$ 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 VubV_{ub} from Inclusive B Decays and the Resummation of End Point Logs

In this paper we discuss the theoretical difficulties in extracting $V_{ub}$ 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 $20\%-50\%$ 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 $V_{ub}$ 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