Neurally Implementable Semantic Networks

We propose general principles for semantic networks allowing them to be implemented as dynamical neural networks. Major features of our scheme include: (a) the interpretation that each node in a network stands for a bound integration of the meanings of all nodes and external events the node links with; (b) the systematic use of nodes that stand for categories or types, with separate nodes for instances of these types; (c) an implementation of relationships that does not use intrinsically typed links between nodes.Comment: 32 pages, 12 figure

Renormalization-group anatomy of transverse-momentum dependent parton distribution functions in QCD

The ultraviolet and rapidity divergences of transverse-momentum dependent parton distribution functions with lightlike and transverse gauge links is studied, also incorporating a soft eikonal factor. We find that in the light-cone gauge with $q^-$-independent pole prescriptions extra divergences appear which amount, at one-loop, to a cusp-like anomalous dimension. We show that such contributions are absent when the Mandelstam-Leibbrandt prescription is used. In the first case, the soft factor cancels the anomalous-dimension defect, while in the second case its ultraviolet-divergent part reduces to unity.Comment: 10 pages, 3 figures; needs ws-mpla-hep.cls (supplied). Talk presented by the first author at Workshop on "Recent Advances in Perturbative QCD and Hadronic Physics", 20--25 July 2009, ECT*, Trento, Italy, in Honor of Prof. Anatoly Efremov's 75th birthda

Fully Unintegrated Parton Correlation Functions and Factorization in Lowest Order Hard Scattering

Motivated by the need to correct the potentially large kinematic errors in approximations used in the standard formulation of perturbative QCD, we reformulate deeply inelastic lepton-proton scattering in terms of gauge invariant, universal parton correlation functions which depend on all components of parton four-momentum. Currently, different hard QCD processes are described by very different perturbative formalisms, each relying on its own set of kinematical approximations. In this paper we show how to set up formalism that avoids approximations on final-state momenta, and thus has a very general domain of applicability. The use of exact kinematics introduces a number of significant conceptual shifts already at leading order, and tightly constrains the formalism. We show how to define parton correlation functions that generalize the concepts of parton density, fragmentation function, and soft factor. After setting up a general subtraction formalism, we obtain a factorization theorem. To avoid complications with Ward identities the full derivation is restricted to abelian gauge theories; even so the resulting structure is highly suggestive of a similar treatment for non-abelian gauge theories.Comment: 44 pages, 69 figures typos fixed, clarifications and second appendix adde

Next-to-Leading Order Hard Scattering Using Fully Unintegrated Parton Distribution Functions

We calculate the next-to-leading order fully unintegrated hard scattering coefficient for unpolarized gluon-induced deep inelastic scattering using the logical framework of parton correlation functions developed in previous work. In our approach, exact four-momentum conservation is maintained throughout the calculation. Hence, all non-perturbative functions, like parton distribution functions, depend on all components of parton four-momentum. In contrast to the usual collinear factorization approach where the hard scattering coefficient involves generalized functions (such as Dirac $\delta$-functions), the fully unintegrated hard scattering coefficient is an ordinary function. Gluon-induced deep inelastic scattering provides a simple illustration of the application of the fully unintegrated factorization formalism with a non-trivial hard scattering coefficient, applied to a phenomenologically interesting case. Furthermore, the gluon-induced process allows for a parameterization of the fully unintegrated gluon distribution function.Comment: 22 pages, Typos Fixed, Reference Added, Minor Clarification Adde

Relative distributions of W's and Z's at low transverse momenta

Despite large uncertainties in the $W^\pm$ and $Z^0$ transverse momentum ($q_T$) distributions for q_T\lsim 10 GeV, the ratio of the distributions varys little. The uncertainty in the ratio of $W$ to $Z$ $q_T$ distributions is on the order of a few percent, independent of the details of the nonperturbative parameterization.Comment: 13 pages in revtex, 5 postscript figures available upon request, UIOWA-94-0

Dilepton production near partonic threshold in transversely polarized proton-antiproton collisions

It has recently been suggested that collisions of transversely polarized protons and antiprotons at the GSI could be used to determine the nucleon's transversity densities from measurements of the double-spin asymmetry for the Drell-Yan process. We analyze the role of higher-order perturbative QCD corrections in this kinematic regime, in terms of the available fixed-order contributions as well as of all-order soft-gluon resummations. We find that the combined perturbative corrections to the individual unpolarized and transversely polarized cross sections are large. We trace these large enhancements to soft gluon emission near partonic threshold, and we suggest that with a physically-motivated cut-off enhancements beyond lowest order are moderated relative to resummed perturbation theory, but still significant. The unpolarized dilepton cross section for the GSI kinematics may therefore provide information on the relation of perturbative and nonperturbative dynamics in hadronic scattering. The spin asymmetry turns out to be rather robust, relatively insensitive to higher orders, resummation, and the cut-offs.Comment: 23 pages, 19 figures as eps. Some discussion and references added. Final version to appear in Phys. Rev.

Transverse momentum dependent parton distribution and fragmentation functions with QCD evolution

We assess the current phenomenological status of transverse momentum dependent (TMD) parton distribution functions (PDFs) and fragmentation functions (FFs) and study the effect of consistently including perturbative QCD (pQCD) evolution. Our goal is to initiate the process of establishing reliable, QCD-evolved parametrizations for the TMD PDFs and TMD FFs that can be used both to test TMD factorization and to search for evidence of the breakdown of TMD factorization that is expected for certain processes. In this article, we focus on spin-independent processes because they provide the simplest illustration of the basic steps and can already be used in direct tests of TMD factorization. Our calculations are based on the Collins-Soper-Sterman (CSS) formalism, supplemented by recent theoretical developments which have clarified the precise definitions of the TMD PDFs and TMD FFs needed for a valid TMD-factorization theorem. Starting with these definitions, we numerically generate evolved TMD PDFs and TMD FFs using as input existing parametrizations for the collinear PDFs, collinear FFs, nonperturbative factors in the CSS factorization formalism, and recent fixed-scale fits. We confirm that evolution has important consequences, both qualitatively and quantitatively, and argue that it should be included in future phenomenological studies of TMD functions. Our analysis is also suggestive of extensions to processes that involve spin-dependent functions such as the Boer-Mulders, Sivers, or Collins functions, which we intend to pursue in future publications. At our website, we have made available the tables and calculations needed to obtain the TMD parametrizations presented herein. © 2011 American Physical Society

Transverse momentum dependent parton distributions in a light-cone quark model

The leading twist transverse momentum dependent parton distributions (TMDs) are studied in a light-cone description of the nucleon where the Fock expansion is truncated to consider only valence quarks. General analytic expressions are derived in terms of the six amplitudes needed to describe the three-quark sector of the nucleon light-cone wave function. Numerical calculations for the T-even TMDs are presented in a light-cone constituent quark model, and the role of the so-called pretzelosity is investigated to produce a nonspherical shape of the nucleon.Comment: references added and typos corrected; version to appear in Phys. Rev.

Algebraic renormalization of supersymmetric gauge theories with dimensionful parameters

It is usually believed that there are no perturbative anomalies in supersymmetric gauge theories beyond the well-known chiral anomaly. In this paper we revisit this issue, because previously given arguments are incomplete. Specifically, we rule out the existence of soft anomalies, i.e., quantum violations of supersymmetric Ward identities proportional to a mass parameter in a classically supersymmetric theory. We do this by combining a previously proven theorem on the absence of hard anomalies with a spurion analysis, using the methods of Algebraic Renormalization. We work in the on-shell component formalism throughout. In order to deal with the nonlinearity of on-shell supersymmetry transformations, we take the spurions to be dynamical, and show how they nevertheless can be decoupled.Comment: Final version, typoes fixed. Revtex, 48 page