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

Systematic Visuo-Textual Analysis: A Framework for Analysing Visual and Textual Data

As qualitative research has evolved, researchers now often combine interviews with the production of photographs, artefacts, collages, maps or drawings and the like. However, in practice, the artefacts produced are used to eliciting experiences and stimulating conversations rather than as data, per se, which is often due to the lack of guidelines for how to deal with the artefacts as data in a systematic analytical process. In this article, we present the Systematic Visuo-Textual Analysis, a framework developed to provide much-needed support for qualitative researchers in analysing artefacts in combination with interviews. Drawing on existing frameworks for visual and textual analysis the focus of this framework is to analyse visual and textual datasets separately and in conjunction with one another through several levels of interpretation from noticing descriptive elements and focussing on specific linguistic and artistic elements through to developing conceptual themes. Drawing on examples from our own research, we will demonstrate the practical application of the Systematic Visuo-Textual Analysis

Using LEGO® To Understand Emotion Work In Doctoral Education

In this paper, we present a project of the University of Kent Graduate School that utilises this paradox of playfulness and creativity. LEGO® is used in workshops to explore doctoral students’ emotions around the complex and solitary experience of a PhD research. We argue LEGO® is uniquely generative for exploring emotion work. After a brief overview of the background and context to the doctoral training workshop, we provide a brief review of emotion work. We then describe the LEGO® workshop we developed for our students, before explaining our approach to data collection and analysis. We then present our results, using verbatim statements from conversations with students around their LEGO® models. We present the interconnected building elements of height, walls and positioning, which are particularly impactful in highlighting the emotion work with LEGO® models. We connect the findings to a brief discussion in relation to the literature around emotion work. We have found that LEGO®’ bricks structure, solidity, and variety ensure its openness to metaphorical investment and promote the creation of narratives. Thus, building LEGO® models enabled participants to engage creatively with routinization of practices and emotion work, as well their positive support networks. We conclude with final thoughts on the value of LEGO® and steps for further developing the existing workshop

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

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

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.

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.