TMD Parton Distribution and Fragmentation Functions with QCD Evolution (1101.5057v2)

Abstract: 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, non-perturbative 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.

• The paper establishes a framework for evolving TMD PDFs and FFs using the CSS formalism, addressing rapidity divergences and non-perturbative contributions.
• It demonstrates that incorporating QCD evolution significantly alters TMD functions, as evidenced by detailed numerical analyses.
• The findings highlight the importance of evolved TMDs in refining theoretical predictions for processes like Drell–Yan, SIDIS, and e+e– collisions.

TMD Parton Distribution and Fragmentation Functions with QCD Evolution: A Summary

The paper "TMD Parton Distribution and Fragmentation Functions with QCD Evolution" by S. Mert Aybat and Ted C. Rogers provides a detailed investigation into the current understanding of transverse momentum dependent (TMD) parton distribution functions (PDFs) and fragmentation functions (FFs) with the inclusion of perturbative QCD (pQCD) evolution. The authors aim to establish a consistent framework for the evolution of TMD PDFs and TMD FFs and assess their implications in both theoretical and phenomenological contexts.

Background and Motivation

The framework of TMD-factorization extends the conventional collinear factorization by incorporating intrinsic transverse momentum dependencies in PDFs and FFs, broadening the scope of QCD applications to less inclusive processes. Standard factorization approaches, epitomized by integrated PDFs and FFs, incorporate momentum components transversely integrated but fall short in addressing many current research questions about the parton's internal transverse momentum dynamics. TMD-factorization fills this gap, necessitating different approximations, alongside a recalibration of the TMD definitions aligned with recent theoretical developments in QCD.

The intrinsic momentum carried by partons is crucial for understanding hadron structure, especially in processes sensitive to small transverse momentum scales, such as the Drell-Yan process, single-inclusive deep inelastic scattering (SIDIS), and back-to-back hadron production in $e^+e^-$ collisions. TMD PDFs and FFs are also pivotal in exploring the spin structure of hadrons, where they represent functions like the Boer-Mulders and Sivers functions.

Methodology and Findings

The authors utilize the Collins-Soper-Sterman (CSS) formalism, augmented by modern theoretical insights, to derive evolved TMD PDFs and FFs. Evolving these functions involves considering QCD evolution equations that respect the requirements of factorization, maximal universality, and internal consistency. The choice of specific scales, energy variables, and the incorporation of soft factors are pivotal to these calculations. Through numerical methods, the authors demonstrate the significant quantitative impact of evolution on TMD functions and argue for its inclusion in future phenomenological studies.

The paper discusses a formalism that successfully resolves issues related to rapidity divergences, Wilson line self-interactions, and the universality of definitions. Moreover, the results indicate strong scale dependence of TMDs even at the zeroth-order parton model level due to non-perturbative contributions.

Implications and Future Directions

The findings imply that evolved TMDs are indispensable in testing QCD predictions at varying energy scales, offering insights into processes that show potential for QCD factorization's breakdown. This research provides the groundwork for subsequent theoretical and empirical investigations into spin-dependent TMDs, which require further elaboration on the phenomena governing spin effects and non-universality in TMD-factorization.

Moreover, the authors highlight the relevance of establishing fits for TMDs that incorporate evolution, analogous to the role of collinear PDFs in integrated processes. Such advancements could substantially enhance our capability to analyze current and upcoming experimental data from facilities like JLab, RHIC, and the LHC.

In conclusion, Aybat and Rogers move the field towards a more cohesive understanding of how turbulent gluon and quark interactions can be systematically approached in QCD through TMD evolution. This paper marks the initiation of tuning theoretical frameworks to match the ongoing and future high-energy physics experiments, thereby enriching our comprehension of hadronic structures.