PDFxTMDLib: A High-Performance C++ Library for Collinear and Transverse Momentum Dependent Parton Distribution Functions

TL;DR

PDFxTMDLib presents a high-performance C++ library that unifies access to collinear PDFs and TMDs within a single extensible framework, addressing key limitations of LHAPDF and TMDLib. Built on principles of separation of concerns, compile-time polymorphism, and type erasure, it offers a modular architecture with a common API, metadata-driven factories, and pluggable components for reading, interpolating, and extrapolating grid data. The authors validate the library against LHAPDF and TMDLib through Drell–Yan simulations and direct cPDF/TMD comparisons, reporting a modest performance gain over LHAPDF and excellent agreement in a variety of kinematic regimes. A novel lhagrid_tmd1 format for TMDs, extended uncertainty and QCD coupling capabilities to TMDs, and Python bindings further broaden the tool’s utility, enabling standardized access and diagnostic analyses for phenomenology while retaining compatibility with existing ecosystems. The work positions PDFxTMDLib as a practical, future-ready framework capable of integrating higher-dimensional distributions (e.g., DPDFs, DTMDs) and custom file formats, with ongoing expansion planned for broader PDF/TMD support.

Abstract

Collinear parton distribution functions (cPDFs) and transverse momentum dependent distributions (TMDs) are essential for calculating cross sections in high-energy physics, particularly within collinear and kt-factorization frameworks. Currently, there exists two libraries, such as LHAPDF and TMDLib, to obtain these physical objects. However, there are limitations in both libraries, especially for TMDs, such as restricted customization and extensibility. Users are limited to the implementations provided by these libraries and cannot easily support unconventional PDFs. Moreover, no standard TMD library currently provides a consistent framework for QCD coupling evaluation or for studying uncertainties at the distribution level--features that are important for diagnostic and comparative analyses in phenomenological research. To address these shortcomings, we introduce PDFxTMDLib, a modern C++ library designed to offer a robust and flexible solution. This library supports both collinear PDFs and TMDs while allowing greater customization. It also opens the way to support higher-order distributions. In this article, we describe the structure of PDFxTMDLib. We also demonstrate its validity and performance by integrating it into the PYTHIA Monte Carlo event generator to compute Drell-Yan cross sections. Additionally, comparisons of PDFs obtained from PDFxTMDLib with those from LHAPDF and TMDLib confirm the reliability of PDFxTMDLib's results.

Figures (8)

• Figure 1: UML diagram providing a general view of the PDFSet class and its interactions with other components in the PDFxTMDLib architecture.
• Figure 2: UML diagrams illustrating the structures of the GenericCPDFFactory (left) and GenericTMDFactory (right) classes within the PDFxTMDLib architecture.
• Figure 3: UML diagram detailing the structure and interactions of the PDFSet class within the PDFxTMDLib architecture.
• Figure 4: UML diagram showcasing the interactions of factory classes (GenericCPDFFactory, GenericTMDFactory, CouplingFactory) within the PDFxTMDLib architecture.
• Figure 5: UML class diagram of the GenericPDF class, showcasing its template parameters, internal members, public methods, and associations with the IReader, IInterpolator, and IExtrapolator interfaces.