https://doi.org/10.1007/s41781-025-00157-0
Research
PDFxTMDLib: A High-Performance C++ Library for Collinear and Transverse Momentum-Dependent Parton Distribution Functions
School of Particles and Accelerators, Institute for Research in Fundamental Sciences (IPM), P.O.Box 19395-5531, Tehran, Iran
a
This email address is being protected from spambots. You need JavaScript enabled to view it.
Received:
13
November
2025
Accepted:
27
December
2025
Published online: 13 February 2026
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 
-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. In addition, comparisons of PDFs obtained from PDFxTMDLib with those from LHAPDF and TMDLib confirm the reliability of PDFxTMDLib’s results.
Key words: PDFxTMDLib / Collinear Parton Distribution Functions / Transverse Momentum Parton Distribution Functions / PDFs / TMDs / UPDFs / Collinear factorization / kt-factorization / Interpolation Library / LHAPDF / TMDLib
Supplementary Information The online version contains supplementary material available at https://doi.org/10.1007/s41781-025-00157-0.
© The Author(s) 2026
Open Access
This article is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License, which permits any non-commercial use, sharing, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if you modified the licensed material. You do not have permission under this licence to share adapted material derived from this article or parts of it. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by-nc-nd/4.0/.
