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<p>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 <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(k_t\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>k</mi> <mi>t</mi> </msub> </math></EquationSource> </InlineEquation>-factorization frameworks. Currently, there exists two libraries, such as <Emphasis FontCategory="NonProportional">LHAPDF</Emphasis> and <Emphasis FontCategory="NonProportional">TMDLib</Emphasis>, 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.</p><p>To address these shortcomings, we introduce <Emphasis FontCategory="NonProportional">PDFxTMDLib</Emphasis>, 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 <Emphasis FontCategory="NonProportional">PDFxTMDLib</Emphasis>. 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 <Emphasis FontCategory="NonProportional">PDFxTMDLib</Emphasis> with those from <Emphasis FontCategory="NonProportional">LHAPDF</Emphasis> and <Emphasis FontCategory="NonProportional">TMDLib</Emphasis> confirm the reliability of <Emphasis FontCategory="NonProportional">PDFxTMDLib</Emphasis>’s results.</p>

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

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年2月13日

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  • R. Kord Valeshabadi,
  • S. Rezaie

摘要

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 \(k_t\) k t -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.