QCDNUM
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| QCDNUM | |
|---|---|
| Name | QCDNUM |
| Title | QCDNUM |
| Developer | NIKHEF |
| Released | 1980s |
| Latest release | ongoing |
| Programming language | Fortran |
| Operating system | Unix, Linux, macOS, Windows |
| License | Open-source / academic |
QCDNUM QCDNUM is a Fortran-based package for the numerical solution of Dokshitzer–Gribov–Lipatov–Altarelli–Parisi evolution equations used in perturbative quantum chromodynamics. The program is designed to produce fast and precise parton distribution functions suitable for analyses in high-energy experiments and global fits, interfacing with Monte Carlo tools and analysis frameworks. Developed at NIKHEF and used by collaborations in particle physics, the code emphasizes computational efficiency, numerical stability, and compatibility with legacy and modern analysis pipelines.
Introduction
QCDNUM provides a numerical engine for evolving parton distribution functions (PDFs) and fragmentation functions across scales, addressing requirements of experiments such as CERN, DESY, Fermilab, SLAC National Accelerator Laboratory, and KEK. It is employed in conjunction with global-analysis groups including CTEQ-TEA, NNPDF, MMHT, HERAPDF, and ABMP for phenomenology related to collisions at facilities like Large Hadron Collider, HERA, Tevatron, and B-factory. The package targets theorists and experimentalists working within collaborations such as ATLAS Collaboration, CMS Collaboration, LHCb Collaboration, and ALICE Collaboration.
Features and Capabilities
QCDNUM implements fixed-order evolution in leading order, next-to-leading order, and higher orders where splitting functions are available, supporting variable-flavour-number schemes as used in heavy-quark treatments by groups like ACOT and FONLL. It supplies convolution integrals and Mellin-space techniques compatible with coefficient functions from calculations by authors associated with Altarelli–Parisi, Dokshitzer, Gribov–Lipatov, and modern perturbative computations by teams behind NNLOJET and FEWZ. Interoperability features include interfaces to analysis tools used by Rivet, HEPData, ROOT, and fitting frameworks developed by Professor. The code supports tabulated PDFs, interpolation grids akin to formats used by LHAPDF, and fast evaluation kernels that enable dense grid scans employed in global fits by CTEQ-TEA and NNPDF.
Theoretical Background and Algorithms
The package numerically solves the DGLAP equations derived from perturbative QCD, relying on splitting functions computed by pioneers like Altarelli–Parisi and extended by modern computations involving groups at CERN Theory Department and research by individuals affiliated with Institut de Physique Théorique. Algorithms include discrete Mellin-transform techniques, fast convolution methods inspired by work of researchers at DESY and matrix-exponentiation routines similar to those used in evolution studies by Dokshitzer collaborators. Treatments for heavy-flavour thresholds implement prescriptions comparable to the ACOT and FONLL schemes developed in collaboration between theorists at Brookhaven National Laboratory and INFN. Renormalization- and factorization-scale choices align with procedures common to analyses performed by ATLAS Collaboration and CMS Collaboration.
Implementation and Software Architecture
QCDNUM is written primarily in Fortran, structured as modular routines for evolution kernels, grid management, and interpolation, following practices seen in legacy scientific codes from CERN. Its architecture separates numerical back end from user-facing I/O routines, facilitating bindings to languages and frameworks used in analysis environments like ROOT and scripting ecosystems maintained at DESY and SLAC National Accelerator Laboratory. Memory- and CPU-optimized data structures implement tabulated grids and fast lookup tables comparable to those in LHAPDF and APFEL, enabling integration with fast calculation frameworks used by NNPDF and CTEQ-TEA. Parallelization strategies reflect batch-computing workflows typical at National Energy Research Scientific Computing Center and cluster systems at CERN.
Usage and Applications
Practically, QCDNUM is applied to generate evolved PDFs for cross-section predictions in measurements by ATLAS Collaboration, CMS Collaboration, and LHCb Collaboration, and to provide inputs for parton-shower matching in event generators like PYTHIA, HERWIG, and SHERPA. It is utilized in PDF fits by groups such as NNPDF, MMHT, and CTEQ-TEA for determinations of the strong coupling constant αs and heavy-quark masses used in analyses published by collaborations at CERN and DESY. The package supports phenomenology studies for electroweak precision measurements in experiments run by CDF, D0, and neutrino scattering experiments at facilities like FNAL. QCDNUM also finds use in theoretical investigations at institutes such as INFN, IPPP Durham, and Institute for Nuclear Theory.
Validation and Benchmarks
Validation of QCDNUM has historically involved comparisons with independent evolution codes and benchmark tables produced by theory working groups at CERN and DESY. Benchmarks examine consistency with results from programs developed by teams at University of Durham, Humboldt University, and Brookhaven National Laboratory, and cross-checks against analytic Mellin-space solutions used in academic comparisons published in journals where researchers from SLAC National Accelerator Laboratory and FNAL contribute. Performance benchmarks report execution times and numerical accuracy on platforms ranging from workstation clusters at CERN to national supercomputing centers like National Energy Research Scientific Computing Center.
Development History and Licensing
QCDNUM originated at research centers including NIKHEF during the late 1980s and has evolved through contributions by scientists affiliated with institutions such as CERN, DESY, INFN, and SLAC National Accelerator Laboratory. The codebase has been maintained with community contributions and documentation practices similar to those adopted by collaborative projects at CERN. Licensing is oriented toward academic and open scientific use, facilitating redistribution within collaborations like ATLAS Collaboration and CMS Collaboration while enabling integration with community tools like LHAPDF and Rivet.