Features

NeoPDF is designed to be a modern, extensible, and high-performance library for PDF interpolation. This page details the physics and technical features, design rationale, and future plans.

Summary of the Current Supported Features

	Feature	Status	Notes
APIs & FFIs	Rust API	✅	Fully supported
	Python API	✅	Fully supported
	C/C++ API	✅	Fully supported
	Fortran API	❌	Not yet implemented
Features	Multi-flavor grids	❌	Planned
	Nuclear PDFs interpolation	✅	Fully supported
	Strong Coupling interpolation	✅	Fully supported
	Different Hadronic states	✅	Fully supported
	Custom interpolation	✅	Supported (user-defined strategies)
	Analytical DGLAP interpolation	❌	Planned

Physics Features

Hadron Types and PDF Classification

Multiple types of Convolutions

PDF interpolations are mainly used to convolve with partonic cross-sections in order to get theoretical predictions. For various technical reasons, these theory predictions are stored in some fast interpolating grids. Mondern interpolating libraries such as PineAPPL supports grids with arbitrarily many convolutions. For instance, it support processes such as:

proton + proton -> Pion + Pion + X

An interpolation grid of this kind needs two different convolution functions: a (polarised) PDF for the protons and a fragmentation function for the pions. When users convolve this grid with the two functions, they must either pass the functions in the right order to avoid calculating wrong predictions (see this issue for more details). NeoPDF circumvents this issue by adding the following keys to the metadata:

HadronPID: 2212/212/...
Polarized: true/false
SetType: PDf/Fragfn

NeoPDF provides comprehensive support for different types of hadronic structure functions and most importantly distinguish between them, which is essential for precision QCD calculations.

• Parton vs Nuclear PDFs:

  • Parton PDFs describe the momentum distribution of quarks and gluons within protons and neutrons, fundamental for understanding the internal structure of hadrons. These are crucial for Standard Model predictions at hadron colliders like the LHC.
  • Nuclear PDFs extend this framework to describe parton distributions within nuclei, accounting for nuclear binding effects, shadowing, and anti-shadowing. These are essential for heavy-ion collisions and understanding nuclear structure effects in high-energy physics experiments.

• Polarized vs Unpolarized PDFs:

  • Unpolarized PDFs represent the standard momentum distributions and are used in most collider physics calculations.
  • Polarized PDFs describe the spin-dependent parton distributions, crucial for understanding the proton's spin structure and for experiments with polarized beams. These are essential for the RHIC spin program and future electron-ion colliders (EIC).

  The difference between polarized and unpolarized PDFs provides direct insight into the proton's spin decomposition and tests of QCD in the spin sector.

• Timelike vs Spacelike PDFs:

  • Spacelike PDFs (the standard case) describe parton distributions in deep-inelastic scattering and hadron-hadron collisions.
  • Timelike PDFs (Fragmentation Functions) describe the hadronization of partons into hadrons, essential for understanding jet structure and hadron production in \(e^+e^-\) collisions and hadron-hadron collisions.

  This distinction is crucial for precision phenomenology, as the evolution equations and factorization theorems differ between the two cases.

Multi-Parameter Interpolations

NeoPDF supports interpolation across multiple physical parameters:

• \(\alpha_s(M_Z)\) Dependence: The strong coupling constant \(\alpha_s(M_Z)\) is a fundamental parameter of QCD that affects PDF evolution and cross-section predictions. Different PDF sets use different values (typically ranging from 0.116 to 0.120), and interpolating between them allows for:

  • Uncertainty quantification in \(\alpha_s\) determination
  • Consistent treatment of \(\alpha_s\) variations in global fits
  • Testing the sensitivity of observables to the strong coupling constant

• Nuclear Dependence \((A, Z)\): Nuclear PDFs depend on the atomic mass number \(A\) and atomic number \(Z\) of the target nucleus. Interpolating in \((A, Z)\) space enables:

  • Predictions for nuclei not included in existing sets
  • Systematic studies of nuclear effects across the periodic table
  • Applications to heavy-ion physics and neutrino-nucleus scattering

Multi-Flavor Grids (Planned)

NeoPDF will support grids with varying numbers of active flavors \(n_f\), providing a consistent treatment of heavy quark effects across all scales. Advanced schemes like FONLL and ACOT require careful handling of flavor thresholds and mass effects. NeoPDF's multi-flavor support will enable:

• Precision predictions for heavy flavor production
• Proper matching across flavor thresholds
• Consistent treatment of charm and bottom quark effects

Analytical Interpolation (Planned)

Future versions will support DGLAP-based analytical interpolation. Such an analytical-based interpolation will provide:

• Consistent treatment of scale evolution
• Reduced interpolation artifacts
• More accurate extrapolation beyond the grid boundaries

Technical Features

Language Interoperability

NeoPDF provides native APIs across multiple programming languages, enabling seamless integration into diverse computational workflows:

• Native Rust API: The core library is written in Rust, providing zero-cost abstractions, memory safety, and high performance. Rust's ownership system ensures thread safety and prevents common programming errors that could lead to incorrect physics results.

• Python Bindings: Comprehensive Python interface using PyO3, enabling integration with the rich ecosystem of scientific Python libraries (NumPy, SciPy, Matplotlib, etc.). This is crucial for data analysis, visualization, and integration with existing physics analysis frameworks.

• C/C++ Bindings: Direct C and C++ interfaces for integration with legacy codes and high-performance computing applications. The C API provides a stable ABI for long-term compatibility, while the C++ API offers object-oriented convenience.

No-Code Migration

NeoPDF maintains API compatibility with LHAPDF, enabling seamless migration:

• Drop-in Replacement: Existing LHAPDF code can often be migrated by simply changing import statements, with no modifications to the core physics logic required.

• Preserved Function Signatures: Key functions like xfxQ2(), alphasQ2(), and mkPDF() maintain the same signatures as LHAPDF, ensuring compatibility with existing analysis codes.

This compatibility is crucial for the physics community, as it allows for immediate adoption without requiring extensive code rewrites or validation efforts.

Thread and Memory Safety

NeoPDF leverages Rust's safety guarantees for robust multi-threaded applications:

• Memory Safety: Rust's ownership system prevents common memory errors (use-after-free, double-free, data races) that could lead to incorrect physics results or program crashes.

• Thread Safety: Built-in support for safe concurrent access to PDF objects, essential for parallel event generation and Monte Carlo simulations.

• FFI Safety: Careful design of the foreign function interface ensures that safety guarantees extend to Python, C, and C++ code, preventing crashes and undefined behavior.

Extensible Interpolation

NeoPDF's modular architecture enables easy extension and customization:

• Pluggable Interpolation Strategies: The library supports multiple interpolation algorithms (bilinear, bicubic, tricubic, N-dimensional) and can be extended with custom interpolation schemes.

• Custom Grid Types: The framework can accommodate new grid formats and data structures, enabling support for emerging PDF sets and specialized applications.

• Performance Tuning: Different interpolation strategies can be selected based on the specific requirements of accuracy vs. speed, allowing optimization for different use cases.

Performance Optimization

NeoPDF is designed for high-performance computing environments:

• Zero-Cost Abstractions: Rust's compilation model ensures that high-level abstractions don't incur runtime overhead, providing both safety and performance.

• Cache-Friendly Design: Data structures are optimized for modern CPU cache hierarchies, reducing memory access latency and improving performance for large-scale calculations.

• SIMD Optimization: The library can leverage CPU vector instructions for parallel evaluation of multiple points, crucial for Monte Carlo event generation and large-scale simulations.

• Benchmarking: Comprehensive benchmarking against LHAPDF ensures that performance improvements don't come at the cost of accuracy, maintaining the precision required for physics calculations.

Architecture Overview

graph TD;
    A[User (Rust/Python/C/C++)] --> B[API Layer];
    B --> C[Core Engine (Rust)];
    C --> D[Grid Data & Metadata];
    C --> E[Interpolation Strategies];
    D --> F[PDF Set Files];

• API Layer: Exposes a consistent interface in each language.
• Core Engine: Handles all logic, grid management, and interpolation.
• Grid Data: Efficiently loads and manages PDF grid data and metadata.
• Interpolation Strategies: Pluggable, with default (log)-bicubic, bilinear, and (log)-tricubic.

Benchmark Against LHAPDF

NeoPDF implements (log)-bicubic interpolation by default, with optional \(N\)-dimensional strategies. Lower-dimensional (bilinear, (log)-tricubic) are also available for performance tuning.

Benchmark against LHAPDF

The difference between NeoPDF and LHAPDF, using the default interpolation, is below machine precision for floating-point numbers.