NeoPDF: A fast interpolation library for collinear and transverse momentum-dependent parton distributions

TL;DR

NeoPDF addresses the need for a unified, fast, and accurate interpolation framework for both collinear PDFs and transverse momentum-dependent distributions (TMDs). It introduces a modular, grid-based design with a Chebyshev-based global interpolation that reduces grid size while preserving numerical precision, and extends interpolation across $A$ and $\tilde{\alpha}_s$ as well as $k_T$ for TMDs. The library maintains backward compatibility with LHAPDF via a no-code migration approach and delivers multi-language interfaces (Rust core with Fortran, C/C++, Python, Mathematica bindings), alongside a binary, compressed file format for efficient storage. Benchmark results show that NeoPDF matches LHAPDF accuracy to machine precision while offering faster loading and interpolation, and achieves superior accuracy for TMDs compared with TMDlib, with manageable trade-offs in evaluation time for higher-dimensional interpolations. These features position NeoPDF as a scalable, future-proof tool for high-precision QCD phenomenology at the LHC, EIC, and future colliders, with planned extensions to GTMDs, GPDs, GM-VFNS, and potential GPU acceleration.

Abstract

We present NeoPDF, an interpolation library that supports both collinear and transverse momentum-dependent parton distribution functions. NeoPDF is designed to be fast and reliable, with modern functionalities that target both current and future hadron collider experiments. It aims to address the shortcomings of existing interpolation libraries while providing additional features to support generic non-perturbative functions. Some of the features include a new interpolation based on Chebyshev polynomials, as well as the ability to interpolate along the nucleon number $A$, the reference strong coupling $α_s(M_Z)$, and the parton's intrinsic transverse momentum $k_T$. NeoPDF implements its own file format using binary serialisation and lossless compression, prioritising speed and efficiency. A no-code migration design is provided for LHAPDF in order to remove the frictions associated with transitioning to NeoPDF. The library is written in Rust with interfaces for various programming languages such as Fortran, C, C++, Python, and Mathematica. We benchmark NeoPDF against LHAPDF and TMDlib for various sets and show that it is both fast and accurate.

Figures (9)

• Figure 1: A diagrammatic representation of the NeoPDF data structure. The GridPDF object represents an instance of a given PDF set. It can contain multiple members, represented by the GridArray object. Each GridArray in turn contains a single or multiple subgrids---represented by the SubGrid object---which hold the information on the grid knots and values. Each subgrid $S_k$ is hyperrectangle defined by the Cartesian product of $N$ one-dimensional intervals, with $N$ representing the number of dependent variables.
• Figure 2: Relative interpolation accuracy for the two representative PDFs give in Eqs. \ref{['eq:abmp']} and \ref{['eq:herepdf20']}. The linear (green) and cubic spline (blue) interpolants both use the same total number of grid points $n_{\rm pts} = 100$. The Chebyshev interpolants are given with both low- and high-density grids, $n_{\rm pts} = 49$ (purple) and $n_{\rm pts} = 99$ (red) respectively. While the linear and cubic spline interpolants are expressed in terms of a single subgrid $\left[ 10^{-6}, 1 \right]_{(100)}$, the Chebyshev counterparts are represented in terms of two subgrids $\left[ 10^{-6}, 0.2, 1 \right]_{(n, n)}$ where $n=25,50$ depending on the density of the grid. The exact results that are being interpolated are shown in (dashed) black.
• Figure 3: Loading time for PDF sets in LHAPDF and NeoPDF, averaged over 20 independent runs, as a function of the number of members in the ensemble. Results are shown for sets of $50$, $10^2$, and $10^3$ members. For visualisation purposes, the times for the latter two sets are rescaled by factors of $1/5$ and $1/50$, respectively. Similarly, the eager (NeoPDF$_{\rm LHA}$ and NeoPDF) and lazy (NeoPDF$_{\rm Lazy}$) loading methods have been scaled by factors of $2.5$ and $20$, respectively.
• Figure 4: Interpolation accuracy of NeoPDF compared to LHAPDF, calculated using the Difference in Units of Last Places $\delta_{\rm ULPS}$. The results are shown for the MSHT20 NNLO set for the gluon distribution $f_g$ across the full $(x, Q)$--plane. The $x$ values of the MSHT20 set spans the region $\left[10^{-6}, 1\right]$ while the hard scale $Q$ is defined within the domain $\left[1, 3.162 \times 10^{4}\right]~\mathrm{GeV}$.
• Figure 5: Benchmark of the interpolation evaluation time for the gluon distribution $f_g$ using the NNPDF4.0@NNLO set. The average wall-clock time per evaluation are shown as a function of the number of $(x, Q)$ points (top) together with the ratio relative to LHAPDF (bottom).