ChiliPDF: Chebyshev interpolation for parton distributions

Abstract

Parton distribution functions (PDFs) are an essential ingredient for theoretical predictions at colliders. Since their exact form is unknown, their handling and delivery for practical applications relies on approximate numerical methods. We discuss the implementation of PDFs based on a global interpolation in terms of Chebyshev polynomials. We demonstrate that this allows for significantly higher numerical accuracy at lower computational cost compared with local interpolation methods such as splines. Whilst the numerical inaccuracy of currently used local methods can become a nontrivial limitation in high-precision applications, in our approach it is negligible for practical purposes. This holds in particular for differentiation and for Mellin convolution with kernels that have end point singularities. We illustrate our approach for these and other important numerical operations, including DGLAP evolution, and find that they are performed accurately and fast. Our results are implemented in the C++ library ChiliPDF.