Fast evolution of parton distributions

TL;DR

The paper presents partonevolution, a fast PDF evolution library that uses inverse Mellin transforms with an optimized parabolic contour to achieve high-precision results with few evaluations. It demonstrates that N-space evolution can outperform traditional x-space approaches in both speed and accuracy, while maintaining compatibility for cross-checks. The work outlines a practical, extensible framework for evolving parton distributions up to next-to-leading order, with a clear path toward NNLO extension and applications to PDF uncertainty analyses. Overall, the method offers a robust tool for on-the-fly PDF evolution in phenomenological studies and global fits.

Abstract

I report on a numerical program for the evolution of parton distributions. The program uses the Mellin-transform method with an optimized contour. Due to this optimized contour the program needs only a few evaluations of the integrand and is therefore extremely fast. In addition, the program can also be used to reproduce the results of the x-space method.