# Efficient interpolation and evolution of parton distribution functions

## TL;DR

This paper introduces a highly efficient numerical method using Chebyshev interpolation for evolving parton distribution functions, achieving higher accuracy with fewer grid points and accommodating complex features like NNLO kernels and multiple scales.

## Contribution

The paper develops a Chebyshev-based numerical approach for DGLAP equations that improves accuracy and efficiency for PDFs and DPDs, including NNLO kernels and independent scales.

## Key findings

- Higher numerical accuracy with fewer grid points for PDF evolution.
- Feasible evolution of DPDs with multiple renormalization scales.
- Inclusion of NNLO DGLAP kernels and flavor matching in the method.

## Abstract

We present an efficient numerical solution of the DGLAP equations for single and double parton distribution functions (PDFs and DPDs), based on the Chebyshev interpolation of these functions. For PDF evolution, our method allows for a higher numerical accuracy using a considerably smaller number of grid points compared to other methods. The DPD evolution is realized using an affordable number of grid points, and allows for two independent renormalization scales for the two partons. Both methods include NNLO DGLAP kernels and flavor matching.