Efficient computation of Fourier-Bessel transforms for transverse-momentum dependent parton distributions and other functions

TL;DR

This paper introduces a numerical method for efficiently computing Fourier-Bessel transforms on finite or infinite intervals, crucial for analyzing transverse-momentum dependent parton distributions in QCD.

Contribution

The paper presents a novel algorithm that allows accurate Fourier-Bessel transforms with a grid independent of the Bessel function's argument, improving computational efficiency.

Findings

Demonstrates high accuracy across various functions

Applicable to transverse-momentum dependent parton distributions

Works on both finite and infinite intervals

Abstract

We present a method for the numerical computation of Fourier-Bessel transforms on a finite or infinite interval. The function to be transformed needs to be evaluated on a grid of points that is independent of the argument of the Bessel function. We demonstrate the accuracy of the algorithm for a wide range of functions, including those that appear in the context of transverse-momentum dependent parton distributions in Quantum Chromodynamics.