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

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.

Comments: 58 pages, 16 figures. v2: added clarifications; new section about integrands that grow as z goes to infinity