Evolution and interpolation of double parton distributions using Chebyshev grids

Abstract

Double parton distributions are the nonperturbative ingredients needed for computing double parton scattering processes in hadron-hadron collisions. They describe a variety of correlations between two partons in a hadron and depend on a large number of variables, including two independent renormalization scales. This makes it challenging to compute their scale evolution with satisfactory numerical accuracy while keeping computational costs at a manageable level. We show that this problem can be solved using interpolation on Chebyshev grids, extending the methods we previously developed for ordinary single-parton distributions. Using an implementation of these methods in the C++ library ChiliPDF, we study for the first time the evolution of double parton distributions beyond leading order in perturbation theory.

arXiv comment48 pages, 17 figures. v2: added figure 3, added clarifications, corrected typos

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• A semi-analytical $x$-space solution for parton evolution -- Application to non-singlet and singlet DGLAP equation