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

• Published in: The journal of high energy physics Vol. 2024; no. 7; pp. 72 - 29
• Main Authors: Haug, Juliane, Schüle, Oliver, Wunder, Fabian
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 09.07.2024; Springer Nature B.V; SpringerOpen
• Subjects: Algorithms; Analytic functions; Classical and Quantum Gravitation; Differential equations; Elementary Particles; Evolutionary computation; Factorization; Mathematical analysis; Methods; Ordinary differential equations; Parton Distributions; Partons; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; Renormalization Group; String Theory; Subsystems; Factorization; Renormalization Group; Parton Distributions
• ISSN: 1029-8479; 1126-6708; 1127-2236; 1029-8479
• DOI: 10.1007/JHEP07(2024)072

A bstract We present a novel semi-analytical method for parton evolution. It is based on constructing a family of analytic functions spanning x -space which is closed under the considered evolution equation. Using these functions as a basis, the original integro-differential evolution equation transforms into a system of coupled ordinary differential equations, which can be solved numerically by restriction to a suitably chosen finite subsystem. The evolved distributions are obtained as analytic functions in x with numerically obtained coefficients, providing insight into the analytic behavior of the evolved parton distributions. As a proof-of-principle, we apply our method to the leading order non-singlet and singlet DGLAP equation. Comparing our results to traditional Mellin-space methods, we find good agreement. The method is implemented in the code POMPOM in Mathematica as well as in Python.