QCD Evolution 2024

A semi-analytical x-space solution for parton evolution

30 May 2024, 17:30

30m

Aula Foscolo (University of Pavia)

Thursday

Speaker

Juliane Haug (Universität Tübingen)

Description

I will present a novel semi-analytical method for parton evolution. The talk is based on work done with co-authors Oliver Schüle and Fabian Wunder, the corresponding preprint is $\mathtt{\text{arXiv:2404.18667}}$.

The presented method 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 applied our method to the leading order non-singlet and singlet DGLAP equation. Comparing our results to traditional Mellin-space methods, we found good agreement. The method has been implemented in the code $\mathtt{\text{POMPOM}}$ in $\mathtt{\text{Mathematica}}$ as well as in $\mathtt{\text{Python}}$.

Presentation materials

POMPOM_Juliane_Haug_QCD_Evolution_2024.pdf