Speaker
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 $\texttt{arXiv:2404.18667}$.
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 $\texttt{POMPOM}$ in $\texttt{Mathematica}$ as well as in $\texttt{Python}$.
