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References & Citations
High Energy Physics - Phenomenology
Title: A semi-analytical $x$-space solution for parton evolution -- Application to non-singlet and singlet DGLAP equation
(Submitted on 29 Apr 2024 (v1), last revised 30 Apr 2024 (this version, v2))
Abstract: 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 $\texttt{POMPOM}$ in $\texttt{Mathematica}$ as well as in $\texttt{Python}$.
Submission history
From: Fabian Wunder [view email][v1] Mon, 29 Apr 2024 12:55:22 GMT (15707kb,A)
[v2] Tue, 30 Apr 2024 14:54:10 GMT (15708kb,A)
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