A semi-analytical $x$-space solution for parton evolution -- Application to non-singlet and singlet DGLAP equation
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866912182445277184 |
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| author | Haug, Juliane Schüle, Oliver Wunder, Fabian |
| author_facet | Haug, Juliane Schüle, Oliver Wunder, Fabian |
| contents | 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 $\texttt{Python}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_18667 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A semi-analytical $x$-space solution for parton evolution -- Application to non-singlet and singlet DGLAP equation Haug, Juliane Schüle, Oliver Wunder, Fabian High Energy Physics - Phenomenology 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 $\texttt{Python}$. |
| title | A semi-analytical $x$-space solution for parton evolution -- Application to non-singlet and singlet DGLAP equation |
| topic | High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2404.18667 |