تقرير
A Novel Algorithm for Nested Summation and Hypergeometric Expansions
| العنوان: | A Novel Algorithm for Nested Summation and Hypergeometric Expansions |
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| المؤلفون: | McLeod, Andrew J., Munch, Henrik, Papathanasiou, Georgios, von Hippel, Matt |
| سنة النشر: | 2020 |
| المجموعة: | High Energy Physics - Phenomenology High Energy Physics - Theory |
| مصطلحات موضوعية: | High Energy Physics - Theory, High Energy Physics - Phenomenology |
| الوصف: | We consider a class of sums over products of Z-sums whose arguments differ by a symbolic integer. Such sums appear, for instance, in the expansion of Gauss hypergeometric functions around integer indices that depend on a symbolic parameter. We present a telescopic algorithm for efficiently converting these sums into generalized polylogarithms, Z-sums, and cyclotomic harmonic sums for generic values of this parameter. This algorithm is illustrated by computing the double pentaladder integrals through ten loops, and a family of massive self-energy diagrams through $O(\epsilon^6)$ in dimensional regularization. We also outline the general telescopic strategy of this algorithm, which we anticipate can be applied to other classes of sums. Comment: 36 pages, 2 figures; v2: references added, typos corrected, improved introduction and comparison with existing methods, matches published version |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.1007/JHEP11(2020)122 |
| URL الوصول: | http://arxiv.org/abs/2005.05612 |
| رقم الأكسشن: | edsarx.2005.05612 |
| قاعدة البيانات: | arXiv |
| DOI: | 10.1007/JHEP11(2020)122 |
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