Phase-space integrals through Mellin-Barnes representation
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866915908623007744 |
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| author | Ahmed, Taushif Hasan, Syed Mehedi Rapakoulias, Andreas |
| author_facet | Ahmed, Taushif Hasan, Syed Mehedi Rapakoulias, Andreas |
| contents | We compute angular phase-space integrals with three and four denominators analytically, working within dimensional regularisation via the Mellin-Barnes (MB) representation. The approach converts multifold MB integrals into real parametric integrals and expresses all results in terms of Goncharov polylogarithms (GPLs). For three denominators, all-massless results are obtained to $\mathcal{O}(ε^2)$ and the single-massive case to $\mathcal{O}(ε)$; for four denominators, both the massless and single-massive cases are solved to $\mathcal{O}(ε^0)$. Integrals with multiple massive momenta follow from a partial fraction decomposition reducing them to the single-massive case. Recursion relations relating integrals with higher denominator powers to master integrals are derived. These are essential ingredients to solving full phase-space integrals. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_01505 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Phase-space integrals through Mellin-Barnes representation Ahmed, Taushif Hasan, Syed Mehedi Rapakoulias, Andreas High Energy Physics - Phenomenology High Energy Physics - Theory We compute angular phase-space integrals with three and four denominators analytically, working within dimensional regularisation via the Mellin-Barnes (MB) representation. The approach converts multifold MB integrals into real parametric integrals and expresses all results in terms of Goncharov polylogarithms (GPLs). For three denominators, all-massless results are obtained to $\mathcal{O}(ε^2)$ and the single-massive case to $\mathcal{O}(ε)$; for four denominators, both the massless and single-massive cases are solved to $\mathcal{O}(ε^0)$. Integrals with multiple massive momenta follow from a partial fraction decomposition reducing them to the single-massive case. Recursion relations relating integrals with higher denominator powers to master integrals are derived. These are essential ingredients to solving full phase-space integrals. |
| title | Phase-space integrals through Mellin-Barnes representation |
| topic | High Energy Physics - Phenomenology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2604.01505 |