Phase-space integrals through Mellin-Barnes representation
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866914987287511040 |
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| author | Ahmed, Taushif Hasan, Syed Mehedi Rapakoulias, Andreas |
| author_facet | Ahmed, Taushif Hasan, Syed Mehedi Rapakoulias, Andreas |
| contents | This letter introduces a novel analytical approach to calculating phase-space integrals, crucial for precision in particle physics. We develop a method to compute angular components using multifold Mellin-Barnes integrals, yielding results in terms of Goncharov polylogarithms for integrals involving three denominators. Our results include expressions for massless momenta up to $\cal{O}(ε^2)$ and for one massive momentum up to $\cal{O}(ε)$. Additionally, we derive recursion relations that reduce integrals with higher powers of denominators to simpler ones. We detail how to combine the angular part with the radial one which requires a careful handling of singularities. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_18886 |
| institution | arXiv |
| publishDate | 2024 |
| 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 This letter introduces a novel analytical approach to calculating phase-space integrals, crucial for precision in particle physics. We develop a method to compute angular components using multifold Mellin-Barnes integrals, yielding results in terms of Goncharov polylogarithms for integrals involving three denominators. Our results include expressions for massless momenta up to $\cal{O}(ε^2)$ and for one massive momentum up to $\cal{O}(ε)$. Additionally, we derive recursion relations that reduce integrals with higher powers of denominators to simpler ones. We detail how to combine the angular part with the radial one which requires a careful handling of singularities. |
| title | Phase-space integrals through Mellin-Barnes representation |
| topic | High Energy Physics - Phenomenology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2410.18886 |