Ladders and rainbows in Minimal Subtraction
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866916789680603136 |
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| author | Balduf, Paul-Hermann |
| author_facet | Balduf, Paul-Hermann |
| contents | In dimensional regularization with $D=D_0-2ε$, the minimal subtraction (MS) scheme is characterized by counterterms that only consist of singular terms in $ε$. We develop a general method to compute the infinite sums of massless ladder or rainbow Feynman integrals in MS at $D_0$. Our method is based on relating the MS-solution to a kinematic solution at a coupling-dependent renormalization point. If the $ε$-dependent Mellin transform of the kernel diagram of the insertions can be computed in closed form, we typically obtain a closed form expression for the all-order solution in MS. As examples, we consider Yukawa theory and $ϕ^4$ theory in $D_0=4$, and $ϕ^3$ theory in $D_0=6$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2503_02079 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Ladders and rainbows in Minimal Subtraction Balduf, Paul-Hermann High Energy Physics - Theory 81T15, 81T17 In dimensional regularization with $D=D_0-2ε$, the minimal subtraction (MS) scheme is characterized by counterterms that only consist of singular terms in $ε$. We develop a general method to compute the infinite sums of massless ladder or rainbow Feynman integrals in MS at $D_0$. Our method is based on relating the MS-solution to a kinematic solution at a coupling-dependent renormalization point. If the $ε$-dependent Mellin transform of the kernel diagram of the insertions can be computed in closed form, we typically obtain a closed form expression for the all-order solution in MS. As examples, we consider Yukawa theory and $ϕ^4$ theory in $D_0=4$, and $ϕ^3$ theory in $D_0=6$. |
| title | Ladders and rainbows in Minimal Subtraction |
| topic | High Energy Physics - Theory 81T15, 81T17 |
| url | https://arxiv.org/abs/2503.02079 |