Angular integrals with three denominators via IBP, mass reduction, dimensional shift, and differential equations
Abstract Angular integrals arise in a wide range of perturbative quantum field theory calculations. In this work we investigate angular integrals with three denominators in d = 4 – 2ε dimensions. We derive integration-by-parts relations for this class of integrals, leading to explicit recursion rela...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2025-03-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP03(2025)141 |
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| Summary: | Abstract Angular integrals arise in a wide range of perturbative quantum field theory calculations. In this work we investigate angular integrals with three denominators in d = 4 – 2ε dimensions. We derive integration-by-parts relations for this class of integrals, leading to explicit recursion relations and a reduction to a small set of master integrals. Using a differential equation approach we establish results up to order ε for general integer exponents and masses. Here, reduction identities for the number of masses, known results for two-denominator integrals, and a general dimensional-shift identity for angular integrals considerably reduce the required amount of work. For the first time we find for angular integrals a term contributing proportional to a Euclidean Gram determinant in the ε-expansion. This coefficient is expressed as a sum of Clausen functions with intriguing connections to Euclidean, spherical, and hyperbolic geometry. The results of this manuscript are applicable to phase-space calculations with multiple observed final-state particles. |
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| ISSN: | 1029-8479 |