On the photon self-energy to three loops in QED
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| Format: | Preprint |
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2024
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| _version_ | 1866909958063259648 |
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| author | Forner, Felix Nega, Christoph Tancredi, Lorenzo |
| author_facet | Forner, Felix Nega, Christoph Tancredi, Lorenzo |
| contents | We compute the photon self-energy to three loops in Quantum Electrodynamics. The method of differential equations for Feynman integrals and a complete $ε$-factorization of the former allow us to obtain fully analytical results in terms of iterated integrals involving integration kernels related to a K3 geometry. We argue that our basis has the right properties to be a natural generalization of a canonical basis beyond the polylogarithmic case and we show that many of the kernels appearing in the differential equations, cancel out in the final result to finite order in $ε$. We further provide generalized series expansions that cover the whole kinematic space so that our results for the self-energy may be easily evaluated numerically for all values of the momentum squared. From the local solution at $p^2=0$, we extract the photon wave function renormalization constant in the on-shell scheme to three loops and confirm its agreement with previously obtained results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_19042 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the photon self-energy to three loops in QED Forner, Felix Nega, Christoph Tancredi, Lorenzo High Energy Physics - Theory High Energy Physics - Phenomenology We compute the photon self-energy to three loops in Quantum Electrodynamics. The method of differential equations for Feynman integrals and a complete $ε$-factorization of the former allow us to obtain fully analytical results in terms of iterated integrals involving integration kernels related to a K3 geometry. We argue that our basis has the right properties to be a natural generalization of a canonical basis beyond the polylogarithmic case and we show that many of the kernels appearing in the differential equations, cancel out in the final result to finite order in $ε$. We further provide generalized series expansions that cover the whole kinematic space so that our results for the self-energy may be easily evaluated numerically for all values of the momentum squared. From the local solution at $p^2=0$, we extract the photon wave function renormalization constant in the on-shell scheme to three loops and confirm its agreement with previously obtained results. |
| title | On the photon self-energy to three loops in QED |
| topic | High Energy Physics - Theory High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2411.19042 |