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arXiv · 2411.19042

On the photon self-energy to three loops in QED

Felix Forner·Christoph Nega·Lorenzo Tancredi
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Abstract

We compute the photon self-energy to three loops in Quantum Electrodynamics. The method of differential equations for Feynman integrals and a complete $\epsilon$-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 $\epsilon$. 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.

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Felix Forner, Christoph Nega, Lorenzo Tancredi. 2024-11-28. On the photon self-energy to three loops in QED. https://arxiv.org/abs/2411.19042

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