Box integrals with fermion bubbles for low-energy measurements of the weak mixing angle

Nico Böttcher; Niklas Schwanemann; Stefan Weinzierl

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arXiv · 2312.06773

Box integrals with fermion bubbles for low-energy measurements of the weak mixing angle

Nico Böttcher·Niklas Schwanemann·Stefan Weinzierl

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Abstract

The Moller experiment and the P2 experiment aim at measuring the weak mixing angle at low scales. The Moller experiment uses $e^- e^- \rightarrow e^- e^-$-scattering, the P2 experiment uses $e^- N \rightarrow e^- N$-scattering. In both cases, two-loop electroweak corrections have to be taken into account, and here in particular diagrams which give rise to large logarithms. In this paper we compute a set of two-loop electroweak Feynman integrals for point-like particles, which are obtained from a box integral by the insertion of a light fermion loop. By rationalising all occurring square roots we show that these Feynman integrals can be expressed in terms of multiple polylogarithms. We present the results in a form, which makes the large logarithms manifest. We provide highly efficient numerical evaluation routines for these integrals.

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Nico Böttcher, Niklas Schwanemann, Stefan Weinzierl. 2023-12-11. Box integrals with fermion bubbles for low-energy measurements of the weak mixing angle. https://arxiv.org/abs/2312.06773

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