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

Nico Böttcher (PRISMA Cluster of Excellence, Institut für Physik Johannes Gutenberg-Universität Mainz, Mainz, 55099, Germany) ; Niklas Schwanemann (PRISMA Cluster of Excellence, Institut für Physik Johannes Gutenberg-Universität Mainz, Mainz, 55099, Germany) ; Stefan Weinzierl (PRISMA Cluster of Excellence, Institut für Physik Johannes Gutenberg-Universität Mainz, Mainz, 55099, Germany)

The Moller experiment and the P2 experiment aim at measuring the weak mixing angle at low scales. The Moller experiment uses $$e^- e^- \rightarrow e^- e^-$$ e - e - e - e - -scattering, the P2 experiment uses $$e^- N \rightarrow e^- N$$ e - N 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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      "surname": "Schwanemann", 
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      "surname": "Weinzierl", 
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      "source": "Springer", 
      "value": "The Moller experiment and the P2 experiment aim at measuring the weak mixing angle at low scales. The Moller experiment uses  $$e^- e^- \\rightarrow e^- e^-$$  <math> <mrow> <msup> <mi>e</mi> <mo>-</mo> </msup> <msup> <mi>e</mi> <mo>-</mo> </msup> <mo>\u2192</mo> <msup> <mi>e</mi> <mo>-</mo> </msup> <msup> <mi>e</mi> <mo>-</mo> </msup> </mrow> </math>  -scattering, the P2 experiment uses  $$e^- N \\rightarrow e^- N$$  <math> <mrow> <msup> <mi>e</mi> <mo>-</mo> </msup> <mi>N</mi> <mo>\u2192</mo> <msup> <mi>e</mi> <mo>-</mo> </msup> <mi>N</mi> </mrow> </math>  -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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Published on:
14 May 2024
Publisher:
Springer
Published in:
European Physical Journal C , Volume 84 (2024)
Issue 5
Pages 1-22
DOI:
https://doi.org/10.1140/epjc/s10052-024-12843-1
Copyrights:
The Author(s)
Licence:
CC-BY-4.0

Fulltext files: