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.
{ "_oai": { "updated": "2024-06-18T00:31:43Z", "id": "oai:repo.scoap3.org:85422", "sets": [ "EPJC" ] }, "authors": [ { "affiliations": [ { "country": "Germany", "value": "PRISMA Cluster of Excellence, Institut f\u00fcr Physik Johannes Gutenberg-Universit\u00e4t Mainz, Mainz, 55099, Germany", "organization": "PRISMA Cluster of Excellence, Institut f\u00fcr Physik Johannes Gutenberg-Universit\u00e4t Mainz" } ], "surname": "B\u00f6ttcher", "given_names": "Nico", "full_name": "B\u00f6ttcher, Nico" }, { "affiliations": [ { "country": "Germany", "value": "PRISMA Cluster of Excellence, Institut f\u00fcr Physik Johannes Gutenberg-Universit\u00e4t Mainz, Mainz, 55099, Germany", "organization": "PRISMA Cluster of Excellence, Institut f\u00fcr Physik Johannes Gutenberg-Universit\u00e4t Mainz" } ], "surname": "Schwanemann", "given_names": "Niklas", "full_name": "Schwanemann, Niklas" }, { "affiliations": [ { "country": "Germany", "value": "PRISMA Cluster of Excellence, Institut f\u00fcr Physik Johannes Gutenberg-Universit\u00e4t Mainz, Mainz, 55099, Germany", "organization": "PRISMA Cluster of Excellence, Institut f\u00fcr Physik Johannes Gutenberg-Universit\u00e4t Mainz" } ], "surname": "Weinzierl", "email": "weinzierl@uni-mainz.de", "full_name": "Weinzierl, Stefan", "given_names": "Stefan" } ], "titles": [ { "source": "Springer", "title": "Box integrals with fermion bubbles for low-energy measurements of the weak mixing angle" } ], "dois": [ { "value": "10.1140/epjc/s10052-024-12843-1" } ], "publication_info": [ { "page_end": "22", "journal_title": "European Physical Journal C", "material": "article", "journal_volume": "84", "artid": "s10052-024-12843-1", "year": 2024, "page_start": "1", "journal_issue": "5" } ], "$schema": "http://repo.scoap3.org/schemas/hep.json", "acquisition_source": { "date": "2024-06-18T00:31:10.551828", "source": "Springer", "method": "Springer", "submission_number": "e58fdc7c2d0911ef9fecbe60ec5a7b90" }, "page_nr": [ 22 ], "license": [ { "url": "https://creativecommons.org/licenses//by/4.0", "license": "CC-BY-4.0" } ], "copyright": [ { "holder": "The Author(s)", "year": "2024" } ], "control_number": "85422", "record_creation_date": "2024-05-14T12:30:17.542774", "_files": [ { "checksum": "md5:f17cec5c52ae7fddc75fab7b2ab71940", "filetype": "xml", "bucket": "3e9360e0-db39-49ad-a5d1-eb8850aacc4c", "version_id": "277a241b-1268-4147-80d5-9a021c27a008", "key": "10.1140/epjc/s10052-024-12843-1.xml", "size": 12958 }, { "checksum": "md5:9ef51538ca96e2a7ef8e4269005853dd", "filetype": "pdf/a", "bucket": "3e9360e0-db39-49ad-a5d1-eb8850aacc4c", "version_id": "a93e0a7b-437d-4174-bb22-7d2e6f71ad38", "key": "10.1140/epjc/s10052-024-12843-1_a.pdf", "size": 587433 } ], "collections": [ { "primary": "European Physical Journal C" } ], "abstracts": [ { "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." } ], "imprints": [ { "date": "2024-05-14", "publisher": "Springer" } ] }