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Recurrence relations and dispersive techniques for precision multiloop calculations

A. Aleksejevs, S. Barkanova, and A. I. Davydychev

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Phys. Rev. D 113, 056031 – Published 31 March, 2026

DOI: https://doi.org/10.1103/828n-wdc1

Abstract

Ab initio predictions of two-loop electroweak contributions to observables are increasingly essential for precision collider experiments, yet their evaluation remains very challenging. We connect recurrence techniques and dispersive methods in order to evaluate complex multiloop Feynman diagrams. By expressing multipoint Passarino-Veltman functions in a two-point basis and using shifted space-time dimensions with recurrence relations, we minimize the number of required dispersive integrals. This approach reduces computation time and enables a precise and efficient analysis of one- and two-loop diagrams.

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Phys. Rev. D 113, 056031– Published 31 March, 2026
  • Received 1 December 2025
  • Accepted 12 February 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

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