Three-loop contributions to the ρ parameter and iterated integrals of modular forms

Abreu, Samuel; Becchetti, Matteo; Duhr, Claude; Marzucca, Robin

Abstract

We compute fully analytic results for the three-loop diagrams involving two different massive quark flavours contributing to the ρ parameter in the Standard Model. We find that the results involve exactly the same class of functions that appears in the well-known sunrise and banana graphs, namely elliptic polylogarithms and iterated integrals of modular forms. Using recent developments in the understanding of these functions, we analytically continue all the iterated integrals of modular forms to all regions of the parameter space, and in each region we obtain manifestly real and fast-converging series expansions for these functions.

Citation

Abreu, S., Becchetti, M., Duhr, C., & Marzucca, R. (2020). Three-loop contributions to the ρ parameter and iterated integrals of modular forms. Journal of High Energy Physics, 2020(2), Article 050. https://doi.org/10.1007/jhep02%282020%29050

• Journal Article Type: Article
• Acceptance Date: Jan 14, 2020
• Online Publication Date: Feb 7, 2020
• Publication Date: 2020
• Deposit Date: Feb 12, 2020
• Publicly Available Date: Feb 12, 2020
• Journal: Journal of High Energy Physics
• Print ISSN: 1126-6708
• Electronic ISSN: 1029-8479
• Publisher: Scuola Internazionale Superiore di Studi Avanzati (SISSA)
• Peer Reviewed: Peer Reviewed
• Volume: 2020
• Issue: 2
• Article Number: 050
• DOI: https://doi.org/10.1007/jhep02%282020%29050
• Public URL: https://durham-repository.worktribe.com/output/1277515