Genus drop involving non-hyperelliptic curves in Feynman integrals

Fuente: arXiv
Enregistré dans:
Détails bibliographiques
Auteurs principaux: Yang, Feiyu, Gong, Jianyu, Zhang, Yang
Format: Preprint
Publié: 2026
Sujets:
Accès en ligne:
Tags: Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
_version_ 1866910201371688960
author Yang, Feiyu
Gong, Jianyu
Zhang, Yang
author_facet Yang, Feiyu
Gong, Jianyu
Zhang, Yang
contents For both theoretical and phenomenological studies, it is important to analyze the function types of Feynman integrals. The phenomenon of genus drop between different representations of hyperelliptic Feynman integrals was discussed in \cite{Marzucca2024Genusdrop}. In this paper, we reformulate the extra-involution mechanism of \cite{Marzucca2024Genusdrop} as a special case of an unramified double covering between algebraic curves, and show that this covering mechanism also explains genus drops accompanied by a curve-type change from non-hyperelliptic to hyperelliptic for a class of three-loop Feynman diagrams. We also demonstrate that within a specific framework, the origin of the discrete spacetime symmetry that leads to the genus drop in hyperelliptic cases is manifest. This work also points out that there exist non-hyperelliptic Feynman integrals that exhibit no apparent genus drop.
format Preprint
id arxiv_https___arxiv_org_abs_2605_07729
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Genus drop involving non-hyperelliptic curves in Feynman integrals
Yang, Feiyu
Gong, Jianyu
Zhang, Yang
High Energy Physics - Theory
High Energy Physics - Phenomenology
Algebraic Geometry
For both theoretical and phenomenological studies, it is important to analyze the function types of Feynman integrals. The phenomenon of genus drop between different representations of hyperelliptic Feynman integrals was discussed in \cite{Marzucca2024Genusdrop}. In this paper, we reformulate the extra-involution mechanism of \cite{Marzucca2024Genusdrop} as a special case of an unramified double covering between algebraic curves, and show that this covering mechanism also explains genus drops accompanied by a curve-type change from non-hyperelliptic to hyperelliptic for a class of three-loop Feynman diagrams. We also demonstrate that within a specific framework, the origin of the discrete spacetime symmetry that leads to the genus drop in hyperelliptic cases is manifest. This work also points out that there exist non-hyperelliptic Feynman integrals that exhibit no apparent genus drop.
title Genus drop involving non-hyperelliptic curves in Feynman integrals
topic High Energy Physics - Theory
High Energy Physics - Phenomenology
Algebraic Geometry
url https://arxiv.org/abs/2605.07729