Feynman integrals

S Weinzierl - arXiv preprint arXiv:2201.03593, 2022 - Springer
Feynman integrals are indispensable for precision calculations in quantum field theory. They
occur as soon as one goes beyond the leading order in perturbative quantum field theory …

The ice cone family and iterated integrals for Calabi-Yau varieties

C Duhr, A Klemm, C Nega, L Tancredi - Journal of High Energy Physics, 2023 - Springer
A bstract We present for the first time fully analytic results for multi-loop equal-mass ice cone
graphs in two dimensions. By analysing the leading singularities of these integrals, we find …

Functions beyond multiple polylogarithms for precision collider physics

JL Bourjaily, J Broedel, E Chaubey, C Duhr… - arXiv preprint arXiv …, 2022 - arxiv.org
Feynman diagrams constitute one of the essential ingredients for making precision
predictions for collider experiments. Yet, while the simplest Feynman diagrams can be …

On a procedure to derive ϵ-factorised differential equations beyond polylogarithms

L Görges, C Nega, L Tancredi, FJ Wagner - Journal of High Energy …, 2023 - Springer
A bstract In this manuscript, we elaborate on a procedure to derive ϵ-factorised differential
equations for multi-scale, multi-loop classes of Feynman integrals that evaluate to special …

Feynman integrals in dimensional regularization and extensions of Calabi-Yau motives

K Bönisch, C Duhr, F Fischbach, A Klemm… - Journal of High Energy …, 2022 - Springer
A bstract We provide a comprehensive summary of concepts from Calabi-Yau motives
relevant to the computation of multi-loop Feynman integrals. From this we derive several …

Yangian-invariant fishnet integrals in two dimensions as volumes of Calabi-Yau varieties

C Duhr, A Klemm, F Loebbert, C Nega, F Porkert - Physical Review Letters, 2023 - APS
We argue that ℓ-loop Yangian-invariant fishnet integrals in two dimensions are connected to
a family of Calabi-Yau ℓ folds. The value of the integral can be computed from the periods of …

The SAGEX review on scattering amplitudes Chapter 3: Mathematical structures in Feynman integrals

S Abreu, R Britto, C Duhr - Journal of Physics A: Mathematical …, 2022 - iopscience.iop.org
Dimensionally-regulated Feynman integrals are a cornerstone of all perturbative
computations in quantum field theory. They are known to exhibit a rich mathematical …

The l-loop banana amplitude from GKZ systems and relative Calabi-Yau periods

A Klemm, C Nega, R Safari - Journal of High Energy Physics, 2020 - Springer
A bstract We use the GKZ description of periods and certain classes of relative periods on
families of Barth-Nieto Calabi-Yau (l− 1)-folds in order to solve the l-loop banana amplitudes …

Genus drop in hyperelliptic Feynman integrals

R Marzucca, AJ McLeod, B Page, S Pögel, S Weinzierl - Physical Review D, 2024 - APS
The maximal cut of the nonplanar crossed box diagram with all massive internal propagators
was long ago shown to encode a hyperelliptic curve of genus 3 in momentum space …

Loop-by-loop differential equations for dual (elliptic) Feynman integrals

M Giroux, A Pokraka - Journal of High Energy Physics, 2023 - Springer
A bstract We present a loop-by-loop method for computing the differential equations of
Feynman integrals using the recently developed dual form formalism. We give explicit …