Feynman integrals, introduced by physicist Richard Feynman in the 1940s, are crucial mathematical tools for describing particle behavior in quantum field theory. They help calculate the likelihood of particles following specific paths, essential for making precise predictions based on the standard model of particle interactions. Recently, a team from Mainz University’s PRISMA+ Cluster of Excellence, including Dr. Sebastian Pögel, Dr. Xing Wang, and Prof. Dr. Stefan Weinzierl, developed a method to efficiently evaluate complex Feynman integrals linked to Calabi–Yau geometries, published in Physical Review Letters. This work enhances the accuracy of theoretical predictions for particle interactions and deepens understanding of the mathematical structures in particle physics.
Feynman integrals account for the temporary emergence of additional particles during subatomic interactions, with their complexity often determined by geometry. While simpler integrals like those shaped as spheres or toruses are well understood, Calabi–Yau geometries present challenges due to added dimensions. The research emphasizes a novel “epsilon-factorized form” for banana integrals—a specific category of Calabi–Yau Feynman integrals—facilitating precise evaluations and expanding access to previously challenging integrals, which may provide insights for future high-energy experiments.
