2023/05/23 by Xu-hang Jian, Xing Wang, Jiang, Xuhang +5 · 1 citation
Health Professions · Mathematics · Physics and Astronomy · #Adolescent and Pediatric Healthcare #Algebraic and Geometric Analysis #FOS: Physical sciences #High Energy Physics - Phenomenology (hep-ph) #High Energy Physics - Theory (hep-th) #Particle physics theoretical and experimental studies
paper · pdf · doi:10.48550/arxiv.2305.13951
openalex publication_date 2023/05/23 · openalex created_date 2023/05/27 · openalex updated_date 2026/07/28
In this paper, we investigate two-loop non-planar triangle Feynman integrals involving elliptic curves. In contrast to the Sunrise and Banana integral families, the triangle families involve non-trivial sub-sectors. We show that the methodology developed in the context of Banana integrals can also be extended to these cases and obtain ε-factorized differential equations for all sectors. The letters are combinations of modular forms on the corresponding elliptic curves and algebraic functions arising from the sub-sectors. With uniform transcendental boundary conditions, we express our results in terms of iterated integrals order-by-order in the dimensional regulator, which can be evaluated efficiently. Our method can be straightforwardly generalized to other elliptic integral families and have important applications to precision physics at current and future high-energy colliders.