arXiv subjects
Publications and source records attributed to Jingbang Zhao.
In this talk, we discuss how to generalize ideas developed for Banana integrals to two two-loop non-planar triangle Feynman integrals involving elliptic curves, which have non-trivial sub-sectors and whose Picard-Fuchs operators share less symmetry than Banana integrals, to obtain the canonical differential equations and to solve them with suitable boundary conditions.
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 $\varepsilon$-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.