Discontinuities of banana integrals in dispersion relation representation

Abstract

We derive the discontinuities of banana integrals using the dispersion relation iteratively. We find a series of identities between the parameterized discontinuities of banana integrals (p-DOBIs). Similar to elliptic integrals, these identities enable the reduction of various p-DOBIs to be a linear combination of some fundamental ones. We present a practical application of p-DOBIs for deriving Picard-Fuchs operator. Then we establish the expression of generalized dispersion relation, which enables us to obtain the dispersion relation representation of arbitrary banana integrals. Moreover, we propose a hypothesis for generalized dispersion relation and p-DOBIs, which provides a simple way to calculate the discontinuities and transform dispersion relation representation to p-DOBIs.

7 pages, 1 figure. Published in Chinese Physics Letters

References in corpus (8)

• The two-loop sunrise graph in two space-time dimensions with arbitrary masses in terms of elliptic dilogarithms
• Feynman Integrals in Dimensional Regularization and Extensions of Calabi-Yau Motives
• Taming Calabi-Yau Feynman integrals: The four-loop equal-mass banana integral
• Bananas of equal mass: any loop, any order in the dimensional regularisation parameter
• The three-loop equal-mass banana integral in $\epsilon$-factorised form with meromorphic modular forms
• The ice cone family and iterated integrals for Calabi-Yau varieties
• A numerical test of differential equations for one- and two-loop sunrise diagrams using configuration space techniques
• Algorithms for minimal Picard-Fuchs operators of Feynman integrals

Cited by in corpus (4)

• Unraveling $K(1690)$ as a pseudoscalar $ud\bar{d}\bar{s}$ tetraquark state
• Possible bound states in the triple-${\eta }_c$ and triple-$J/\psi$ systems
• Study of the ${\Omega }_{ccc}{\Omega }_{ccc}$ and ${\Omega }_{bbb}{\Omega }_{bbb}$ dibaryons in QCD Sum Rules
• Recurrence Relations and Dispersive Techniques for Precision Multi-Loop Calculations