New Series Representations for the Two-Loop Massive Sunset Diagram

Abstract

We derive new convergent series representations for the two-loop sunset diagram with three different propagator masses m1, m2 and m3 and external momentum p by techniques of analytic continuation on a well-known triple series that corresponds to the Lauricella Fc function. The convergence regions of the new series contain regions of interest to physical problems. These include some ranges of masses and squared external momentum values which make them useful from Chiral Perturbation Theory to some regions of the parameter space of the Minimal Supersymmetric Standard Model. The analytic continuation results presented on the Lauricella series could be used in other settings as well.

arXiv comment25 pages, 11 figures

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• $\epsilon$-Expansion of Multivariable Hypergeometric Functions Appearing in Feynman Integral Calculus
• Analytic continuations and numerical evaluation of the Appell $F_1$, $F_3$, Lauricella $F_D^{(3)}$ and Lauricella-Saran $F_S^{(3)}$ and their Application to Feynman Integrals
• Analytic continuations of the Horn $H_1$ and $H_5$ functions
• GKZ-system of the 2-loop self energy with 4 propagators
• Feynman Integrals of Grassmannians
• GKZ hypergeometric systems of the three-loop vacuum Feynman integrals
• GKZ hypergeometric systems of the four-loop vacuum Feynman integrals