An Analytic Approach to Sunset Diagrams in Chiral Perturbation Theory: Theory and Practice

Abstract

We demonstrate the use of several code implementations of the Mellin-Barnes method available in the public domain to derive analytic expressions for the sunset diagrams that arise in the two-loop contribution to the pion mass and decay constant in three-flavoured chiral perturbation theory. We also provide results for all possible two-mass configurations of the sunset integral, and derive a new one-dimensional integral representation for the one mass sunset integral with arbitrary external momentum. Thoroughly annotated Mathematica notebooks are provided as ancillary files, which may serve as pedagogical supplements to the methods described in this paper.

arXiv comment30 pages, plain latex, 3 figures; 7 mathematica notebooks provided as ancillary files; v2 is the version accepted and published in the European Physical Journal A in the Tools for Experiment and Theory Section; minor typos corrected; notation improved; bibliography extended; mathematica files submitted with this version are also supported on the journal web-site as supplementary materials

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Cited by in corpus (8)

• Iterated Elliptic and Hypergeometric Integrals for Feynman Diagrams
• Multiple Series Representations of $N$-fold Mellin-Barnes Integrals
• Efficient Evaluation of Massive Mellin--Barnes Integrals
• Analytic representation of $F_K/F_{\pi }$ in two loop chiral perturbation theory
• New Series Representations for the Two-Loop Massive Sunset Diagram
• An Analytic Analysis of the Pion Decay Constant in Three-Flavoured Chiral Perturbation Theory
• Analytic representations of $m_K$, $F_K$, $m_{\eta }$ and $F_{\eta }$ in two loop $SU(3)$ chiral perturbation theory
• Chiral Perturbation Theory Reflections on Effective Theories of the Standard Model