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An analytic approach to sunset diagrams in chiral perturbation theory: Theory and practice

  • B. AnanthanarayanEmail author
  • Johan Bijnens
  • Shayan Ghosh
  • Aditya Hebbar
Special Article - Tools for Experiment and Theory
Part of the following topical collections:
  1. Exotic phenomena at the interface of nuclear and particle physics

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 in the Electronic Supplementary Material to this paper, which may serve as pedagogical supplements to the methods described in this paper.

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Copyright information

© SIF, Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • B. Ananthanarayan
    • 1
    Email author
  • Johan Bijnens
    • 2
  • Shayan Ghosh
    • 1
  • Aditya Hebbar
    • 1
    • 3
  1. 1.Centre for High Energy PhysicsIndian Institute of ScienceKarnatakaIndia
  2. 2.Department of Astronomy and Theoretical PhysicsLund UniversityLundSweden
  3. 3.Department of Physics and AstronomyUniversity of DelawareNewarkUSA

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