Eur. Phys. J. A (2016) 52: 374
https://doi.org/10.1140/epja/i2016-16374-8

Special Article - Tools for Experiment and Theory

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

¹ Centre for High Energy Physics, Indian Institute of Science, Bangalore-560012, Karnataka, India
² Department of Astronomy and Theoretical Physics, Lund University, Sölvegatan 14A, SE 223-62, Lund, Sweden
³ Department of Physics and Astronomy, University of Delaware, 19716, Newark, DE, USA

^* e-mail: anant@cts.iisc.ernet.in

Received: 9 August 2016
Accepted: 9 December 2016
Published online: 30 December 2016

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.