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

Ananthanarayan, B.; Bijnens, Johan LU ; Ghosh, Shayan and Hebbar, Aditya (2016) In European Physical Journal A 52(12).
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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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
European Physical Journal A
volume
52
issue
12
publisher
Springer
external identifiers
  • scopus:85007416059
  • wos:000391427500002
ISSN
1434-6001
DOI
10.1140/epja/i2016-16374-8
language
English
LU publication?
yes
id
9c686d46-1d79-4a71-be2e-4f5fa2817aaa
date added to LUP
2017-01-13 10:09:18
date last changed
2017-09-18 11:31:20
@article{9c686d46-1d79-4a71-be2e-4f5fa2817aaa,
  abstract     = {<p>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.</p>},
  articleno    = {374},
  author       = {Ananthanarayan, B. and Bijnens, Johan and Ghosh, Shayan and Hebbar, Aditya},
  issn         = {1434-6001},
  language     = {eng},
  month        = {12},
  number       = {12},
  publisher    = {Springer},
  series       = {European Physical Journal A},
  title        = {An analytic approach to sunset diagrams in chiral perturbation theory : Theory and practice},
  url          = {http://dx.doi.org/10.1140/epja/i2016-16374-8},
  volume       = {52},
  year         = {2016},
}