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Pion-pion scattering at low energy

Bijnens, J. LU orcid ; Colangelo, G. ; Ecker, G. ; Gasser, J. and Sainio, M. E. (1997) In Nuclear Physics B 508(1-2). p.263-310
Abstract

We present technical details of the evaluation of the elastic ππ scattering amplitude to two loops in chiral perturbation theory. In particular, we elaborate on the renormalization procedure at the two-loop order and on the evaluation of the relevant Feynman diagrams that can all be expressed in terms of elementary functions. For the sake of clarity, we discuss these matters both in the N-component φ4 theory (in its symmetric phase) and in chiral perturbation theory. Estimates for the relevant low-energy constants of O(p6) are presented. Threshold parameters and phase shifts are then calculated for two sets of O(p4) coupling constants and compared with experiment. We comment on the extraction of... (More)

We present technical details of the evaluation of the elastic ππ scattering amplitude to two loops in chiral perturbation theory. In particular, we elaborate on the renormalization procedure at the two-loop order and on the evaluation of the relevant Feynman diagrams that can all be expressed in terms of elementary functions. For the sake of clarity, we discuss these matters both in the N-component φ4 theory (in its symmetric phase) and in chiral perturbation theory. Estimates for the relevant low-energy constants of O(p6) are presented. Threshold parameters and phase shifts are then calculated for two sets of O(p4) coupling constants and compared with experiment. We comment on the extraction of threshold parameters from phase shift data.

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author
; ; ; and
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Chiral perturbation theory, Chiral symmetry, Pion-pion scattering
in
Nuclear Physics B
volume
508
issue
1-2
pages
48 pages
publisher
North-Holland
external identifiers
  • scopus:0031584012
ISSN
0550-3213
DOI
10.1016/S0550-3213(97)80013-2
language
English
LU publication?
yes
id
a2aaaab5-21fb-4c37-adbb-038f3c47dfed
date added to LUP
2019-05-03 09:12:50
date last changed
2024-04-16 03:58:41
@article{a2aaaab5-21fb-4c37-adbb-038f3c47dfed,
  abstract     = {{<p>We present technical details of the evaluation of the elastic ππ scattering amplitude to two loops in chiral perturbation theory. In particular, we elaborate on the renormalization procedure at the two-loop order and on the evaluation of the relevant Feynman diagrams that can all be expressed in terms of elementary functions. For the sake of clarity, we discuss these matters both in the N-component φ<sup>4</sup> theory (in its symmetric phase) and in chiral perturbation theory. Estimates for the relevant low-energy constants of O(p<sup>6</sup>) are presented. Threshold parameters and phase shifts are then calculated for two sets of O(p<sup>4</sup>) coupling constants and compared with experiment. We comment on the extraction of threshold parameters from phase shift data.</p>}},
  author       = {{Bijnens, J. and Colangelo, G. and Ecker, G. and Gasser, J. and Sainio, M. E.}},
  issn         = {{0550-3213}},
  keywords     = {{Chiral perturbation theory; Chiral symmetry; Pion-pion scattering}},
  language     = {{eng}},
  month        = {{12}},
  number       = {{1-2}},
  pages        = {{263--310}},
  publisher    = {{North-Holland}},
  series       = {{Nuclear Physics B}},
  title        = {{Pion-pion scattering at low energy}},
  url          = {{http://dx.doi.org/10.1016/S0550-3213(97)80013-2}},
  doi          = {{10.1016/S0550-3213(97)80013-2}},
  volume       = {{508}},
  year         = {{1997}},
}