Document Type
Article
Date
6-16-2001
Language
English
Disciplines
Physics
Description/Abstract
First it is shown that the tree amplitude for pion pion scattering in the minimal linear sigma model has an exact expression which is proportional to a geometric series in the quantity (s-$m_\pi^2$)/($m_B^2-m_\pi^2$), where $m_B$ is the sigma mass which appears in the Lagrangian and is the only a priori unknown parameter in the model. This induces an infinite series for every predicted scattering length in which each term corresponds to a given order in the chiral perturbation theory counting. It is noted that, perhaps surprisingly, the pattern, though not the exact values, of chiral perturbation theory predictions for both the isotopic spin 0 and isotopic spin 2 s-wave pion-pion scattering lengths to orders $p^2$, $p^4$ and $p^6$ seems to agree with this induced pattern. The values of the $p^8$ terms are also given for comparison with a possible future chiral perturation theory calculation. Further aspects of this approach and future directions are briefly discussed.
Recommended Citation
Schechter, Joseph; Black, Deirdre; and Park, Nae Woong, "Remark on Pion Scattering Lengths" (2001). Physics - All Scholarship. 256.
https://surface.syr.edu/phy/256
Source
Harvested from Arxiv.org
Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.
Additional Information
3 pages, no figures More information available at http://arxiv.org/abs/0904.2161
First author and Syracuse University author listed for additional authors see the article.