Repository logo
 

REMARK ON PION SCATTERING LENGTHS


Type

Article

Change log

Authors

Black, Deirdre 
Fariborz, Amir H 
Jora, Renata 
Park, Nae Woong 
Schechter, Joseph 

Abstract

jats:p 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 [Formula: see text], where mjats:subB</jats:sub> 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 pjats:sup2</jats:sup>, pjats:sup4</jats:sup> and pjats:sup6</jats:sup> seems to agree with this induced pattern. The values of the pjats:sup8</jats:sup> terms are also given for comparison with a possible future chiral perturbation theory calculation. Further aspects of this approach and future directions are briefly discussed. </jats:p>

Description

Keywords

Linear Sigma model, pion-pion scattering lengths, chiral perturbation theory

Journal Title

MODERN PHYSICS LETTERS A

Conference Name

Journal ISSN

0217-7323
1793-6632

Volume Title

Publisher

World Scientific Pub Co Pte Lt
Sponsorship
Science and Technology Facilities Council (ST/G000581/1)
Science and Technology Facilities Council (ST/J000434/1)