Chirally symmetric quark description of low energyscattering
- 1 April 2002
- journal article
- Published by American Physical Society (APS) in Physical Review D
- Vol. 65 (7)
- https://doi.org/10.1103/physrevd.65.076008
Abstract
Weinberg's theorem for \pi-\pi scattering, including the Adler zero at threshold in the chiral limit, is analytically proved for microscopic quark models that preserve chiral symmetry. Implementing Ward-Takahashi identities, the isospin 0 and 2 scattering lengths are derived in exact agreement with Weinberg's low energy results. Our proof applies to alternative quark formulations including the Hamiltonian and Euclidean space Dyson-Schwinger approaches. Finally, the threshold \pi-\pi scattering amplitudes are calculated using the Dyson-Schwinger equations in the rainbow-ladder truncation, confirming the formal derivation.Comment: 10 pages, 7 figures, RevtexKeywords
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