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Chirally symmetric quark description of low energy π-πscattering

Pedro Bicudo·Stephen Cotanch·Felipe Llanes-Estrada·Pieter Maris·Emilio Ribeiro·Adam Szczepaniak
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Abstract

Weinberg's theorem for π-πscattering, 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 π-πscattering amplitudes are calculated using the Dyson-Schwinger equations in the rainbow-ladder truncation, confirming the formal derivation.

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Pedro Bicudo, Stephen Cotanch, Felipe Llanes-Estrada, Pieter Maris, Emilio Ribeiro, Adam Szczepaniak. 2001-12-02. Chirally symmetric quark description of low energy π-πscattering. https://doi.org/10.1103/physrevd.65.076008

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