Chirally symmetric quark description of low energy pi-pi scattering

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Bicudo, Pedro
Cotanch, Stephen
Maris, Pieter
Szczepaniak, Adam
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American Physical Soc
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Weinberg’s theorem for π-π scattering, including the Adler zero at threshold in the chiral limit, is analyticall 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-π scattering amplitudes are calculated using the Dyson- Schwinger equations in the rainbow-ladder truncation, confirming the formal derivation.
© 2002 The American Physical Society. P.B. acknowledges Gonçalo Marques’ assistance and enlightening discussions with Gastao Krein, George Rupp and Mike Scadron. This work is supported in part by grants DOE DE-FG02-97ER41048 and NSF INT-9807009.
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