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arxiv: hep-ph/9409426 · v2 · submitted 1994-09-27 · ✦ hep-ph

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The Chiral Lagrangian parameters, overline{ell}₁, overline{ell}₂, are determined by the rho--resonance

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classification ✦ hep-ph
keywords overlineresonancechirallagrangianparametersscatteringzeroadler
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The all--important consequence of Chiral Dynamics for $\pi \pi$ scattering is the Adler zero, which forces $\pi \pi$ amplitudes to grow asymptotically. The continuation of this subthreshold zero into the physical regions requires a $P$--wave resonance, to be identified with the $\rho$. It is a feature of $\pi \pi$ scattering that convergent dispersive integrals for the $I=1$ channel are essentially saturated by the $\rho$--resonance and are much larger than those with $I=2$ quantum numbers. These facts predict the parameters $\overline{\ell}_1$, $\overline{\ell}_2$ of the Gasser--Leutwyler Chiral Lagrangian, as well as reproducing the well--known KSFR relation and self-consistently generating the $\rho-$resonance.

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