The Chiral Lagrangian parameters, $\overline{\ell}_1$, $\overline{\ell}_2$, are determined by the $ρ$--resonance

M. R. Pennington; J. Portoles

doi:10.1016/0370-2693(94)01551-M

paper

The Chiral Lagrangian parameters, $ℓ_{1}$ , $ℓ_{2}$ , are determined by the $ρ$ --resonance

arXiv:hep-ph/9409426 · doi:10.1016/0370-2693(94)01551-M

Abstract

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

Plain LaTeX file, 13 pages, 3 figures not included (available from the Authors under request). A comparison of our procedure with Chiral Perturbation Theory has been included. Results have not changed. Accepted for publication in Phys. Lett. B

The Chiral Lagrangian parameters, ℓ1​, ℓ2​, are determined by the ρ--resonance

Abstract

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The Chiral Lagrangian parameters, $ℓ_{1}$ , $ℓ_{2}$ , are determined by the $ρ$ --resonance