The Chiral Coupling Constants $\lb{1}$ and $\lb{2}$ from \pipi Phase Shifts

Abstract

A Roy equation analysis of the available $\pi \pi$ phase shift data is performed with the $I=0$ S- wave scattering length $a_0^0$ in the range predicted by the one-loop standard chiral perturbation theory. A suitable dispersive framework is developed to extract the chiral coupling constants \lb{1}, \lb{2} and yields \lb{1}$=-1.70\pm 0.15$ and \lb{2}$\approx 5.0$. We remark on the implications of this determination to (combinations of) threshold parameter predictions of the three lowest partial waves.

36 pages using latex with 1 figure embedded using epsf

References in corpus (7)

• Elastic $\pi \pi$ scattering to two loops
• The Low Energy $\pi \pi$ Amplitude to One and Two Loops
• $K_{l4}$ - Decays Beyond One Loop
• Consistency of the Chiral Pion-Pion Scattering Amplitudes with Axiomatic Constraints
• The Chiral Lagrangian parameters, ${\overline{\ell }}_1$, ${\overline{\ell }}_2$, are determined by the $\rho$--resonance
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• $K_{\ell 4}$ Form-Factors and $\pi$-$\pi$ Scattering
• A Review on Partial-wave Dynamics with Chiral Effective Field Theory and Dispersion Relation
• Low Energy Constants from Kl4 Form-Factors
• Comment on the Prediction of Two-loop Standard Chiral Perturbation Theory for Low-Energy ππScattering
• Positivity Constraints on Chiral Perturbation Theory Pion-Pion Scattering Amplitudes
• The Low Energy Expansion for Pion-Pion Scattering and Crossing Symmetry in Dispersion Relations
• Determination of SU(2) Chiral Perturbation Theory low energy constants from a precise description of pion-pion scattering threshold parameters
• Higher Threshold Parameters in pi pi Scattering
• Scattering Lengths and Medium and High Energy $\pi \pi$ Scattering
• Low Energy Constants from High Energy Theorems
• Pion-Pion Scattering in Chiral Perturbation and Dispersion Relation Theories
• The theoretical study of $D_s^{+}\to {\pi }^{+}{\pi }^0{\pi }^0$