The Chiral Coupling Constants $\text{lb}1$ and $\text{lb}2$ 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.

Comments: 36 pages using latex with 1 figure embedded using epsf