We set up a general framework to describe $\pi \pi$ scattering below 1 GeV based on chiral low-energy expansion with possible spin-0 and -1 resonances. Partial wave amplitudes are obtained with the $N/D$ method, which satisfy unitarity, analyticity, and approximate crossing symmetry. A comparison with the phase shift data in the $J=0\mathrm{}$ channel favors a scalar resonance near the $\rho$ mass.

• Received 10 July 1998

DOI:https://doi.org/10.1103/PhysRevD.59.034005