Analytic Hard-Pion Calculation of theT=J=0 ππPhase Shift

Using chiral SU(2) current algebra, we have derived a dynamical equation for the form factor which describes the sigma-field matrix element between single-pion states. With the aid of the model of Gell-Mann, Oakes, and Renner, we solve this equation in an effective-range approximation, and from unitarity deduce the $T=J=0\mathrm{} \pi \pi$ phase shift. Our analysis strongly favors the "up-down" set of phenomenological $\pi \pi$ phase shifts, and rules out a narrow $\epsilon$ resonance.