Meson Production inp+dCollisions and theI=0π−πInteraction. IV. Double-Pion Production and Pion-Pion Scattering

We present an analysis of the measurements on the reaction $p+d\to {\mathrm{He}}^3+2\mathrm{}\pi$, and show that the anomalous bump in the ${\mathrm{He}}^3$ spectrum cannot be accounted for by $\pi$-${\mathrm{He}}^3$ final-state interactions, by Bose statistics for the two pions, or by the deuteron and ${\mathrm{He}}^3$ wave functions. However, the anomaly can be satisfactorily explained by a strong final-state interaction between the two pions. We determine the $S$-wave $\pi -\pi$ scattering length in the $I=0\mathrm{}$ state to be 2ħ/μc.