Isobar production inπ−p→π+π−nnear threshold

An isobar-model partial-wave analysis of 4140 ${\pi }^{-}p\to {\pi }^{+}{\pi }^{-}n$ bubble-chamber events at total center-of-mass energies between 1330 and 1380 MeV is reported. Included in the analysis is a chiral-symmetry background calculated from the phenomenological Lagrangian. Significant results of the analysis are that production is dominated by the initial $P11\mathrm{}$ wave and that, in this wave, final-state $\epsilon N$ production is more important than $\pi \Delta$ production. We show that the recent single-arm-spectrometer data confirm the bubble-chamber data, where the two overlap. We discuss the determination of the chiral-symmetry-breaking parameter $\xi$. The analysis establishes that the present data is consistent with several models of the symmetry breaking, although it favors the vector breaking model of Weinberg, $\xi =0\mathrm{}$. Using a dispersion relation we show that $\epsilon N$ production in the tail of the Roper ($P11\mathrm{}$) resonance significantly affects the extraction of $\xi$ from total-cross-section data; hence in pion production $\xi$ cannot be determined independently of the isobar amplitudes. As a further application of the results of the analysis we determine the value of the $\Delta \pi \Delta$ coupling constant. Our result depends on the value taken for the $\Delta$ mass and what assumptions one makes to determine the large $\pi \Delta$ amplitudes; but, in any case, it is considerably less than the theoretical predictions which follow from SU(6), U(12), the quark model, and superconvergence relations. We also perform, in this paper, a Goldberger-Treiman-MIT-bag-model calculation which agrees with the other theoretical predictions. We further show that by attributing all $P33\mathrm{}$ inelasticity to $\pi \Delta$ production the results of a recent elastic-phase-shift analysis imply upper bounds on the $\Delta \pi \Delta$ coupling constant which are consistent with the value implied by the isobar analysis.