Analysis of recentπ+plow-energy differential cross-section measurements

Abstract

The recent ${\ensuremath{\pi}}^{+}p$ differential cross-section measurements between $20$ and $100$ MeV (pion lab kinetic energy) have been analyzed in the context of an extended threshold expansion of the $K$ matrix. The analysis shows that the bulk of the database is self-consistent. Our results in the ${S}_{31}$ channel disagree with the ones obtained in the Karlsruhe phase-shift analyses (which have been based exclusively on the old $\ensuremath{\pi}N$ database); we report differences of (approximately) one degree in the corresponding phase-shift values and of almost 25% in the $s$-wave scattering length ${a}_{3}$ (our value: ${a}_{3}=\ensuremath{-}0.077\ifmmode\pm\else\textpm\fi{}0.003$ ${m}_{\ensuremath{\pi}}^{\ensuremath{-}1})$. These differences reflect the extent of the discrepancy between the old and the new low-energy ${\ensuremath{\pi}}^{+}p$ database; they cannot be attributed to the method of the analysis. A comparison of the present result for the ${a}_{3}$ with the values of the $\ensuremath{\pi}N$ scattering lengths, recently obtained from measurements of the $1s$ energy-level shift and width in pionic hydrogen and deuterium, leads to the conclusion that, within the present (experimental and theoretical) accuracies, the various results are not incompatible with the isospin symmetry of the strong interaction.