Determination of the π±p→π±π+n Cross Section Near Threshold

Abstract

The total cross section for the ${\ensuremath{\pi}}^{\ensuremath{-}}p\ensuremath{\rightarrow}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\pi}}^{+}n$ reaction has been measured at incident pion kinetic energies of 200, 190, 184, and 180 MeV. In addition, the ${\ensuremath{\pi}}^{+}p\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{+}n$ reaction was measured at 200 and 184 MeV. A fit of the cross sections by heavy baryon chiral perturbation theory yields values of $8.5\ifmmode\pm\else\textpm\fi{}0.6({m}_{\ensuremath{\pi}}^{\ensuremath{-}3})$ and $2.5\ifmmode\pm\else\textpm\fi{}0.1({m}_{\ensuremath{\pi}}^{\ensuremath{-}3})$ for the reaction matrix elements ${A}_{10}$ and ${A}_{32}$, which correspond to values for the $s$-wave isospin-0 and isospin-2 $\ensuremath{\pi}\ensuremath{-}\ensuremath{\pi}$ scattering lengths of ${a}_{0}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.23\ifmmode\pm\else\textpm\fi{}0.08({m}_{\ensuremath{\pi}}^{\ensuremath{-}1})$ and ${a}_{2}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\ensuremath{-}0.031\ifmmode\pm\else\textpm\fi{}0.008({m}_{\ensuremath{\pi}}^{\ensuremath{-}1})$, respectively.