Abstract
We study the low energy pion-hyperon interaction considering effective nonlinear chiral invariant Lagrangians including pions, \ensuremath{\rho} mesons, \ensuremath{\sigma} mesons, hyperons, and corresponding resonances. Then we calculate the S- and P-wave phase shifts, total cross sections, angular distributions, and polarizations for the momentum in the center-of-mass frame up to $k=400$ MeV. With these results we discuss the $\mathrm{CP}$ violation in the $\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\Xi}}\ensuremath{\Lambda}\ensuremath{\pi}$ and $\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\Omega}}\ensuremath{\Xi}\ensuremath{\pi}$ weak decays.
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