$πΛ$ scattering phase shifts and CP violation in $Ξ\to πΛ$ decay

Abstract

CP-violating signals in weak $ Ξ\to πΛ$ decay require the knowledge of $πΛ$ $S$- and $P$-wave scattering phases at ${m}_Ξ$ center-of-mass energy. We have calculated these phases in baryon chiral perturbation theory with the ground-state $Σ$ in $s$ and $u$ channels and ${3 \over 2}^{+}$ $Σ(1385)$ in the $u$ channel. We do not treat the baryons as heavy. We find $δ_{S} = {1.2}^{\circ}$ and $δ_{P} = -{1.7}^{\circ}$ with the central value of the strong coupling parameter $D$. We also investigate the variation of the scattering phases as functions of the parameter $D$. We compare this result with previous calculations, and discuss its relevance to CP-asymmetry parameters.