$\pi \Lambda$ scattering phase shifts and CP violation in $\Xi \to \pi \Lambda$ decay

Abstract

CP-violating signals in weak $\Xi \to \pi \Lambda$ decay require the knowledge of $\pi \Lambda$ $S$- and $P$-wave scattering phases at $m_{\Xi }$ center-of-mass energy. We have calculated these phases in baryon chiral perturbation theory with the ground-state $\Sigma$ in $s$ and $u$ channels and ${\frac{3}{2}}^{+}$ $\Sigma (1385)$ in the $u$ channel. We do not treat the baryons as heavy. We find ${\delta }_S={1.2}^{\circ }$ and ${\delta }_P=-{1.7}^{\circ }$ 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.

Comments: Numerical errors corrected. As a result, conclusions change