Remarks on CP Asymmetries in $D^0/\overline{D^0}\text{ra}{K}_S{\pi }^{+}{\pi }^{-}$

Abstract

We consider the interference of resonant amplitudes leading to the final state $K_S{\pi }^{+}{\pi }^{-}$ in $D^0/\overline{D^0}$ decays. Each of these amplitudes consists of both Cabibbo allowed and doubly Cabibbo suppressed transitions. The role of strong phase arising out of Breit-Wigner resonant propagators is emphasised. Invoking the $\Delta S=\Delta Q$ rule, $K_S$ in the final state is identified as the mass eigenstate of superposed weak eigenstates $K^0$ and ${\bar{K}}^0$. A nonzero CP asymmetry appears to be possible in three body decays.

Comments: 7 pages, latex, 1 eps figure