Interference Between Cabibbo Allowed and Doubly Forbidden Transitions in $D\text{ra}{K}_{S,L}+{\pi }^{\prime }$s Decays

Abstract

Both Cabibbo allowed and doubly forbidden transitions contribute coherently to $D\to K_{S,L}+{\pi }^{\prime }s$ decays. This leads to several intriguing and even quantitatively significant consequences, among them: (i) A difference between $\Gamma (D^{+}\to K_S{\pi }^{+})$ and $\Gamma (D^{+}\to K_L{\pi }^{+})$ and between $\Gamma (D^0\to K_S{\pi }^0)$ and $\Gamma (D^0\to K_L{\pi }^0)$ of roughly 10\% ; similarly $\Gamma (D^{+}\to [K_S{\pi }^0{]}_{K^{\ast }}{\pi }^{+})\ne \frac{1}{4}\Gamma (D^{+}\to [K^{-}{\pi }^{+}{]}_{K^{\ast }}{\pi }^{+})$, and more generally $\Gamma (D\to {\bar{K}}^0+{\pi }^{\prime }s)\ne 2\Gamma (D\to K_S+{\pi }^{\prime }s)$. (ii) A change in the relative phase between the isospin 3/2 and 1/2 amplitudes as extracted from the observed branching ratios for $D^{+}\to K_S{\pi }^{+}$, $D^0\to K_S{\pi }^0,K^{-}{\pi }^{+}$. (iii) If New Physics intervenes to provide the required {\em weak} phase, then CP asymmetries of up to a few per cent can arise in $D^{+}\to K_S{\pi }^{+}$ vs. $D^{-}\to K_S{\pi }^{-}$, $D^0\to K_S{\pi }^0$ vs. ${\bar{D}}^0\to K_S{\pi }^0$, $D^{+}\to [K_S{\pi }^0{]}_{K^{\ast }}{\pi }^{+}$ vs. $D^{-}\to [K_S{\pi }^0{]}_{K^{\ast }}{\pi }^{-}$, etc.; an asymmetry of the same size, but opposite in sign occurs when the $K_S$ is replaced by a $K_L$ in the final state.

Comments: 6 pages, latex, no figures