Tests of isospin selection rules in exclusive and semi-inclusive decays of chargedDmesons

In the Cabibbo-allowed decays of the charged $D$ meson, the standard model predicts that the isospin of the final state must be pure $T=\frac{3}{2}$ for nonleptonic decays and $T=\frac{1}{2}$ for semileptonic decays. We determine the consequences of these isospin rules for the ratios of $K^{-}$ final states to ${\overline{K}}^0$ final states in both exclusive channels and in semileptonic ones. These ratios are bounded, and present data do not violate these bounds, but they are too sparse to make any definitive tests. Other predictions of the selection rules, such as the Dalitz plot for $\overline{K}\pi \pi$ modes, are also discussed.