Interference between Cabibbo allowed and doubly forbidden transitions in D → KS,L + π′s decays

Both Cabibbo allowed and doubly forbidden transitions contribute coherently to D → KS,L + π′s decays. This leads to several intriguing and even quantitatively significant consequences, among them (i) A difference between Γ(D+ → KSπ+) and Γ(D+ → KLπ+) and between Γ(D0 → KSπ0) and Γ(D0 → KLπ0) of roughly 10%; similarly Γ(D+ → [KSπ0]K∗π+) ≠ 14Γ(D+ → [K−π+]K∗π+), and more generally Γ(D → K0 + π′s) ≠ 2Γ(D → KS + π′s). (ii) A change in the relative phase between the isospin 32 and 12 amplitudes as extracted from the observed branching ratios for D+ → KSπ+, D0 → KSπ0, K−π+. (iii) If New Physics intervenes to provide the required weak phase, then CP asymmetries of up to a few per cent can arise in D+ → KSπ+ vs. D− → KSπ−, D0 → KSπ0 vs. D0 → KSπ0, D+ → [KSπ0]K∗π+ vs. D− → [KSπ0]K∗π−, etc.; an asymmetry of the same size, but opposite in sign occurs when the KS is replaced by a KL in the final state.