SU(3) Sum Rules for Charm Decay

Understand

We present flavor SU(3) sum rules for $D \to PP$ and $D \to PV$ decay amplitudes, that are valid to second order in symmetry breaking by the strange quark mass spurion.

• Decay rate sum rules are also computed to this order.
• Particular attention is given to sum rules arising from the isospin and U-spin subgroups, the former providing sensitive tests for alternative sources of SU(3) breaking.
• We apply the latter together with the postulated $\Delta U = 0$ rule for the large penguin picture to predict the ratio and difference of the direct CP asymmetries for $D \to KK^*$ and $D \to \pi \rho$.