Tests of flavor and nonet symmetry in the decays of charmed mesons into two pseudoscalars

The standard model leads to specific flavor-symmetry properties for the decays of charmed mesons into two members of the pseudoscalar nonet. We derive linear relations amongst the amplitudes for specific decay modes from these properties together with the additional assumption of nonet symmetry, and we use them to set bounds on the branching ratios for various decays. Large violations of these bounds would imply large nonet-symmetry-breaking effects in charm decay, and possibly large flavor-symmetry violations as well. There are experimental indications for such breaking from $D^0$ and $D_s$ decays.