Abstract
Via a tensor formalism it is possible to obtain expressions for spectator and annihilation diagrams in terms of reduced matrix elements of SU(3). They lead to contradictions with the usual spectator picture. The reason lies in the occurrence of a non-trivial tensor, vanishing by virtue of SU(3). Because this symmetry property is reflected in the Clebsch-Gordan coefficients, it is not necessary that also the reduced matrix element, due to this tensor, vanishes itself. Only by this modification is it possible to resolve the contradictions and to make the mapping between diagrams and reduced matrix elements one-to-one. Spectator dominance must be based on this additional amplitude, whereas annihilation dominance is consistent with it being small or zero. The results are presented for the illustrative case of Cabibbo allowed charm decays to two-body final states (octet-octet), and are compared with experimental numbers.
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