Sum rules for inclusive decays of charmed hadrons

Abstract

Inclusive nonleptonic and semileptonic weak decays of the type $c\ensuremath{\rightarrow}h+\mathrm{anything}$ and $c\ensuremath{\rightarrow}h+{l}^{+}+\mathrm{anything}$ are considered, where $c$ is a charmed hadron and $h$ is an ordinary hadron belonging to the 3* and 8 representation of SU(3), respectively. The SU(3) relations for the inclusive decay rates are presented. These would provide tests of the isospin and SU(3) transformation properties of the weak charm-changing current and $\ensuremath{\Delta}C=\ensuremath{\Delta}S$ nonleptonic interaction Hamiltonian in the Glashow-Iliopoulos-Maiani scheme. We also point out that it may be possible to check these relations in the near future.