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Topological tensor invariants and the current algebra approach: Analysis of 196 nonleptonic two-body decays of single and double charm baryons -- a review

We shed new light on the standard current algebra approach to the nonleptonic two-body decays of single and double heavy charm baryons. By making use of the completeness relation for the flavor wave functions of the ground state baryon {\bf 20'} representation we are able to rewrite the results of the current algebra approach in terms of the seven topological tensor invariants describing the decays. The representation of the current algebra results in terms of topological tensor invariants depends only on the initial and final state of the process. The summation over intermediate states inherent to the current algebra result is automatically taken care of in the tensor representation. In this way one arrives at a new, quick and very compact assessment of the results of the current algebra/pole model calculation. For example, one can quickly identify the decays in which the p.v.\ $S$-wave amplitude is predicted to vanish implying zero polarization asymmetries in these decays. We provide tables of the values of the seven topological tensor invariants for all Cabibbo favored and singly and doubly Cabibbo suppressed nonleptonic single and double charm baryon decays. In total we treat 196 charm baryon decays. We also discuss the charm preserving $ΔC=0$ decays of single charm baryons and the usual hyperon decays.