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

Abstract

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 $\Delta C=0$ decays of single charm baryons and the usual hyperon decays.

67 pages, 5 figures, 18 tables

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Cited by in corpus (19)

• Charmed Baryon Physics Circa 2021
• Weak Decays of Antitriplet Charmed Baryons from the Perspective of Flavor Symmetry
• Equivalent $SU(3{)}_f$ approaches for two-body anti-triplet charmed baryon decays
• Heavy-Flavor-Conserving Hadronic Weak Decays of Charmed and Bottom Baryons
• Heavy-Flavor-Conserving Hadronic Weak Decays of Charmed and Bottom Baryons: an Update
• First Measurement of the Decay Asymmetry in the pure W-boson-exchange Decay ${\Lambda }_c^{+}\to {\Xi }^0{K}^{+}$
• Estimates of exchange topological contributions and $CP$-violating observables in ${\Lambda }_b\to \Lambda \varphi$ decay
• Nonleptonic decays of ${\Xi }_{cc}\to {\Xi }_c\pi$ with ${\Xi }_c-{\Xi }_c^{\prime }$ mixing
• Topological amplitudes of charmed baryon decays in the $SU(3{)}_F$ limit
• Generation of $SU(3)$ sum rule for charmed baryon decay
• Study of the nonleptonic decay ${\Xi }_c^0\to {\Lambda }_c^{+}{\pi }^{-}$ in the covariant confined quark model
• Generation of isospin sum rules in heavy hadron weak decays
• Topological $SU(3{)}_f$ approach for two-body ${\Omega }_c$ weak decays
• Isospin sum rules in charmed baryon weak decays
• Topological diagram analysis of ${\mathcal{B}}_{c\overline{3}}\to {\mathcal{B}}_{10}M$ decays in the $SU(3{)}_F$ limit and beyond
• Large CP violation in charmed baryon decays
• Topological amplitudes of bottom baryon decays in the $SU(3{)}_F$ limit
• Revisiting heavy-flavor conserving weak decays of charmed baryons within the nonrelativistic quark model
• The nonleptonic decays ${\Xi }_{cc}^{++}\to {\Xi }_c^{(\prime )+}{\pi }^{+}$ within the nonrelativistic quark model