Equivalent $SU(3)_f$ approaches for two-body anti-triplet charmed baryon decays

Abstract

For the two-body anti-triplet charmed baryon decays, there exist two theoretical analyses based on the $SU(3)$ flavor ($SU(3)_f$) symmetry. One is the irreducible $SU(3)_f$ approach (IRA), which depends on the irreducible $SU(3)_f$ representation of the effective Hamiltonian. The other is the topological-diagram approach (TDA), where the decays are drawn to consist of $W$-boson emission and $W$-boson exchange topologies. We demonstrate that IRA and TDA can be equivalent, such that the IRA parameters can be seen to mix with the TDA topologies. The current observations of $\Xi_c^0\to \Xi^-\pi^+,\Xi^- K^+,\Lambda^0\bar K^0$ might cause theoretical difficulties. With the $SU(3)_f$ symmetry breaking, we explain ${\cal B}(\Xi_c^0\to\Xi^-\pi^+,\Xi^-K^+)$. It is found that a specific $W$-boson exchange topology denoted by $E_M$ only appears in $\Xi_c^0\to{\bf B}M$, by which we explain ${\cal B}(\Xi_c^0\to\Lambda^0\bar K^0)$. In addition, we predict ${\cal B}(\Xi_c^0\to\Sigma^0\bar K^0,\Sigma^+ K^-)= (5.8^{+4.7}_{-3.5},5.4^{+4.9}_{-3.4})\times 10^{-3}$ for future measurements to test if $E_M$ can be a significant contribution.Comment: 13 pages, 7 tables, 1 figure, introduction rephrased, reference added, typos correcte