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

Abstract

For the two-body Bc → BM decays, where Bc denotes the anti-triplet charm baryon and B(M) the octet baryon (meson), there exist two theoretical studies based on the SU(3) flavor [SU(3)f] symmetry. One is the irreducible SU(3)f approach (IRA). In the irreducible SU(3)f representation, the effective Hamiltonian related to the initial and final states forms the amplitudes for Bc → BM. The other is the topological-diagram approach (TDA), where the W-boson emission and W-boson exchange topologies are drawn and parameterized for the decays. As required by the group theoretical consideration, we present the same number of the IRA and TDA amplitudes. We can hence relate the two kinds of the amplitudes, and demonstrate the equivalence of the two SU(3)f approaches. We find a specific W-boson exchange topology only contributing to {Xi}_c^0 →BM. Denoted by EM, it plays a key role in explaining mathcal{B} ( {Xi}_c^0 → Λ0 {K}_S^0 , Σ0 {K}_S^0 , Σ+K−). We consider that {Lambda}_c^{+} → nπ+ and {Lambda}_c^{+} → pπ0 proceed through the constructive and destructive interfering effects, respectively, which leads to mathcal{B} ( {Lambda}_c^{+} → nπ+) » mathcal{B} ( {Lambda}_c^{+} → pπ0) in agreement with the data. With the exact and broken SU(3)f symmetries, we predict the branching fractions of Bc→BM to be tested by future measurements.