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

Abstract

For the two-body ${\mathbf{B}}_c\to \mathbf{B}M$ decays, where ${\mathbf{B}}_c$ denotes the anti-triplet charm baryon and $\mathbf{B}(M)$ 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 ${\mathbf{B}}_c\to \mathbf{B}M$. 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 ${\Xi }_c^0\to \mathbf{B}M$. Denoted by $E_M$, it plays a key role in explaining $\mathcal{B}({\Xi }_c^0\to {\Lambda }^0{K}_S^0,{\Sigma }^0{K}_S^0,{\Sigma }^{+}{K}^{-})$. We consider that ${\Lambda }_c^{+}\to n{\pi }^{+}$ and ${\Lambda }_c^{+}\to p{\pi }^0$ proceed through the constructive and destructive interfering effects, respectively, which leads to $\mathcal{B}({\Lambda }_c^{+}\to n{\pi }^{+})\gg \mathcal{B}({\Lambda }_c^{+}\to p{\pi }^0)$ in agreement with the data. With the exact and broken $SU(3{)}_f$ symmetries, we predict the branching fractions of ${\mathbf{B}}_c\to \mathbf{B}M$ to be tested by future measurements.

arXiv comment14 pages, 7 tables, 1 figure, published version

References in corpus (28)

• Weak Decays Beyond Leading Logarithms
• Mixing and Decay Constants of Pseudoscalar Mesons
• Mixing and Decay Constants of Pseudoscalar Mesons: The Sequel
• Anti-triplet charmed baryon decays with SU(3) Flavor Symmetry
• Singly Cabibbo-suppressed hadronic decays of ${\Lambda }_c^{+}$
• Charmed Baryon Weak Decays with SU(3) Flavor Symmetry
• SU(3)_flavor analysis of two-body weak decays of charmed baryons
• Analysis of Two-Body Decays of Charmed Baryons Using the Quark-Diagram Scheme
• Asymmetries of anti-triplet charmed baryon decays
• Non-leptonic two-body weak decays of ${\Lambda }_c(2286)$
• Two-body hadronic weak decays of antitriplet charmed baryons
• Three-body charmed baryon Decays with SU(3) flavor symmetry
• A diagrammatic analysis of two-body charmed baryon decays with flavor symmetry
• SU(3) symmetry breaking in charmed baryon decays
• Flavor SU(3) Topological Diagram and Irreducible Representation Amplitudes for Heavy Meson Charmless Hadronic Decays: Mismatch and Equivalence
• $K_S^0-K_L^0$ Asymmetries and $CP$ Violation in Charmed Baryon Decays into Neutral Kaons
• Two-body charmed baryon decays involving vector meson with $SU(3)$ flavor symmetry
• Sum rules for $CP$ asymmetries of charmed baryon decays in the $SU(3{)}_F$ limit
• Charmed ${\Omega }_c$ weak decays into $\Omega$ in the light-front quark model
• Charmed Baryon Weak Decays with Decuplet Baryon and SU(3) Flavor Symmetry
• Charmed Baryon Weak Decays with Vector Mesons
• Charmed baryon decays in $SU(3{)}_F$ symmetry
• Two-body charmed baryon decays involving decuplet baryon in the quark-diagram scheme
• Topological tensor invariants and the current algebra approach: Analysis of 196 nonleptonic two-body decays of single and double charm baryons -- a review
• Hadronic weak decays of ${\Lambda }_c$ in the quark model
• A global analysis of charmless two body hadronic decays for anti-triplet charmed baryons
• Cabibbo-favored ${\Lambda }_c^{+}\to \Lambda a_0(980{)}^{+}$ decay in the final state interaction
• $SU(3)$ Flavor Symmetry for Weak Hadronic Decays of ${\mathbf{B}}_{bc}$ Baryons

Cited by in corpus (1)

• Weak Decays of Antitriplet Charmed Baryons from the Perspective of Flavor Symmetry