Three-body charmed baryon decays with SU(3) flavor symmetry

This is the authors' abstract. We don't add key points for this paper.

We study the three-body antitriplet Bc→BₙMM^' decays with the $SU(3)$ flavor [SU(3)f] symmetry, where Bc denotes the charmed baryon antitriplet of (Ξc⁰,-Ξc⁺,Λc⁺), and Bₙ and M(M^') represent baryon and meson octets, respectively. By considering only the S-wave MM^'-pair contributions without resonance effects, the decays of Bc→BₙMM^' can be decomposed into irreducible forms with 11 parameters under SU(3)f, which are fitted by the 14 existing data, resulting in a reasonable value of χ²/d.o.f.=2.8 for the fit. Consequently, we find that the triangle sum rule of $A({{{Λ}}}c⁺{→}n{K̄}⁰{{π}}⁺){-}A({{{Λ}}}c⁺{→}p{K}^{{-}}{{π}}⁺){-}√2A({{{Λ}}}c⁺{→}p{K̄}⁰{{π}}⁰)=0$ given by the isospin symmetry holds under $SU(3{)}f$, where $A$ stands for the decay amplitude. In addition, we predict that $B({{{Λ}}}c⁺{→}n{{π}}⁺{K̄}⁰)=(0.9±{}0.8)×{}{10}^{{-}2}$, which is 3--4 times smaller than the BESIII observation, indicating the existence of the resonant states. For the to-be-observed ${B}c{→}{B}ₙM{M}^{{'}}$ decays, we compute the branching fractions with the $SU(3{)}f$ amplitudes to be compared to the BESIII and LHCb measurements in the future.