Up-down asymmetries of charmed baryon three-body decays

We study the up-down asymmetries in the three-body anti-triplet charmed baryon decays of \(\mathbf{B}_{\mathbf{c}}\rightarrow \mathbf{B}_{\mathbf{n}}MM' \) with the \(SU(3)_f\) flavor symmetry, where \(\mathbf{B}_{\mathbf{c}}\) presents the anti-triplet charmed baryon of \((\Xi _c^0,-\Xi _c^+,\Lambda _c^+)\), while \(\mathbf{B}_{\mathbf{n}}\) and \(M^{(')}\) denote octet baryon and meson states, respectively. By assuming the s-wave meson-pairs to be the dominant constituents in final state configurations, we can write the spin-dependent decay amplitude into parity-conserving and parity-violating parts, parametrized by 6 real parameters under \(SU(3)_f\), respectively. Fitting these parameters by 16 experimental data points with the minimum \(\chi ^2\) method, we obtain that \(\chi ^2/d.o.f=2.4\). With the fitted parameters, we evaluate the up-down asymmetries along with the decay branching ratios of \(\mathbf{B}_{\mathbf{c}}\rightarrow \mathbf{B}_{\mathbf{n}}MM' \). Some of these up-down asymmetries are accessible to the experiments at BESIII, BELLE-II and LHCb.