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 $$\mathbf{B}_{\mathbf{c}}\rightarrow \mathbf{B}_{\mathbf{n}}MM' $$Bc→BnMM′ with the $$SU(3)_f$$SU(3)f flavor symmetry, where $$\mathbf{B}_{\mathbf{c}}$$Bc presents the anti-triplet charmed baryon of $$(\Xi _c^0,-\Xi _c^+,\Lambda _c^+)$$(Ξc0,-Ξc+,Λc+), while $$\mathbf{B}_{\mathbf{n}}$$Bn and $$M^{(')}$$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 $$SU(3)_f$$SU(3)f, respectively. Fitting these parameters by 16 experimental data points with the minimum $$\chi ^2$$χ2 method, we obtain that $$\chi ^2/d.o.f=2.4$$χ2/d.o.f=2.4. With the fitted parameters, we evaluate the up-down asymmetries along with the decay branching ratios of $$\mathbf{B}_{\mathbf{c}}\rightarrow \mathbf{B}_{\mathbf{n}}MM' $$Bc→BnMM′. Some of these up-down asymmetries are accessible to the experiments at BESIII, BELLE-II and LHCb.