Up-down asymmetries of charmed baryon three-body decays

Abstract

We study the up-down asymmetries in the three-body anti-triplet charmed baryon decays of ${\mathbf{B}}_{\mathbf{c}}\to {\mathbf{B}}_{\mathbf{n}}M{M}^{\prime }$ 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 $M^{{(}^{\prime })}$ 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 ${\mathbf{B}}_{\mathbf{c}}\to {\mathbf{B}}_{\mathbf{n}}M{M}^{\prime }$. Some of these up-down asymmetries are accessible to the experiments at BESIII, BELLE-II and LHCb.

Comments: 18 pages, no figure, revised version accepted by EPJC