# Up-down asymmetries of charmed baryon three-body decays

## TL;DR

This paper analyzes the up-down asymmetries in three-body decays of charmed baryons using SU(3) flavor symmetry, fitting parameters to experimental data to predict asymmetries and branching ratios relevant for current experiments.

## Contribution

It introduces a method to parametrize decay amplitudes with SU(3) symmetry and fits these to data to predict asymmetries and branching ratios in charmed baryon decays.

## Key findings

- Fitted parameters yield a chi-squared per degree of freedom of 2.4.
- Predicted asymmetries and branching ratios are accessible to BESIII, BELLE-II, and LHCb.
- The approach provides a framework for analyzing three-body baryon decays using symmetry considerations.

## Abstract

We study the up-down asymmetries in the three-body anti-triplet charmed baryon decays of ${\bf B_c}\to{\bf B_n}MM' $ with the $SU(3)_f$ flavor symmetry, where ${\bf B_c}$ presents the anti-triplet charmed baryon of $(\Xi_c^0,-\Xi_c^+,\Lambda_c^+)$, while ${\bf B_n}$ 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 ${\bf B_c}\to{\bf B_n}MM' $. Some of these up-down asymmetries are accessible to the experiments at BESIII, BELLE-II and LHCb.