A global analysis of charmless two body hadronic decays for anti-triplet charmed baryons

Recently Belle collaboration reported new measurements for the branching fractions with the first observing two processes of $\mathcal{B}(\Xi_c^0\to\Lambda K^0_S)$, $\mathcal{B}(\Xi_c^0\to\Sigma^0 K^0_S)$ and updating data for $\mathcal{B}(\Xi_c^0\to\Sigma^+ K^-)$. Combined with other known data on charmless two body decays of anti-triplet charmed baryons, a lot of information can be derived with the assistance of $SU(3)$ flavour symmetry. Using $SU(3)$ relations between different decay modes, we can give some predictions based on the new measurements which can be tested with the high luminosity experiments in the future. More interestingly, we find that a global fit is now possible with the addition of new Belle data. In general, there are 18 complex $SU(3)$ invariant amplitudes. We find that a scenario of all amplitudes being real can fit the data well with a $\chi^2/d.o.f$ only $0.773$. This indicates that neglecting the phases of the amplitudes is a reasonable assumption. When more data become available, one may be able to get more information for phases in the amplitudes. We give several comments on the feature of global fit regarding the branching fractions, relations between different decays, and decays involving $K^0$ and $\bar K^0$. Many of the unknown branching fractions and polarization asymmetry parameters of anti-triplet charmed baryon for charmless two body decays are predicted to be accessible by experiments at Belle, Belle~II, BES-III, and LHCb. The validity of $SU(3)$ for charmless two body hadronic decays can be more accurately tested.