### Speaker

### Description

We utilize the flavor SU(3) symmetry analysis on the semi-leptonic

decays of anti-triplet charmed baryons($\Lambda^{+}_{c},\Xi_{c}^{+,0}$) to obtain

the results of $\Xi_{c}$ branching fraction:

$\mathcal{B}(\Xi_c^0\to\Xi^-e^+\nu)=4.10\pm0.46\%$,

$\mathcal{B}(\Xi_c^0\to\Xi^-\mu^+\nu_{\mu})=3.98\pm0.57\%$ and find a heavy

deviation between the results of a process $\Xi_c^0\to\Xi^-l^+\nu$ :

$\mathcal{B}(\Xi_c^0\to\Xi^-e^+\nu)=1.31(04\pm07\pm38)\%$,

$\mathcal{B}(\Xi_c^0\to\Xi^-\mu^+\nu_{\mu})=1.27(06\pm10\pm 37)\%$ reported

by Belle Collaboration and SU(3) flavor analysis. In this work, the contributions of

vector and axial-vector currents in the semi-leptonic decay process of anti-triplet

heavy baryons are considered and we respectively analyze their SU(3) symmetry

breaking degrees to illustrate the big discrepancy between experimental data and

SU(3) symmetry analysis. Recently Belle-II collaboration reported new

measurements for the branching ratios for $\mathcal{B}(\Xi_c^0\to\Lambda
K^0_S)$, $\mathcal{B}(\Xi_c^0\to\Sigma^0 K^0_S)$ and

$\mathcal{B}(\Xi_c^0\to\Sigma^+ K^-)$. Combined with other known data on

charmless two body decays of an anti-triplet charmed baryon, a lot of information

can be derived with the assistance of flavor $SU(3)$ symmetry. Using $SU(3)$

relations between different decay modes, we find that the new Belle-II data would

predict $\mathcal{B}(\Xi_{c}^{0}\to p \pi^{-})=(5.817\pm1.79)\%$,

$\mathcal{B}(\Xi_{c}^{0}\to p K^{-})=\mathcal{B}(\Xi_{c}^{0}\to \Sigma^{+}
\pi^{-})=(1.113\pm0.349)\times 10^{-4}$ which can be tested in the future. Earlier

data show that $\Xi^0_c \to \Xi^- K^+$ decays is violated at 2$\sigma$ level which

casts duolt on the validity of $SU(3)$ symmetry. More careful analysis should be

carried out. To this end, we find that with the new Bell-II data, a global fit to data is

now possible if the $SU(3)$ irreducible amplitudes are all real. We find a resonable

$\chi^2/d.o.f=1.24$ and the deviation for the $\Xi^0_c \to \Xi^- K^+$ is reduced to

within 1$\sigma$ level. We give several comments on the feature of global fit. As a

prediction, we predict the unknown branching ratios and asymmetry parameters of

anti-triplet charmed baryon for charmless two body decays, which are accessible

to the experiments at Belle, BES and LHCb.