Analysis of Charmed Baryon Decays with Strong Phases under SU(3) Symmetry

The SU(3) analysis is considered a powerful tool in charmed baryon decays. Motivated by recent measurements of anti-triplet charmed baryon two-body decays from the Belle, Belle II, and BESIII Collaborations, we have finally determined the last two IRA form factors, $f^{a\prime}$ and $g^{a\prime}$, which were absent in previous work. By considering both real and complex form factor cases in our work, we find that the phases of the form factors are necessary and that complex form factors can explain the experimental data well. Using the fitted form factors, we further numerically study the equivalence of the SU(3) irreducible representation amplitude (IRA) and topological diagrammatic approach (TDA) methods. We find that the IRA and TDA methods can be numerically equivalent with the addition of the new form factors. Based on the conclusions above, and considering some interesting scenarios, the CP violation effects can be predicted in these processes at the order of $O(10^{-3})$. This suggests a promising opportunity to observe CP violation for the first time in charmed baryon decays. Although our predictions depend on some assumptions, considering that the experimental data is far from sufficient to determine CPV through SU(3) analysis, our study is meaningful and instructive for observing CPV at experimental facilities.