Hadronic Weak Decays of Charmed Baryons in the Topological Diagrammatic Approach: An Update

TL;DR

This paper updates the analysis of two-body charmed baryon decays using the topological diagram and SU(3) approaches, incorporating new LHCb data to improve the fit and explore potential CP violation at the per mille level.

Contribution

It provides a comprehensive global fit of charmed baryon decay data within TDA and IRA frameworks, utilizing recent measurements to refine amplitude parameters and phase differences.

Findings

Fit results are more accurate with reduced uncertainties.

The analysis supports the possibility of direct CP violation at the per mille level.

The number of tensor invariants and topological amplitudes are consistent in both approaches.

Abstract

There exist two distinct ways in realizing the approximate SU(3) flavor symmetry of QCD to describe the two-body nonleptonic decays of charmed baryons: the irreducible SU(3) approach (IRA) and the topological diagram approach (TDA). The TDA has the advantage that it is more intuitive, graphic and easier to implement model calculations. We perform a global fit to the currently available data of two-body charmed baryon decays within the framework of the TDA and IRA. The number of the minimum set of tensor invariants in the IRA and the topological amplitudes in the TDA is the same, namely, five in the tree-induced amplitudes and four in the penguin amplitudes. Since we employ the new LHCb measurements to fix the sign ambiguity of the decay parameters $\beta$ and $\gamma$, the fit results for the magnitudes of $S$- and $P$-wave amplitudes and their phase shift $\delta_P-\delta_S$ in both the TDA and IRA are more trustworthy than our previous analyses with uncertainties substantially improved. These results can be tested in the near future. The perspective of having direct {\it CP} violation in the charmed baryon sector at the per mille level is briefly discussed.