# Sum rules for $CP$ asymmetries of charmed baryon decays in the $SU(3)_F$ limit

## TL;DR

This paper develops a method to derive sum rules for $CP$ asymmetries in charmed baryon decays within the $SU(3)_F$ symmetry limit, providing new relations and predictions relevant for experimental searches.

## Contribution

It introduces a simple approach to find $CP$ violation sum rules in charmed baryon decays based on flavor $SU(3)$ symmetry, expanding the set of testable relations.

## Key findings

- Hundreds of $CP$ violation sum rules identified.
- Predicted branching fraction for $\\Xi^+_c\to pK^-\pi^+$ is $(1.7\pm 0.5)\%$.
- Fragmentation-fraction ratio $f_{\Xi_b}/f_{\Lambda_b}$ determined as $0.065\pm 0.020$.

## Abstract

Motivated by the recent LHCb observation of $CP$ violation in charm, we study $CP$ violation in the charmed baryon decays. A simple method to search for the $CP$ violation relations in the flavor $SU(3)$ limit, which is associated with a complete interchange of $d$ and $s$ quarks, is proposed. With this method, hundreds of $CP$ violation sum rules in the doubly and singly charmed baryon decays can be found. As examples, the $CP$ violation sum rules in two-body charmed baryon decays are presented. Some of the $CP$ violation sum rules could help the experiment to find better observables. As byproducts, the branching fraction of $\Xi^+_c\to pK^-\pi^+$ is predicted to be $(1.7\pm 0.5)\%$ in the $U$-spin limit and the fragmentation-fraction ratio is determined as $f_{\Xi_b}/f_{\Lambda_b}=0.065\pm 0.020$ using the LHCb data.