U-Spin Sum Rules for CP Asymmetries of Three-Body Charmed Baryon Decays

Abstract: Triggered by a recent LHCb measurement and prospects for Belle II, we derive U-spin symmetry relations between integrated CP asymmetries of three-body $\Lambda_c^+$ and $\Xi_c^+$ decays. The sum rules read $A_{CP}(\Lambda_c^+\rightarrow p K^- K^+) + A_{CP}(\Xi_c^+\rightarrow \Sigma^+ \pi^- \pi^+) = 0$, $A_{CP}(\Lambda_c^+\rightarrow p \pi^- \pi^+) + A_{CP}(\Xi_c^+\rightarrow \Sigma^+ K^- K^+) = 0$, and $A_{CP}(\Lambda_c^+\rightarrow \Sigma^+ \pi^- K^+) + A_{CP}(\Xi_c^+\rightarrow pK^-\pi^+) = 0$. No such U-spin sum rule exists between $A_{CP}(\Lambda_c^+\rightarrow p K^- K^+)$ and $A_{CP}(\Lambda_c^+\rightarrow p \pi^- \pi^+)$. All of these sum rules are associated with a complete interchange of $d$ and $s$ quarks. Furthermore, there are no U-spin CP asymmetry sum rules which hold to first order U-spin breaking.