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 $A_{CP}({\Lambda }_c^{+}\to p{K}^{-}{K}^{+})+A_{CP}({\Xi }_c^{+}\to {\Sigma }^{+}{\pi }^{-}{\pi }^{+})=0$, $A_{CP}({\Lambda }_c^{+}\to p{\pi }^{-}{\pi }^{+})+A_{CP}({\Xi }_c^{+}\to {\Sigma }^{+}{K}^{-}{K}^{+})=0$, and $A_{CP}({\Lambda }_c^{+}\to {\Sigma }^{+}{\pi }^{-}{K}^{+})+A_{CP}({\Xi }_c^{+}\to p{K}^{-}{\pi }^{+})=0$. No such U-spin sum rule exists between $A_{CP}({\Lambda }_c^{+}\to p{K}^{-}{K}^{+})$ and $A_{CP}({\Lambda }_c^{+}\to p{\pi }^{-}{\pi }^{+})$. 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.

Comments: 17 pages, 6 figures