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Home > Physical Review D (APS) > <math><mi>U</mi></math>-spin sum rules for <math><mi>C</mi><mi>P</mi></math> asymmetries of three-body charmed baryon decays |

Grossman, Yuval (Department of Physics, LEPP, Cornell University, Ithaca, New York 14853, USA) ; Schacht, Stefan (Department of Physics, LEPP, Cornell University, Ithaca, New York 14853, USA)

12 February 2019

**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.

**Published in: ****Physical Review D 99 (2019)**
**Published by: **APS

**DOI: **10.1103/PhysRevD.99.033005

**arXiv: **1811.11188

**License: **CC-BY-4.0