$U$-spin sum rules for $CP$ 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 ${A}_{CP}\left({\Lambda }_{c}^{+}\to p{K}^{-}{K}^{+}\right)+{A}_{CP}\left({\Xi }_{c}^{+}\to {\Sigma }^{+}{\pi }^{-}{\pi }^{+}\right)=0$, ${A}_{CP}\left({\Lambda }_{c}^{+}\to p{\pi }^{-}{\pi }^{+}\right)+{A}_{CP}\left({\Xi }_{c}^{+}\to {\Sigma }^{+}{K}^{-}{K}^{+}\right)=0$, and ${A}_{CP}\left({\Lambda }_{c}^{+}\to {\Sigma }^{+}{\pi }^{-}{K}^{+}\right)+{A}_{CP}\left({\Xi }_{c}^{+}\to p{K}^{-}{\pi }^{+}\right)=0$. No such $U$-spin sum rule exists between ${A}_{CP}\left({\Lambda }_{c}^{+}\to p{K}^{-}{K}^{+}\right)$ and ${A}_{CP}\left({\Lambda }_{c}^{+}\to p{\pi }^{-}{\pi }^{+}\right)$. 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)