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.

17 pages, 6 figures

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• Exploiting CP-asymmetries in rare charm decays
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• Sum rules for $CP$ asymmetries of charmed baryon decays in the $SU(3{)}_F$ limit
• Enhancement of charm CP violation due to nearby resonances
• Rescattering mechanism of weak decays of double-charm baryons
• Charmed baryon decays in $SU(3{)}_F$ symmetry
• Final-state rescattering mechanism of charmed baryon decays
• Direct CP violation in beauty and charm hadron decays
• Search for $CP$ violation in ${\Xi }_c^{+}\to p{K}^{-}{\pi }^{+}$ decays using model-independent techniques
• A $U$-Spin Anomaly in Charm CP Violation
• Up-down asymmetries of charmed baryon three-body decays
• SU(3)${}_F$ Analysis for Beauty Baryon Decays
• Non-leptonic beauty baryon decays and $CP$-asymmetries based on $SU(3)$-Flavor analysis
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• Strong CP violation in spin-1/2 singly charmed baryons
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• $U$-spin conjugate $CP$ violation relations in bottom baryon decays
• Relations between $b\to c\tau \nu$ Decay Modes in Scalar Models
• Implications of recent LHCb data on CPV in b-baryon four body decays
• Weak decays of bottom-charm baryons: ${\mathcal{B}}_{bc}\to {\mathcal{B}}_{b}P$
• $CP$-violation and $U$-spin symmetry in four-body bottom baryon decays
• Search for $CP$ violation in ${\Xi }_c^{+}\to {\Sigma }^{+}{h}^{+}{h}^{-}$ and ${\Lambda }_c^{+}\to p{h}^{+}{h}^{-}$ at Belle II