CP asymmetries in three-body B+- decays to charged pions and kaons

Abstract

CP asymmetries have been measured recently by the LHCb collaboration in three-body $B^{+}$ decays to final states involving charged pions and kaons. Large asymmetries with opposite signs at a level of about 60% have been observed in $B^{\pm }\to {\pi }^{\pm }(\mathrm{or}{K}^{\pm }){\pi }^{+}{\pi }^{-}$ and $B^{\pm }\to {\pi }^{\pm }{K}^{+}{K}^{-}$ for restricted regions in the Dalitz plots involving ${\pi }^{+}{\pi }^{-}$ and $K^{+}{K}^{-}$ with low invariant mass. U-spin is shown to predict corresponding $\Delta S=0$ and $\Delta S=1$ asymmetries with opposite signs and inversely proportional to their branching ratios, in analogy with a successful relation predicted thirteen years ago between asymmetries in $B_s\to K^{-}{\pi }^{+}$ and $B^0\to K^{+}{\pi }^{-}$. We compare these predictions with the measured integrated asymmetries. Effects of specific resonant or non-resonant partial waves on enhanced asymmetries for low-pair-mass regions of the Dalitz plot are studied in $B^{\pm }\to {\pi }^{\pm }{\pi }^{+}{\pi }^{-}$. The closure of low-mass ${\pi }^{+}{\pi }^{-}$ and $K^{+}{K}^{-}$ channels involving only $\pi \pi \leftrightarrow K\bar{K}$ rescattering may explain by CPT approximately equal magnitudes and opposite signs measured in $B^{\pm }\to {\pi }^{\pm }{\pi }^{+}{\pi }^{-}$ and $B^{\pm }\to {\pi }^{\pm }{K}^{+}{K}^{-}$.

Comments: References added and updated, to be published in Physics Letters B