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

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 $B^\pm\to π^\pm({\rm or} K^\pm)π^+π^-$ and $B^\pm \to π^\pm K^+K^-$ for restricted regions in the Dalitz plots involving $π^+π^-$ and $K^+K^-$ with low invariant mass. U-spin is shown to predict corresponding $ΔS=0$ and $ΔS=1$ asymmetries with opposite signs and inversely proportional to their branching ratios, in analogy with a successful relation predicted thirteen years ago between asymmetries in $B_s\to K^-π^+$ and $B^0 \to K^+ π^-$. 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 $B^\pm \to π^\pm π^+π^-$. The closure of low-mass $π^+π^-$ and $K^+K^-$ channels involving only $ππ\leftrightarrow K\bar K$ rescattering may explain by CPT approximately equal magnitudes and opposite signs measured in $B^\pm\to π^\pmπ^+π^-$ and $B^\pm \to π^\pm K^+K^-$.