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±→π±(or K±)π+π− and B±→π±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 Bs→K−π+ and B0→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±→π±π+π−. The closure of low-mass π+π− and K+K− channels involving only ππ↔KK¯ rescattering may explain by CPT approximately equal magnitudes and opposite signs measured in B±→π±π+π− and B±→π±K+K−.