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TThe LHCb collaboration has recently reported evidence for non-zero CPasymmetries in $B^+$ decays into $\pi^+ K^+ K^-,\; \pi^+\pi^+\pi^-,\; K^+ K^+K^- $ and $K^+\pi^+\pi^-$. The branching ratios for these decays have also beenmeasured with different values ranging from $5\times 10^{-6}$ to $51\times10^{-6}$. If flavor $SU(3)$ symmetry is a good symmetry for $B$ decays, in thecase that the dominant amplitude is momentum independent it is expected thatbranching ratios $Br$ and CP violating rate differences $\Delta_{CP} = \Gamma -\overline{\Gamma}$ satisfy, $Br(\pi^+\pi^+\pi^-) = 2Br(\pi^+ K^+ K^-)$,$Br(K^+K^+K^-) = 2 Br(K^+\pi^+\pi^-)$, and $\Delta_{CP}(\pi^+\pi^+\pi^-) =2\Delta_{CP}(\pi^+ K^+K^-) = - \Delta_{CP}(K^+K^+K^-) =-2\Delta_{CP}(K^+\pi^+\pi^-)$. The experimental data do not exhibit theexpected pattern for the branching ratios. The rate differences for $B^+\to\pi^+\pi^+\pi^-$ and $B^+\to K^+ K^+ K^-$ satisfy the relation between $\DeltaS =0$ and $\Delta S=1$ well, but the other two do not, with the CP asymmetrieshaving different signs than expected. In this work we study how to includingmomentum dependent and also $SU(3)$ breaking effects on these decays to explainexperimental data. We find that only including lowest order derivative terms,in the $SU(3)$ limit, the decay patterns cannot be explained. Large $SU(3)$breaking effects are needed to explain the data.

Large SU(3) breaking effects and CP violation in $B^+ $ decays into three charged SU(3) octet pseudoscalar mesons