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CP Violation in $B^\pm\to γπ^\pmπ^+π^-$

We consider CP violating effects in decays of the type $B^\pm\to γa^\pm_{1,2}$ where $a_{1,2}$ are the $J^P=1^+$ and $2^+$ resonances each decaying to the common final state via $a^\pm_{1,2} \toπ^\pmρ^0$. The resonances enhance the CP asymmetries and also knowledge of their masses and widths facilitates calculations of the effects. Several types of CP asymmetries are sizable ($\sim10$--30\%) requiring about (3--10)${}\times10^8$ $B^\pm$ mesons for detection at the $3σ$ level thereby providing a method for measuring the angle $α$ in the unitarity triangle. \bigskip