Simulation Methods of the Processes $B to pi^+ pi^- V$ including $rho^0-omega$ Mixing Effects

Simulation methods for the decays $ B to {pi}^+ {pi}^- V$, where $V$ is a $1^{--}$ vector-meson, are presented in detail. Emphasis is put on the use of the helicity formalism and the use of effective Lagrangians. We show the importance of ${{rho}^{0}}-{omega}$ mixing in enhancing the direct $CP$ violation (DCPV) when the pion-pion invariant mass is near the mass of the $omega$.