Simulation Methods of the Processes B to π^+ π^- V including rho⁰-ω 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 $\omega$.