Direct CP Violation In B --> pi^+ pi^- V With rho^0--omega Mixing Effects: Phenomenological Approach

We present a detailed study of direct CP violation and branching ratios in the channels $B^{0,pm} to pi^{+}pi^{-} V^{0,pm}$, where $V$ is a vector meson ($K^{* 0,pm}$ or $rho^{pm}$). Emphasis is placed upon the important role played by ${{rho}^{0}}-{omega}$ mixing effects in the estimation of the CP-violating asymmetry parameter, $a_{cp}$, associated with the difference of $B$ and $bar B$ decay amplitudes. A thorough study of the helicity amplitudes is presented as a function of the pion-pion invariant mass. All of the calculations and simulations considered correspond to channels which will be analyzed at the LHCb facility.