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.