Direct CP violation in ${B\rightarrow \pi^{+}\pi^{-} V}$ with $\rho^{0}$-$\omega$ mixing effects: phenomenological approach

Abstract.

We present a detailed study of direct CP violation and the branching ratios in the channels $B^{0,\pm} \rightarrow \pi^{+}\pi^{-} V^{0,\pm}$, where V is a vector meson ($K^{* 0,\pm}$ or $\rho^{\pm}$). Emphasis is put 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 the 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.