Enhanced direct CP violation in B±,0→π+π-K±,0

We investigate in a phenomenological way direct CP violation in the hadronic decays B±,0→π+π-K±,0 where the effect of ρ-ω mixing is included. If Nceff (the effective parameter associated with factorization) is constrained using the most recent experimental branching ratios (to ρ0K0, ρ±K±, ρ±K0, ρ0K± and ωK±) from the BABAR, BELLE and CLEO Collaborations, we get a maximum CP violating asymmetry amax in the range -25% to +49% for B-→π+π-K- and -24% to +55% for B-bar0→π+π-K-bar0. We also find that CP violation is strongly dependent on the Cabibbo-Kobayashi-Maskawa matrix elements. Finally, we show that the sign of sin δ is always positive in the allowed range of Nceff and hence, a measurement of direct CP violation in B±,0→π+π-K±,0 would remove the mod(π) ambiguity in arg[-VtsVtb*/VusVub*]