The Unitarity Triangle through Bd → ρ ± π ∓ decays

We analyze the impact of the CP-violating observables in the Bd → ρ ± π ∓ system, combined with the precise measurement of sin 2β , in the extraction of the CKM matrix. We explore two strategies for determining the Unitarity Triangle in these modes. Computing the penguin parameters (r±, φ±) and the ratio of two trees (rt, φt) within QCD factorization yields a precise determination of ( ¯ ρ, ¯ η), reflected by a weak dependence on φ±, which is shown to be a second order effect, as in the Bd → π + π − system. Moreover, we find that the dependence on penguin ampl itudes r± in Bd → ρ ± π ∓ is less pronounced than in the Bd → π + π − case, since penguin contributions r± ≈ rππ/3, implying an important simplification in our analysis. Ind ependent experimental tests of the factorization framework are proposed and discussed, using Bd → π + π − and Bd → ρ ± ρ ∓ modes.