The Unitarity Triangle through Bd→ ρ± π∓ decays

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We analyze the impact of the CP-violating observables in the Bd→ ρ± π∓ system, combined with the precise measurement of 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 amplitudes 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. Independent experimental tests of the factorization framework are proposed and discussed, using Bd → π+ π- and Bd → ρ± ρ∓ modes.