The Unitarity Triangle through $B_d\to {\rho }^{\pm }{\pi }^{\mp }$ decays

Abstract

We analyze the impact of the CP-violating observables in the $B_d\to {\rho }^{\pm }{\pi }^{\mp }$ system, combined with the precise measurement of $\sin 2\beta$, in the extraction of the CKM matrix. We explore two strategies for determining the Unitarity Triangle in these modes. Computing the penguin parameters $(r_{\pm },{\varphi }_{\pm })$ and the ratio of two trees $(r_t,{\varphi }_t)$ within QCD factorization yields a precise determination of $(\bar{\rho },\bar{\eta })$, reflected by a weak dependence on ${\varphi }_{\pm }$, which is shown to be a second order effect, as in the $B_d\to {\pi }^{+}{\pi }^{-}$ system. Moreover, we find that the dependence on penguin amplitudes $r_{\pm }$ in $B_d\to {\rho }^{\pm }{\pi }^{\mp }$ is less pronounced than in the $B_d\to {\pi }^{+}{\pi }^{-}$ case, since penguin contributions $r_{\pm }\approx r_{\pi \pi }/3$, implying an important simplification in our analysis. Independent experimental tests of the factorization framework are proposed and discussed, using $B_d\to {\pi }^{+}{\pi }^{-}$ and $B_d\to {\rho }^{\pm }{\rho }^{\mp }$ modes.

Comments: 4 pages, 2 figures (requires epsfig, psfrag), To appear in the proceedings of the International Europhysics Conference on High Energy Physics, 21-27 July 2005, Lisboa, Portugal