Expected Accuracy in a Measurement of the CKM Angle $\alpha$ Using a Dalitz Plot Analysis of $\boldmath B^0 \to \rho \pi$ Decays in the BTeV Project

Abstract

A precise measurement of the angle $\alpha$ in the CKM triangle is very important for a complete test of Standard Model. A theoretically clean method to extract $\alpha$ is provided by B$^0 \to \rho \pi$ decays. Monte Carlo simulations to obtain the BTeV reconstruction efficiency and to estimate the signal to background ratio for these decays were performed. Finally the time-dependent Dalitz plot analysis, using the isospin amplitude formalism for tree and penguin contributions, was carried out. It was shown that in one year of data taking BTeV could achieve an accuracy on $\alpha$ better than 5$^{\circ}$.