Study of Branching Fractions and CP-Violating Asymmetries in B Meson Decays to Rho And Pion Final State with the BABAR Detector

We present measurements of branching fractions and CP-violating asymmetries in B-meson decays to {rho}{sup +}{pi}{sup 0}, {rho}{sup 0}{pi}{sup +} and {rho}{sup 0}{pi}{sup 0}. The data sample comprises 89 x 10{sup 6} {Upsilon}(4S) {yields} B{bar B} decays collected with the BABAR detector at the PEP-II asymmetric-energy B Factory at SLAC. We find the charge-averaged branching fractions {Beta}(B{sup +} {yields} {rho}{sup +}{pi}{sup 0}) = (10.9 {+-} 1.9(stat) {+-} 1.9(syst)) x 10{sup -6} and {Beta}(B{sup 0} {yields} {rho}{sup 0}{pi}{sup +}) = (9.5 {+-} 1.1 {+-} 0.9) x 10{sup -6}, and we set a 90% confidence-level upper limit {Beta}(B{sup 0} {yields} {rho}{sup 0}{pi}{sup 0}) < 2.9 x 10{sup -6}. We measure the charge asymmetries A{sub CP}{rho}{sup +}{pi}{sup 0} = 0.24 {+-} 0.16 {+-} 0.06 and {Alpha}{sub CP}{sup {rho}{sup 0}{pi}{sup +}} = -0.19 {+-} 0.11 {+-} 0.02. We also present the preliminary measurement of CP-violating asymmetries in B{sup 0} {yields} ({rho}{pi}){sup 0} {yields} {pi}{sup +}{pi}{sup -}{pi}{sup 0} decays using a time-dependent Dalitz plot analysis. The results are obtained from a data sample of 213 million {Upsilon}(4S) {yields} B{bar B} decays, collected by the BABAR detector at the PEP-II asymmetric-energy B Factory at SLAC. This analysis extends the narrow-{rho} quasi-two-body approximation used in the previous analysis,more » by taking into account the interference between the {rho} resonances of the three charges. We measure 16 coefficients of the bilinear form factor terms occurring in the time-dependent decay rate of the B{sup 0} meson with the use of a maximum-likelihood fit. We derive the physically relevant quantities from these coefficients. We measure the direct CP-violation parameters {Alpha}{sub {rho}{pi}} = -0.088 {+-} 0.049 {+-} 0.013 and C = 0.34 {+-} 0.11 {+-} 0.05, where the first errors are statistical and the second systematic. For the mixing-induced CP-violation parameter we find S = -0.10 {+-} 0.14 {+-} 0.04, and for the dilution and strong phase shift parameters respectively, we obtain {Delta}C = 0.15 {+-} 0.11 {+-} 0.03 and {Delta}S = 0.22 {+-} 0.15 {+-} 0.03. For the angle {alpha} of the Unitarity Triangle we measure (113{sub -17}{sup +27} {+-} 6){sup o}; only a weak constraint is achieved at the significance level of more than two standard deviations. Finally, for the relative strong phase {delta}{sub +-} between the B{sup 0} {yields} {rho}{sup -}{pi}{sup +} and B{sup 0} {yields} {rho}{sup +}{pi}{sup -} transitions we find (-67{sub -31}{sup +28} {+-} 7){sup o}, with a similarly weak constraint at two standard deviations and beyond.« less