Improved Measurement of $B^{+}\to {\rho }^{+}{\rho }^0$ and Determination of the Quark-Mixing Phase Angle $\alpha$

We present improved measurements of the branching fraction $\mathcal{B}$, the longitudinal polarization fraction $f_L$, and the direct $CP$ asymmetry ${\mathcal{A}}_{CP}$ in the $B$ meson decay channel $B^{+}\to {\rho }^{+}{\rho }^0$. The data sample was collected with the BABAR detector at SLAC. The results are $\mathcal{B}(B^{+}\to {\rho }^{+}{\rho }^0)=(23.7\pm 1.4\pm 1.4)\times {10}^{-6}$, $f_L=0.950\pm 0.015\pm 0.006$, and ${\mathcal{A}}_{CP}=-0.054\pm 0.055\pm 0.010$, where the uncertainties are statistical and systematic, respectively. Based on these results, we perform an isospin analysis and determine the Cabibbo-Kobayashi-Maskawa phase angle $\alpha =\arg (-V_{td}{V}_{tb}^{*}/V_{ud}{V}_{ub}^{*})$ to be $({92.4}_{-6.5}^{+6.0})°$.

Figure 1

Projections of the fit (solid curve) onto the (a) $m_{\mathrm{ES}}$ and (b) $m_{{\pi }^{+}{\pi }^{-}}$ variables. A requirement on the likelihood ratio that retains 38% of the signal, 0.1% of the continuum background, and 1.3% of the $B\overline{B}$ background has been applied. The peak in the $B\overline{B}$ background at $m_{{\pi }^{+}{\pi }^{-}}\approx 0.78\mathrm{GeV}/c^2$ is from $B^{+}\to {\rho }^{+}\omega$ events with $\omega \to {\pi }^{+}{\pi }^{-}$.